# Cronbach’s Alpha

One problem with the split-half method is that the reliability estimate obtained using any random split of the items is likely to differ from that obtained using another. One solution to this problem is to compute the Spearman-Brown corrected split-half reliability coefficient for every one of the possible split-halves and then find the mean of those coefficients.  This is the motivation for Cronbach’s alpha.

Cronbach’s alpha is superior to Kuder and Richardson Formula 20 since it can be used with continuous and non-dichotomous data. In particular, it can be used for testing with partial credit and for questionnaires using a Likert scale.

Definition 1: Given variable x1, …, xk and x0 = $\sum\nolimits_{j=1}^k x_k$ and  Cronbach’s alpha is defined to be

Property 1: Let xj = tj + ej where each ej is independent of tj and all the ej are independent of each other. Also let x0 = $\sum\nolimits_{j=1}^k x_j$ and t0 = $\sum\nolimits_{j=1}^k t_j$. Then the reliability of x0α where α is Cronbach’s alpha.

Here we view the xj as the measured values, the tj as the true values and the ej as the measurement error values. Click here for a proof of Property 1.

Observation: Cronbach’s alpha provides a useful lower bound on reliability (as seen in Property 1). Cronbach’s alpha will generally increase when the correlations between the items increase. For this reason the coefficient measures the internal consistency of the test. Its maximum value is 1, and usually its minimum is 0, although it can be negative (see below).

A commonly-accepted rule of thumb is that an alpha of 0.7 (some say 0.6) indicates acceptable reliability and 0.8 or higher indicates good reliability. Very high reliability (0.95 or higher) is not necessarily desirable, as this indicates that the items may be entirely redundant. These are only guidelines and the actual value of Cronbach’s alpha will depend on many things. E.g. as the number of items increases, Cronbach’s alpha tends to increase too even without any increase in internal consistency.

The goal in designing a reliable instrument is for scores on similar items to be related (internally consistent), but for each to contribute some unique information as well.

Observation: There are an number reasons why Cronbach’s alpha could be low or even negative even for a perfectly valid test. Two such reasons are reverse coding and multiple factors.

Reverse coding: Suppose you use a Likert scale of 1 to 7 with 1 meaning strongly disagree and 7 meaning strongly agree. Suppose two of your questions are: Q1: “I like pizza” and Q20: “I dislike pizza”. These questions ask the same thing, but with reverse wording. In order to apply Cronbach’s alpha properly you need to reverse the scoring of any negatively phrased question, Q20 in our example. Thus if a response to Q20 is say 2, it needs to be scored as 6 instead of 2 (i.e. 8 minus the recorded score).

Multiple factors: Cronbach’s alpha is useful where all the questions are testing more or less the same thing, called a “factor”. If there are multiple factors then you need to determine which questions are testing which factors. If say there are 3 factors (e.g. happiness with your job, happiness with your marriage and happiness with yourself), then you need to split the questionnaire/test into three tests, one containing the questions testing factor 1, one with the questions testing factor 2 and the third with questions testing factor 3. You then calculate Cronbach’s alpha for each of the three tests. The process of determining these “hidden” factors and splitting the test by factor is called Factor Analysis (see Factor Analysis).

Example 1: Calculate Cronbach’s alpha for the data in Example 1 of Kuder and Richardson Formula 20 (repeated in Figure 1 below).

Figure 1 – Cronbach’s Alpha for Example 1

The worksheet in Figure 1 is very similar to the worksheet in Figure 1 of Kuder and Richardson Formula 20. Row 17 contains the variance for each of the questions. E.g. the variance for question 1 (cell B17) is calculated by the formula =VARP(B4:B15). Other key formulas used to calculate Cronbach’s alpha in Figure 1 are described in Figure 2.

Figure 2 – Key formulas for the worksheet in Figure 1

We see from cell B22 that Cronbach’s alpha .73082, the same as the KR20 reliability calculated for Example 1 of Kuder and Richardson Formula 20.

Observation: If the variances of the xj vary widely, the xj can be standardized to obtain a standard deviation of 1 prior to calculating Cronbach’s alpha.

Observation: To determine how each question on a test impacts the reliability, Cronbach’s alpha can be calculated after deleting the ith variable, for each i ≤ k. Thus for a test with k questions, each with score xj, Cronbach’s alpha is calculated for $x^*_i$ for all i where $x^*_i$ = $\sum\nolimits_{j \neq i} x_j$.

If the reliability coefficient increases after an item is deleted, you can assume that the item is not highly correlated with the other items. Conversely, if the reliability coefficient decreases, you can assume that the item is highly correlated with the other items.

Example 2: Calculate Cronbach’s alpha for the survey in Example 1, where any one question is removed.

The necessary calculations are displayed in Figure 3.

Figure 3 – Cronbach’s Alpha for Example 2

Each of the columns B through L represents the test with one question removed. Column B corresponds to question #1, column C corresponds to question #2, etc. Figure 4 displays the formulas corresponding to question #1 (i.e. column B); the formulas for the other questions are similar. Some of the references are to cells shown in Figure 1.

Figure 4 – Key formulas for worksheet in Figure 3

As can be seen from Figure 3, the omission of any single question doesn’t change the Cronbach’s alpha very much. Removal of Q8 affects the result the most.

Observation: Another way to calculate Cronbach’s alpha is to use the Two Factor ANOVA without Replication data analysis tool on the raw data and note that:

Example 3: Calculate the Cronbach’s alpha for Example 1 using ANOVA.

We begin by running Excel’s Anova: Two Factor without Replication data analysis tool using the data in range B4:L15 of the worksheet shown in Figure 1.

Figure 5 – Calculation of Cronbach’s alpha using ANOVA

As you can see from Figure 5, Cronbach’s alpha is .73802, the same value calculated in Figure 1.

Observation: Alternatively, we could use the Real Statistics Two Factor ANOVA data analysis tool, setting the Number of Rows per Sample to 1. We can also obtain the same result using the following supplemental function.

Real Statistics Functions: The following functions are provided in the Real Statistics Resource Pack:

CRONALPHA(R1, k) = Cronbach’s alpha for the data in range R1 if k = 0 (default) and Cronbach’s alpha with kth item (i.e. column) removed if k > 0

CALPHA(R1): array function which returns a row of Cronbach’s alpha for R1 with each item removed

Thus for the data in Example 1, we can obtain the results shown in Figure 1 and 3 using CRONALPHA(B4:L15) = .738019 and CRONALPHA(B4:L15, 1) = .76321. Also the formula CALPHA(B4:L15) can be used to produce the results shown in range B43:L43 of Figure 3.

Example 4: Calculate Cronbach’s alpha for a 10 question questionnaire with Likert scores between 1 and 7 based on the 15 person sample shown in Figure 6.

Figure 6 – Calculation of Cronbach’s alpha for Example 4

As you can see from Figure 6, Cronbach’s alpha is 0.59172, a little below the generally acceptable range. We get the same answer by using the supplemental formula in the Real Statistics Resource Pack, namely CRONALPHA(B4:K18) = 0.59172.

Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the Reliability data analysis tool which can be used to calculate Cronbach’s alpha.

We now show how to calculate Cronbach’s alpha for Example 4 using the Reliability data analysis tool. Start, as usual, by pressing Ctrl-m and choose the Reliability option from the menu that appears. Fill in the dialog box that appears as shown in Figure 7.

Figure 7 – Dialog box for Reliability data analysis tool

The output is shown in Figure 8. Cronbach’s alpha is shown in cell M3, while the Cronbach’s alpha values with one question removed are shown in range M8:V8, which is the same as the output from =CALPHA(B4:K18).

Figure 8 – Cronbach’s alpha option of Reliability data analysis tool

Additional information about Cronbach’s Alpha can be found by clicking here. This includes how to perform hypothesis testing on Cronbach’s Alpha, confidence intervals, statistical power and sample size requirements.

### 470 Responses to Cronbach’s Alpha

1. jeena says:

the test contains 18 questions in which 12 mcq’s,5 two marks questions and 1 three marks questions ,how can i calculate alpha coefficient

• Charles says:

Hi Jeena,
I believe that for each question you simply score 1 for a correct answer and 0 for an incorrect answer, whether the multiple choice question has 2,3 or 4 choices. Then follow the procedure described in Example 1 or Example 3 on webpage http://www.real-statistics.com/reliability/cronbachs-alpha/. You can also use the supplemental formula CRONALPHA provided in the Real Statistics Resource Pack.
Charles

Dear Charles,
as if you have different parts of questionnaire e.g. Yes, No and with 5 scale options.. So would there be two separate evaluations of C Alpha or may i find the one single value as well for both segregated portions of questionnaire ?

• Charles says:

Are you saying that if they answer Yes they have to evaluate something on the scale of 1 to 5, while if they say No they have a separate evaluation also using a scale of 1 to 5?
Charles

• koel says:

Hi,
I would like to know, if i have 5 variables that i want to categorize into a single variable. Out of them, 4 questions are likert scale and 1 is a yes/no question. how can i find the chronbach alpha for the 5 questions?

• Charles says:

Hi Koel,

Provided all the questions measure the same thing you can calculate one Cronbach’s alpha for all the questions.

However, I would not mix Likert scale questions (rate your opinion of Columbus from 1 to 5) with knowledge questions (did Columbus discover America? T/F).

Generally for the Likert scale questions use the Likert scale (say 1 to 5) in calculating Cronbach’s alpha. For True/False questions you can use values that correspond to the Likert scale (e.g. 5 if True means you have an extremely high opinion of Columbus and 3 if No means that you have neutral opinion). Most of the time True/False questions are measuring knowledge and so as stated above it is not appropriate to mix them with Likert scale questions in calculating Cronbach’s alpha.

In general with knowledge-based questions (e.g. True/False or multiple choice questions) you can code them as 1 for the correct answer and 0 for an incorrect answer when calculating Cronbach’s alpha.

Charles

Charles

2. Mary Ann says:

how can i calculate five point scale survey in excel and get the cronbach alpha??? its quite confusing.

• Charles says:

Mary Ann,
Enter your data as in Example 4 on http://www.real-statistics.com/reliability/cronbachs-alpha/. The example shows what to do for a seven point scale, but a five point scale works exactly the same. Then carry out the calculations as in Figure 6 on the same webpage or simply use CRONALPHA(R1) where R1 is the the range containing your data (without headings). CRONALPHA is a supplemental function which is contained in the Real Statistics Resource Pack.
Charles

3. alberto rivas says:

Thank you, Sir. It´s a great example. it contains all that I have searched. ¿Aren´t you teacher?

4. Krsna says:

Hi. I got negative cronbach alpha which made it unacceptable but the questions are just right and fit to my study. What should I do? Thank you for your response. God bless.

• Charles says:

Hi Krsna,

There are an number reasons for getting a low (or even negative) value for cronbach’s alpha for a perfectly valid test. Two reasons are reverse coding and multiple factors.

Reverse coding: Suppose you use a Likert scale of 1 to 7 with 1 meaning strongly disagree and 7 meaning strongly agree. Suppose two of your questions are: Q1: I like pizza and Q20: I dislike pizza. These questions ask the same thing, but with reverse scoring. In order to apply Cronbach’s alpha properly you need to reverse the scoring of the negatively phrased question, Q20. Thus if a response to Q20 is say 2, it needs to be scored as 6 instead of 2 (i.e. 8 minus the score).

Multiple factors: Cronbach’s alpha is useful where all the questions are testing more or less the same thing, called a “factor”. If there are multiple factors then you need to determine which questions are testing which factors. If say there are 3 factors, then you need to split the questionnaire/test into three tests, one containing the questions testing factor 1, one with the questions testing factor 2 and the third with questions testing factor 3. You then calculate cronbach’s alpha for each of the three tests. The process of determining these “hidden” factors and splitting the test by factor is called Factor Analysis. See the webpage http://www.real-statistics.com/multivariate-statistics/factor-analysis/ for more details about how to do this in Excel using Real Statistics.

Charles

5. sivapriyagirish says:

this method was very helpful for an average student like me,thank you very much…

6. Dalia says:

Hi,
Thank you for the great explanation.
My work includes using a 5 point scale by 2 separate groups of raters (trained Vs untrained in that field). Each group will rate 20 different cases.
My questions are:
1- Do I need to use Cronbach’s alpha for each case separately (20 cases x 2 groups) (i.e. 40 times)?
2- How can I assess the consistency within each group for all the cases collectively?
3- How can I know if there is a significant difference between the 2 groups for all the cases collectively?

Apologies for the long questions, but I really appreciate your help.

Best regards,
Dalia

• Charles says:

Hi Dalla,
From what you have described I have the following suggestions:
1. to assess the agreement/disagreement between the two raters you probably want to use something like Cohen’s kappa
2. to assess the consistency within each of the two groups you can use Cronbach’s alpha
3. to assess whether there is a significant difference between the two groups you can use either a t test or Mann-Whitney
All of these tests are described on the Real Statistics website and the Real Statistics Resource Pack can be used to carry out each of these tests.
Charles

7. Mukesh says:

Hi,

I have approximately 200 respondense, could you please let me know how to ho about getting the results of the Cronbach test. Do I have to enter a figure for each respondent to a question?

Thanks,
MC.

• Charles says:

Mukesh,
If you have say 200 people taking the test and each test has 20 questions, then you would create a range similar to that in Figure 1 with 200 rows and 20 columns. You need to enter a figure to each question.
Charles

8. Jonathan says:

Great site. Thank you.

I am looking for simple consistencies within a singular column of measured data, to see how volatile it is. I tried to use your CRONALPHA function to simply analyze one column of data of designated cells, and am getting the “#VALUE” response.

Am I missing something? Thanks much.

Jonathan

• Charles says:

Jonathan,
Cronbach’s alpha is not designed to do what you want. There is no internal consistency to measure when only have one response per subject. To use CRONALPHA you need at least two columns.
Charles

• Jonathan says:

Thank you Charles.

Perhaps I am asking the wrong question. Let’s say I have 120 responses from one subject over time, and what I am trying to do is to look at the consistency and repeatability of the answers from that subject. In other words, I want to see if the data, once I reach a certain point, has a stability to it. While I could do an even-odd correlation from the set, 1st-half / 2nd-half, or something like that, that introduces the limitations you discuss.

Is there something that considers the stability of a great number of data from one subject alone, to look at stability purposes? Thanks very much for a great site.

• Charles says:

Jonathan,

I am afraid that I don’t have much help to offer. I checked the Internet and found a number of sites addressing statistical analysis of single subject data and single subject consistency statistics, including the following:

Unfortunately these sites seem to be addressing something different from what I think you are looking for.

Charles

9. Mabel says:

If I have a 2 group study and want to conduct a cronbach alpha test, do I have to separate it into 2 groups?

• Charles says:

Mabel,
It really depends on what you want to study. E.g. if the groups are just a random split of the sample you could use the split-half method instead of Cronbach’s alpha to measure reliability.
Charles

10. Krsna says:

Thank you Charles. Your response is highly appreciated. My apology for this late reply. God bless.

11. Vien says:

Do you have a reference for this”A commonly-accepted rule of thumb is that an alpha of 0.6-0.7 indicates acceptable reliability”? Thank you very much!

• Charles says:

Vien,

I believe that I got this from the following reference (this is also referenced in Wikipedia)

Ref 1: Kline, P. (2000). The handbook of psychological testing (2nd ed.). London: Routledge, page 13

I have generally seen that .7 is viewed as the minimum acceptable level. Here is such a reference.

Ref 2: George, D., & Mallery, P. (2003). SPSS for Windows step by step: A simple guide and
reference. 11.0 update (4th ed.). Boston: Allyn & Bacon. p. 231

The rules of thumb there are:
> .9 – Excellent, _ > .8 – Good, _ > .7 – Acceptable, _ > .6 – Questionable, _ > .5 – Poor, and < .5 – Unacceptable

Here is yet another example where .6 is used as the minimal acceptable level.

Ref 3: "Cronbach’s alpha (Cronbach, 1951) which quantifies the degree of internal consistency (reliability) of a set of items, was calculated for each subscale, as well as the overall scale. In general, a Cronbach’s alpha of at least .7 is the criterion used to establish an acceptable level of reliability. However, the recommended minimum Cronbach’s alpha for exploratory studies is .6" (Nunnally, J.C. (1978). Psychometric Theory (2nd ed.). New York: McGraw Hill; Robinson, J. P., Shaver, P. R., & Wrightsman, L. S. (Eds.). (1991). Measures of personality an social psychological attitudes. San Diego: Academic Press).

I’m not a student of mathematics. I am leading a research in applied linguistics and I need to calculate a result using Cronbach alpha. I asked my students about the extent to which they became autonomous after introducing language learning strategies on a five-graded Likert scale with scores from 1 to 5. However, I didn’t know how to calculate. On the vertical column, I have to mention the respondents (students) and on the horizontal line, I have only one question (so one item??). Could I calculate alpha with only one column?
I am seeking guidance and I would be very grateful if you could help me.
Thank you.

• Charles says:

You can’t measure consistency between the items (which is what Cronbach’s alpha does) since you only have one item. You need more than one item to use Cronbach’s alpha. My question to you is why do you want to use Cronbach’s alpha? What are you trying to demonstrate?
Charles

• Enriching information.Kudos

• What percentage of the population is recommended for purpose of determining Cronbach Alpha?

• Charles says:

Joseph,
I have generally used the entire population of subjects who have filled in a questionnaire to calculate Cronbach’s alpha.
Charles

13. Karen says:

Hi,
I’m using a sample of 40 and I have 2 sets of questions, one with 9 and the other with 10 questions. I’ve calculated the alpha for both using the formula as you explained and then using the Real Statistics toolpack. I’m getting different alphas when I use the two methods with the toolpack function giving an alpha higher by around 0.08. Why is that?

• Charles says:

Karen,
Please email me the Excel worksheet(s) so that I can figure out happened.
Charles

14. krisliz says:

how did you get the var in example 4. i just don’t get it how it can be computed. is there a formula needed?

• Charles says:

Krisliz,
Cell B24 contains the formula =VARP(L4:L18).
Charles

15. Colleen Royle says:

Hello,
I am using an instrument that has been previously tested for reliability with a Cronbach Alpha of .91 and .93 for overall instrument (there are two variables being tested). The instrument has four subscales and each subscale has a Cronbach Alpha number of >.61 (three subscales are in the .80 range). I used the same instrument and tested Cronbach Alpha and received an overall number of .87 and .86. All of my subscales are substantially lower than the original testing by the instrument author. How do I explain that? We used a similar population. Her study was larger with 64 participants and mine had 40.
Thank you.
Colleen

• Charles says:

Colleen,
A few reasons why your alpha values may differ are: population not really the same as that for the original instrument, randomness (you say that your values were substantially lower, but it may turn out that the difference is not statistically significant), differences in the way the test was administrated(e.g. a noisy environment, people under stress, etc.).
Charles

16. Dianna says:

Hello,

I am having trouble with measures that has items with reverse coding. When I calculate the data with reverse coding, the Cronbach’s Alpha is very low (.2), however when I calculate the Cronbach’s Alpha without using the reverse coding, it is very high (.9). I am wondering if you know why that happens, and what I should do?

• Charles says:

Dianna,
It is hard for me to tell without seeing the data, but I can think of the following possibilities:
– the questions that you have identified as reverse coded are not really reverse coded
– there is an error in the coding or calculation
– reliability is low (not sure why alpha would be high if reverse coding is not done)
Charles

17. Zargoon says:

Regarding example number 3, I have performed Anova: Two Factor without Replication in Excel, but could not see Alpha value as it has been shown in Figure 5 above.

• Charles says:

Zargoon,
I just rechecked and I believe it is correct. Please make sure you analyzed the data from Example 1 (0’s and 1’s only) and not from Example 2.
Charles

• Meg says:

You have to type the alpha value (and that line input) in yourself if using Excel….

• Charles says:

Sorry, but I don’t know what you are referring to.
Charles

18. colene says:

Hi there – hopefully you can answer me 🙂

I would like to run a Cronbachs alfa test (or similar if you have an alteriour suggestion) to include it in my reliability part. (using SPSS)

I have a mixture of variables – Nominal, Ordinal and scale.
Which have a whole range of diferent ranges in values. Some variables have 0-1, others have 1-5, while others go from 0-14000. None are similiarly kategorized. Like, sex is a 0-1. Work hours range pr week from 0-30. A satisfactory question ranges from 1-5, rent payed ranges from 500- 13000… etc..

I’ve kategorized rent, and when I lump them all togheter in SPSS – Cronbachs alfa I get a Cronbachs Alfa of around ,500.

BUT – I have a feeling this is quite pointless? Because of the state of the values – is this so, is Cronbachs Alfa usless – how would I explain that I can’t use Cronbachs Alfa? My corriculum states that it is restricted to indexes – But I can’t quite understand what this means by “indexes”. Certainly we have an index of questions that all aim to answer an underlying question – but it’s not an index where all numbers are grouped simillarilly – so i am unsure what it means… Can’t I use it ? 🙂

• Charles says:

Colene,

I have read a lot of conflicting information regarding the subject you are raising and so I don’t have a precise answer for you. My understanding is that Cronbach’s alpha is most relevant when the test is evaluating a single “factor”. You can certainly calculate Cronbach’s alpha even if the questionnaire contains a mix of multiple choice, true-false and other types of questions. What I would be especially cautious about is when the test is performing different types of evaluations (e.g. Likert scale to assess your satisfaction with a product plus multiple choice to assess your ability to use the product). You definitely need to calculate separate Cronbach alpha for each concept/factor that you are testing.

I’m nor sure what your curriculum means by “indexes”. Cronbach’s alpha itself can be used as an index, but it doesn’t sound like this is what is meant.

The following are a couple of articles on the web that may give you further information (although they may confuse things even more). I suggest that you speak to your professor to get further insights from him/her. Please share with the rest of us any insights you glean.

Charles

19. James Selby says:

Thank you very much for this website!! Absolutely excellent and very useful…!

20. dee says:

hi. i gor high Cronbach for my 4 variables but the correlations are zero. Is it somehing wrong wih my calculations or the data? Need help. Tq

• Charles says:

Dee,
Can you send me a file with the example so that I can take a look at it?
Charles

21. noor hafizah hassan says:

Hye, i would like to run cronbach alpha on each item as my on likert scale..as you show in example 4 that run crunbach alpha on all the items..

How can i do it on each item?
Possible?
Seems it does not clear with me here..
Thanks

• Charles says:

Charles

22. Luke says:

Hi Charles,
Thanks so much for this site. Very helpful.
Reading from one of your observations above, and I quote, “If the variances of the xj vary widely, the xj can be standardized to obtain a standard deviation of 1 prior to calculating Cronbach’s alpha”, end of quote. just wondering how do you do that. Would be grateful for your response.
Thanks

• Charles says:

Hi Luke,
If you have a column of data in range A1:A10. You calculate the mean of the values (say in cell A12) by =AVERAGE(A1:A10) and the standard deviation (say in cell A13) by =STDEV(A1:A10). Now put the formula =STANDARDIZE(A1,A$12,A$13) in cell B1. B1 now contains the standardized value of the data in cell A1. If you highlight the range B1:B10 and press Ctrl-D then column B will contain the standardized values of all the data in range A1:A10.
Charles

23. Luke says:

Thanks so much indeed Charles. I got it.
You have a Blessed day.
Best,

24. Arin says:

Hi Charles,

Thanks so much for the explanation. It’s really easy to follow.
However, I have a question about example 1. How do you get the value for cell B20?
In figure 2, you just said its from M17. But how do you calculate it?
Any explanation on this would be very much appreciated.

Thx 🙂

• Charles says:

Arin,
M17 contains the formula =SUM(B17:L17).
Charles

25. Arin says:

Hi Charles,

I think I got it. Is it the sum of all the variance?
I got 1 different last digit than yours, instead of 3, I got 4.
I don’t know if it matters or not or if I am mistaken.

Thx again.

• Charles says:

Arin,
Yes. It is the sum of the variances. I used the formula =SUM(B17:L17) which sums the values in each of the cells B17 through L17. Although the value displayed for each of these cells contains 5 digits, more than this number of digits are actually stored. If you simply add the numbers that are displayed you get a number which ends in 4. If instead you add the complete numbers (as the formula =SUM(B17:L17) does) then the result will end in 3.
Charles

26. ricky says:

Hello Charles,

I am process of Writing my thesis and I need to find Cronbach’s alpha to state the reliability of my research. I tried usingg SPSS but I keep getting -4 as the alpha which I know is not right. It is a likert scale based questioonaire with a scale of 1 to 5 and the number of questions that I selected to find the Cronbach’s alpha is 10.
I will be glad to send you the questionnaire to see how you can help me.

regards, ricky

I would be willing to send you the data that I used.

I will be very grateful if you can assist me to solve this problem.

• Charles says:

Ricky,
The referenced webpage explains how to calculate Cronbach’s alpha in Excel. If you have downloaded the Real Statistics software you can use the formula =CRONALPHA(R1) where R1 is the range containing your data (formatted as described on the webpage) and the software will do all the calculations for you.
Charles

27. Ricky says:

Hi Charles,

Thanks for your prompt response and the info that you provided. I’ll download the software and give it a try. The 15-day trial version of the SPSS that I initially used kept outputing -4 as my alpha and it was frustrating.

Let me try again and if I encounter any problem, I’ll let you know.

Thanks again.

Ricky

28. juliet says:

Pls can someone send me how to solve cronbach alpha of the example1 above.thanks

29. Ness says:

Hello,

Thank you for the explanation and the answers that you gave, it is very helpful !

I hope that you can help me with my problem, since it is more or less specific..

I’m trying to calculate Cronbach’s alpha for a specific purpose: inter-rater reliability (rather than internal consistency reliability) where raters used Liker-scale to judge some behaviors shown in videos. 8 items were used for the Likert-scale. Until now it seems fine, I can measure Cronbach’s alpha coefficient for one behavior (one observed video) while considering 8 rows (for the 8 items) and n columns (for n raters).

However, there are many videos, and each rater evaluated only 16 videos (among around 600 videos). Each video was rated 24 times. My purpose is to measure the inter-rater reliability for each group of videos (the videos that share a common concept), and later, the overall inter-rater reliability..

My proposition is to measure the Cronbach’s alpha coefficient for each video, and then to measure the average of those coefficients in order to asses the global Cronbach’s alpha coefficient related to one group of videos. I only need to know whether this approach is reliable, I mean computing the average of n Cronbach’s alpha coefficients (that were computed separately for each video) to get the inter-rater reliability for a group of videos makes a sense !

Thank you in advance for your help, I really appreciate it since I could not find an answer anywhere..

Best regards,
Ness

• Charles says:

Ness,

I am not sure what you mean by measuring Cronbach’s alpha for one video. I would think that you would need more than one video even to use Cronbach’s alpha, unless you are comparing what you call “items”. In your explanation you reference 8 items, but I am not sure what the items represent.

My key question to you is why you want to use Cronbach’s alpha in this way, when, if I understand what you are trying to accomplish well enough, there are other tests which fit better with your goal? Perhaps you should be using Fleiss’s Kappa instead. See, for example, the webpage http://www.real-statistics.com/reliability/fleiss-kappa/.

Charles

30. Ermira says:

Hi,

I have 4 questions of type Likert Scale ( each of them contain 4 questions describing the main question).
As far I saw that cronbach alpha is for internal consistency, or it shows how good items are related to describe the main question.
I want to measure inter-rater agreement. Is Cronbach Alpha the right metric for doing this?

Thank you

• Charles says:

Hi Ermira,
Depending on your specific requirements, you could use Cohen’s kappa, Weighted kappa, Fleiss’s kappa, ICC or Kendall’s W. These all measure inter-rater agreement and are described in the website. See http://www.real-statistics.com/reliability/ for more details.
Charles

31. marzieh says:

Dear Charles,
I have made a series of multiple choice questions with 70 items and gave them to a group of ten for piloting but it is really hard to estimate Cronbach’s alpha. I know that it should be more than 0.7 but I don’t know how. Please help me. Thank you so much in advance.
Sincerely,
Marzieh

• Charles says:

Dear Marzieh,
If the person answered the question correctly they score 1 for that question. If they answered it incorrectly they score 0 for that question. Then use the approach in Example 1 of the referenced page or the CRONALPHA formula to calculate Cronbach’s alpha.
Charles

32. farah says:

I still dont understand about why should we change into 6 instead of 2…
N Q20….”Q20 in our example. Thus if a response to Q20 is say 2, it needs to be scored as 6 instead of 2 (i.e. 8 minus the recorded score).”
And why must be 8?

Im very confius…
Hope u can help me…
Thanks

• Charles says:

Farah,

Suppose you pose the following four questions and ask your respondents to give a rating of 1 to 7 for each, where 1 is the weakest response and 7 is the strongest response:

“Do you like pie?”, “Do you like steak?”, “Do you like green beans?” and “Do you dislike pizza?”

The fourth question is reverse phrased: “dislike” instead of “like”. A response of 7 to the first question means that the respondent really likes pie, while a response of 7 to the fourth question means that the respondent really dislikes pizza. This last response is equivalent to a response of 1 to the question “Do you like pizza?”. So in order to “compare apples with apples” (pun intended) you pretend that the last question was “Do you like pizza?” and use a score of 1 instead of 7.

In a similar way, a response of 6 to the question “Do you dislike pizza?” is equivalent to a score of 2 to the question “Do you like pizza?” Note that with a Likert scale of 1 to 7, the reverse coded score is always 8 minus the actual score (here 8 is 7+1). Similarly, if the Likert scale is 1 to 5, the reverse coded score is 6 minus the actual score (here 6 is 5+1).

I hope this helps.

Charles

33. farah says:

I have multiple choice question with one correct answer
How can i get internal consistancy for my questionnaire, should i use similar method in spss to get chronbach alpha vlue for likert scale for my 15 question of MCQ??

First in coding a b c d with 1.2.3.4
But now..i coding them 1 for correct answer and 0 for uncorrect answer

So what should i do next??

• Charles says:

Farah,
When using a Likert scale (such as 1, 2, 3, 4) you should use the appropriate value 1, 2, 3 or 4 for each question, but multiple choice questions are not like questions using a Likert scale. When you are analyzing multiple choice questions you should code 0 (incorrect) and 1 (correct). After the coding just following any of the approaches described on the referenced webpage to obtain Cronbach’s alpha.
Charles

• farah says:

A lot of thank for replied my massage..:)

By the way, what do you mean by following any approaches described on reference webpage to obtain cronbach alpha?

I hv difficulties to analyze my data to get alpha value..
What should i use..anyway..any suggestions?

• Charles says:

Farah,

On the referenced page I showed three ways of computing Cronbach’s alpha:
1. Directly using the definition of Cronbach’s alpha (as in Example)
2. Using ANOVA (as in Example 3)
3. Using the CRONALPHA function found in the Real Statistics Resource Pack (as in Example 4)

Charles

• farah says:

Thank you very much charles:)

34. MJ says:

Hi,

for my thesis I conducted CRONBACH alpha on several measures- the core questionnaire is the Five Facet Mindfulness Questionnaire (FFMQ). My sample is 265 Norwegian University students.

These are the scores I need to explain: FFMQ (0,582) where the individual facets never reach even 0.5, for the Perceived Stress questionnaire (0,345) and for AUDIT (0,396).

My supervisor thinks these are too low and would like me to explain why, and thinks we cannot be sure what the instruments were actually measuring. He wants me to give reasons for this.

Also, the CORRELATION between measures was low even though in the past it usually shows to be high. I am not sure what was different now, and what both a low cronbachs alpha and correlation could indicate.

I have found some reasons that could explain it like Participant Fatique.

I would truly appreciate any help as my thesis defence is due very soon and I am still stuck at this problem.

Best,
MJ

• Charles says:

MJ,
Since this is a standard test, I assume that your supervisor finds that your results are too different from the typical results for the test. You mention that a possible reason is Participant Fatigue, but you need to ask yourself why would students taking this questionnaire have higher levels of fatigue than the typical respondents to this questionnaire? In general, I can only think of two categories of reasons for the discrepancy: (1) the people taking the test are different from the typical people taking the test (different culture, problems with language, etc.) or the environment where the questionnaire is administered is different (too noisy, poor lighting, etc.) or (2) you aren’t measuring the the same thing as is typically measured — e.g. if I remember correctly the FFMQ has 5 different dimensions (factors), in which case you need to calculate Cronbach’s alpha not on the whole questionnaire but for the questions in each of the five dimensions separately.
Charles

35. Gabriel says:

Hi Charles, firstly thank you very much for providing this informative platform for everyone. Your effort is greatly appreciated.

Anyway, i do have some issues regarding alpha cronbach. Hoping that you can give me some clarification. Issues are stated as follows;
(i) In one full set of questionnaire, i have 42 items/ questions measuring different and diverse concepts/ factors. In another word, i cannot put all the items together at one go for Cronbach test (as this will lower the cronbach value as they are measuring different things), so i separate them into few groups say 8 groups of factors (consists of 3-5 or 2-3 items). So theoretically, each group i have different value of Cronbach if i executed cronbach for all the items. The question is do i need to execute the cronbach test for ALL items or groups? Is it necessary to ‘cronbach’ all the items? Can i just ‘cronbach’ just one group?

(ii) In exension of above issue, as you mentioned earlier, in order to use Cronbach, you have at least 2 items right? but we know that the lesser the items, the lower alpha cronbach will be. Say i have low cronbach value for 2 items, but these two items are valid to be in questionnaire just the reported reliability is low, so, do i need to do the cronbach test for that group? or i just ignore it? or there is a better alternative?

(iii) For your information, another issue is there are some items, like 2-3 items they are unique (maybe i have to say, they are not ordinal data, they are nominal data- yes or no etc, meaning to say, they are representing individual factor, so cronbach cannot be used right? is there alternative to replace the cronbach if this is the case? One more issue is multiple choices questions, i have about 8 of them, so, how can i establish reliability of them, is that possible?

Thank you very much

• Charles says:

Gabriel,

(i) You only need to calculate Cronbach’s alpha for the group(s) you are interested in.

(ii) As you know, all other things being equal, in general the more questions you have the higher the value of Cronbach’s alpha will be. For this reason the value of Cronbach’s alpha for two items (i.e. two questions) might seem low compared to a group with more items. There may be better alternatives to Cronbach’s alpha for two items, but I am not aware of them.

(iii) Cronbach’s alpha handles true/false and multiple choice questions with no problem. You code these with 0 for the wrong answer and 1 for the correct answer (as in Example 1 of the referenced webpage).

Charles

36. Chris says:

Just wanted to say what a fantastic resource you have put together here. I’m an educational researcher from a purely Arts background.

I put together a Likert survey, made up of 6 root statements (or factors?), and chose to analyse 3 of them using this method. I had 79 respondents and used a 5 point scale. The first factor consisted of 7 items and the second and third of 4 and 3 respectively. The spreadsheet returned scores .88, .84, and .79. I am well pleased!

I may even have a go at using your site for Factor Analysis and go a step further…

Much, much appreciated.

Chris, New Zealand.

• Charles says:

Chris,
I am very pleased that you found the site useful. Interestingly enough the original impetus for creating the site was that I wanted to perform Factor Analysis in Excel. Once I figured out how to do this I decided to share what I had learned with others who might want to do real statistical analysis using Excel.
Charles

37. Martin says:

I´ve just discovered Real Statistics, and so far it looks fantastic!

I´m looking to automate lots of calculations on a complex data set.

Is it possible to make the formula only calculate certain questions (for a subscale)?
How does the formula handle missing items/participants?

Kind regards,
Martin

• Charles says:

Martin,

Real Statistics has a lot of useful statistical functions and data analysis tools. I am also adding new features all the time.

There are various functions for selecting only certain data from a data range. These consist of standard Excel capabilities (Data > Filter, etc.) and Real Statistics capabilities (e.g. Extracting Columns from a Data Range data analysis tool and ExtractCol function).

Many of the statistical functions ignore any rows with missing data, but the CRONALPHA doesn’t have this capability. You need to first remove any missing data (e,g, by using the Real Statistics function DELROWBLANK or DELROWNonNum or via the Reformatting a Data Range by Rows data analysis tool) and then apply the CRONALPHA function to the reduced data range.

Charles

38. Darius says:

Dear Charles,

I have followed the chat, however, still did not get how to calculate alpha with multiple choice questions.
What do you mean by “correct (1)/incorrect(0)”? For instance, my questionnaire contains some questions, beside of Likert scale questions, with 5 sentences and the respondent is asked to mark those sentences which he associate with the particular subject. That means many different combinations could be marked.
Also there are such questions which require to range 5 sentences from most favourable to least favourable – also the answers could vary alot. How to cope with such questions while calculating alpha?

Thank you very much

• Charles says:

Dear Darius,

For multiple choice questions of the form “Select one of the following four choices a, b, c or d” the approach that I suggested should work, namely if say (c) is the correct choice then use the value 1 if the person selects choice (c) and use the value 0 if the person selects a, b or d.

Questions of the form “Select one or more of the following four choice a, b, c or d”, can be viewed as four True/False questions, namely choice (a) is correct (True or False)?, choice (b) is correct (True or False)?, choice (c) is correct (True or False)? and Choice (d) is correct (True or False)? If say the correct choices are (a) and (d), and a person chooses (a) and (b) instead, then score 1 for question (a), 0 for question (b), 1 for question (c) and 0 for question (d).

I am not sure how best to handle questions of the form “List the following five choices from most favourable to least favourable”. They are similar to having five questions where you rate each on a Likert scale of 1 to 5, but the difference is that you can’t use the same Likert score twice. Perhaps someone else has an idea about how to handle these types of questions

Charles

39. Kyan says:

Hi, I am currently working on my research. I face problem when i generating Cronbach Alpha. My questionnaire contains such question :
It’s quite complicated, how to obtain the Cronbach Alpha value after i key in all?

If answer section B, what i need to fill for section C items? With missing value or without missing value?

Need a guide to complete it as I running out of time.

• Charles says:

Kyan,
Perhaps the easiest approach is to calculate Cronbach’s alpha for the questions in section B (ignoring the people who didn’t answer the questions in section B) and calculate a separate Cronbach’s alpha for the questions in section C (ignoring the people who didn’t answer the questions in section C).
Charles

40. FFX-3 says:

Hello Charles,
I wish to use cronbach to demonstrate some internal consistency of a survey. If this has different sections and the sections each have mixtures of types of questions e.g, likert,dichotomous,multiple choice..how do I test for cronbach please? Thanks

• Charles says:

The important thing is to calculate a separate Cronbach alpha for each group of questions that are testing the same thing. Stated the other way around, you shouldn’t calculate Cronbach’s alpha for a set of questions that are testing different things.

In my view there is no problem mixing true/false and multiple choice questions provided the above paragraph is adhered to.

For multiple choice questions of the form “Select one of the following four choices a, b, c or d” if say (c) is the correct choice then use the value 1 if the person selects choice (c) and use the value 0 if the person selects a, b or d.

Questions of the form “Select one or more of the following four choice a, b, c or d”, can be viewed as four True/False questions, namely choice (a) is correct (True or False)?, choice (b) is correct (True or False)?, choice (c) is correct (True or False)? and Choice (d) is correct (True or False)? If say the correct choices are (a) and (d), and a person chooses (a) and (b) instead, then score 1 for question (a), 0 for question (b), 1 for question (c) and 0 for question (d).

I would not mix Likert scale questions (rate your opinion of Columbus from 1 to 5) with knowledge questions (in which year did Columbus discover America?).

Charles

41. Debbie says:

Hi there,

I have a questionnaire which contains:
1) Yes/No items
2) Likert-scale items

Can I use Cronbach? If yes, how do I perform the coding for 1) & 2) in SPSS?

Debbie

• Charles says:

Hi Debbie,

The important thing is to calculate a separate Cronbach alpha for each group of questions that are testing the same thing. Stated the other way around, you shouldn’t calculate Cronbach’s alpha for a set of questions that are testing different things.

I would not mix Likert scale questions (rate your opinion of Columbus from 1 to 5) with knowledge questions (did Columbus discover America?).

I don’t use SPSS and so am not familiar with the coding in SPSS. For the Real Statistics Resource Pack you would code a Likert scale of 1 to 5 with the numbers 1 through 5. You would code True/False (as well as multiple choice questions) with 1 for the correct answer and 0 for the incorrect answer.

Charles

• Debbie says:

Dear Charles,

Thank you so much! Much appreciated.

Debbie

42. Dear Charles,

Is it possible to determine the reliability of a survey questionnaire even if there are no established correct answer since it deals with their opinions? Should it be possible, what are the steps in computing it using the spreadsheet?

Riza

• Charles says:

Dear Riza,
Yes. E.g. if the answers are in the form of a Likert scale then you could use the Likert scale score to calculate Cronbach’s alpha.
Charles.
.

43. Theophilus says:

please, how do I compute the correlation
between a particular item and the
sum of the rest of the items.

• Charles says:

Say the the data is in range A1:F50 and you want the correlation between the data in column E and the sums of the rest of the items. Now place the formula =sum(A1:F1)-E1 in cell G1, highlight range G1:G50 and press Ctrl-D. The result that you are looking for is calculated by the formula =CORREL(E1:E50,G1:G50).
Charles

I have a mixed set of questions in my questionnaire where some questions are based on 5 point likert scale and some are single response questions not dichotomous. So, how should I calculate the cronbachs-alpha value for all set of questions in my questionnaire.

• Charles says:

The important thing is to calculate a separate Cronbach alpha for each group of questions that are testing the same thing. Stated the other way around, you shouldn’t calculate Cronbach’s alpha for a set of questions that are testing different things.
Regarding your specific request, can you give me some idea of the single response questions that you are using?
Charles

Got your point, thanks. lets say I have question 1. Which parameter do you look for while selecting the service provider?a)call charges b)network availability c)Customer care services d) offer and schemes e) any other. For these types of questions, how to calculate cronbachs alpa value.

45. Faisal says:

Thank you very much for your valued information given above. I really learn a lot. Only I have one question. If I have three different companies answering same questions? Can I measure the internal consistency by conducting Cronbach’s alpha? Even ratters from company A have different circumstances than B or C?

• Charles says:

Faisal,
Cronbach’s alpha doesn’t work with only one question, although there are some other procedures for dealing with one question. I gave a link to one of these in a previous comment. I wouldn’t expect much with such a limited amount of data.
Charles

• Faisal says:

Dear Charles,

Thank you very much for your prompt replay. I mean I would like to ask only one question. I am sorry it was my fault not describes my question very well. I have 10 groups with 43 factors and I have 36 response from three different companies rate my factors. If I have three different companies answering same questions? Can I measure the internal consistency by conducting Cronbach’s alpha? Even ratters from company A have different circumstances than B or C?

• Charles says:

Dear Faisal,
Yes, you can use Cronbach’s alpha to create one value of alpha (or three values, one for each company). It would be interesting to see whether you get different values for the three different companies.
Charles

46. Phoenix says:

Dear Charles,
Really hope you can solve my problems.
My questionnaire consist 3 parts which are
1. Knowledge in action research – Using test form (5 multiple choice answers and 5 open-ended questions)
2. Skills in implementing action research – Using 5 point likert scale
3. Attitude towards action research – Using 5 point likert scale

My problem is how to run reliability test for part 1. Because in this part have few difference types of questions.
Example:
1. multiple choice (A , B , C , D )
2. list out 4 data collection techniques
3. pls arrange 10 steps of implementing action research using number 1 to 10.

My friend advise me to run Kuder Richardson, which one more suitable?

If use Kuder Richardson to get reliability for part 1, then how about the overall reliability for the questionnaire? How to run the test?

Anyway thanks a lot.

• Charles says:

The multiple choice questions can be coded as 0 for a wrong answer and 1 for a correct answer. You could code the 4 data collection techniques as four questions with 0 for an incorrect technique and 1 for a correct tecnique. I am not sure how you want to code the 10 steps question as right or wrong (this is necessary if you want to use Kuder Richardson).

You can use Cronbach’s Alpha. If all the scores are 0 or 1 the result for Kuder Richardson is the same as for Cronbach’s alpha (the referenced webpage). You can also look at the webpage http://www.real-statistics.com/reliability/kuder-richardson-formula-20/.

What is most important is that Kuder Richardson (or Cronbach’s alpha) is calculated only from questions that are measuring/testing the same thing.

Charles

47. ghazala says:

i need draw backs of cronbach alpha test.

• ghazala says:

why cronbach is important for internal consistency?????

• Charles says:

Cronbach’s alpha measures internal consistency. Internal consistency is important because it determines whether a questionnaire or some other measuremnt tool is measurin the same thing. If for example you design a questionnaire to determine whether someone is bipolar, you want to make sure that all the questions are measuring the same thing,
Charles

• Charles says:

A couple of drawbacks:
– Cronbach’s alpha measures internal consistency, but the more items the higher Conbach’s alpha will be even though the internal consistency isn’t any higher.
– Redundant items (e.g. the same question phrased slightly differently) will increase Cronbach’s alpha
Charles

48. Roy Hepner says:

Charles,
First, let me thank you for these excellent tools. They provide wonderful access to statistical results related to educational outcomes.
I run Excel 2010 and have the downloads installed. However, I can run cronalpha, but not with the k switch. Nor can I run calpha. What do you think is missing, misplaced, or uninstalled.
Roy

• Charles says:

Roy,
I introduced these capabilities quite recently. If you are using a version of the software prior to Release 3.0 these capabilities are not included. I suggest that you download the latest version of the software.
Charles

49. Giacomo says:

Hi Charles

Thank you very much for the resource you provide.

My question is the following: I usually run alpha on a very limited sub-sample (about 10 cases) before delivering any questionnaire in order to asses the consistency of it; btw I have no reason for choosing this number, 10 cases. Is there any rule suggesting a minimum number of cases or a minimum ratio cases/variables to have a ‘solid’ alpha?

Giacomo

• Charles says:

Giacomo,

I have seen a number of websites that have information about the minimum sample size for Cronbach’s alpha. I used the following search on google: “minimum sample size for cronbach alpha”

I have also seen the following paper which you may find helpful:

Research in Nursing & Health, 2008, 31, 180–191
Considerations in Determining
Sample Size for Pilot Studies
Melody A. Hertzog*

Charles

• Giacomo says:

Thank you again!

Cheers

Giacomo

50. maggy says:

hie,
what percentage of respondents do i need when using cronbach alpha during pretest? where can i get this reference. a friend told me that i need 10% of the respondence, is it true please help.

• Charles says:

Maggy,

I have seen a number of websites that have information about the minimum sample size for Cronbach’s alpha. I used the following search on google: “minimum sample size for cronbach alpha”

I have also seen the following paper which you may find helpful:

Research in Nursing & Health, 2008, 31, 180–191
Considerations in Determining
Sample Size for Pilot Studies
Melody A. Hertzog*

Charles

51. Napoli Martin says:

Charles, thank you so much for this article; it is very helpful for a math novice like myself. I would be grateful if you could assist me with some questions regarding the calculation of the Cronbach Alpha.

We have a test which deals in direct assessment. To be brief, I would like to calculate the reliability of our testbank broken down into topical groups. While our testbank will contain about 300-400 questions per topic alone, each student is only presented with 10 random questions. I have a population of 800. Does it matter if the questions (all multiple choice) are different for each student? Can I still create 10 columns with 800 rows?

My assumption tells me I cannot, because Q1 for student 1 may have gotten it correct, and student 2 and 3 may have also gotten it correct, however, Q1 for student 2 and 3 could be the same, or, most likely entirely different (although all the concepts are the same).

• Charles says:

I don’t know how to calculate Cronbach’s alpha in this situation.
Charles

52. Reggie says:

Charles:

I am conducting multi-variable regression using 5 independent variables to predict the impact on transportation costs as a proportion of income in 75 metropolitan statistical areas. The data includes employment rates, population density, and value of exports. Is Chronbach’s Alpha an appropriate test for reliability or should I be using a different type of test? If is is appropriate, should I be including the dependent variable in the calculation? Thank you very much.

• Charles says:

Reggie,
I can’t see why you would want to use Cronbach’s alpha in this case. What is the objective of the reliability test you want to pperform?
Charles

53. Lou says:

There are typos in your equations for x_0 and t_0. You should be summing over x_j and t_j (i.e.: $x_0 = /sum_{j=1}^k x_j$ and $t_0 = /sum_{j=1}^k t_j$), respectively.

• Charles says:

Lou,
Thanks for identifying these typos. These sorts of mistakes can really cause confusion for people who are less familiar with the notation, and so I really appreciate your comment. I have now made both corrections.
Charles.

54. Shiba Parhi says:

This a great websites I have gone through several books and websites nowhere I got all these information My sincere respect to you.

Regards
Shiba
Asst Prof

• Charles says:

Shiba,
I am very pleased that you find the website valuable. I am trying to create an easy-to-use, yet powerful resource that is available to everyone who needs to learn, teach or use statistics.
Charles

55. Sona says:

Good afternoon sir.
my tool is checklist. It has three catageries 6 Year(1 catg),7 Year(2catg),8 year(3 catg). 1 catg contains 6 items,2 catg and 3 catg contains 7 items. How i will calculate reliability.
thank you

• Charles says:

Sona,
Unfortunately, you haven’t provided enough information for me to make any recommendations.
Charles

56. sona says:

good afternoon sir. I am conducting a comparative study to assess the developmental milestones of children in rural and urban areas. I am using checklist as a tool. My tool have three categories 6 years,7 years,8 years. Each categories has different questions. 6 years contain 6 question. 7 years category contain 7 questions. 8 years category contains 7 question. I want to check the reliability of tool. Than how I will check the reliability of tool

57. Gracefield says:

What Statistical tool can best be used to test hypothesis of significant INFLUENCE of one variable over the other. the two variables have separate instruments measuring them. Is it T-test, Correlation, Regression, Chi-square, or which
Thanks

58. Frank says:

Thanks for the great resource pack and website. My question: While using Fleiss’ Kappa to measure rater agreement, I experimented with various agreement scenarios but now have trouble interpreting the kappa. With 11 subjects and 5 raters on a 5 point scale, I set everyone’s agreement on the middle of the scale (e.g., 3 on a 1 to 5 scale). Kappa would not calculate until I moved 1 score into another column. So, with all raters=3 for all subjects except one, kappa calculated to -0.01852. Intuitively, I expected a number close to 1. I’m left wondering if the answer is 1 minus the calculation.

59. Udo says:

I have 6 items with SA, A, SD, D, how do I apply cronbach alpha with these figures.

• Charles says:

Udo,
Just assign the values 4 to SA, 3 to A, 2 to D and 1 to SD and use the approach described in the referenced webpage.
Charles

60. Martin says:

Charles,

I have done the split-half methodology against our set of multiple-choice questions; and thus far, the results look good. Since students may not get the same question (although all questions measure the same concept(s)) on their specific exam, I had to sample each conceptual question into groups of 30.

For example, I would have thousand rows with the columns of NumQuestionOffered=30, and NumQuestionCorrect=X

Provided I have the Odd/Even Anlysis Means, StdDevs, etc. ..is it possible to use that data to produce a standardized Cronbach’s Alpha?

• Charles says:

Sorry Martin, but I don’t completely understand what you are trying to do. I see that you are trying to combine questions, but I don’t understand how the split half accomplishes this.
Charles

61. Yvonne says:

Hi firstly thank you so much for this website it has been so helpful. I am doing an MSc just now and am looking at manager’s self-awareness and how closely their followers/direct reports assessment of their leadership styles agree. I have only 7 managers and 26 direct reports results.
I have a few queries from when I apply Cronbach’s alpha – should I be looking at the manager and their direct reports results as individual cronbach’s alpha? Or can I combine all the data as one set of 33 results? Also when I first ran Cronbach alpha on the 6 questions which made up one scale, I got a figure of >1. I worked out this was because the missing data points must be being used as 0s. I first excluded the whole column of data (ie 3 of the criteria for the scale) and got a figure, then I ran it again removing the people with the missing data – and got a similar figure to that of removing the question. Which is correct way of doing this? or how else should I deal with missing data? Also, looking at an earlier response Cronbach’s alpha may not be very accurate/reliable with such a small sample? Any other ideas of how I could analyse the data? The purpose of my MSc question was to discover if the manager’s view of their leadership style matched that of their direct reports. So possibly I do need to do cronbach’s alpha on each manager – rather than using it as one data set?

• Charles says:

Yvonne,

The current implementation of Cronbach’s alpha doesn’t accept any missing data. If you remove an item, this item won’t be included in your analysis. If there is a lot of missing data for one item you might consider removing this item, but in this case you should try to understand why there is so much missng data for this item. Otherwise, I would tend to remove the data for subjects with missing data. Of course this approach only works if there is a small amount of missing data. Otherwise you should consider imputing values for the missing data.

Based on your description, it seems that you are interested in measuring the agreement between raters. Usually intraclass correlation, Cohen’s kappa, Fleiss’ kappa, etc. are used for this (and not Cronbach’s alpha). You can get more information about these measurements on the webpage http://www.real-statistics.com/reliability/

Your situation is the agreement between one rater and a group of raters. This discussed in Chapter 4 of http://orbi.ulg.ac.be/bitstream/2268/39575/1/vanbelle-thesis-5-5-2009.pdf

Charles

62. Yvonne says:

Hi I have another query to add to this. I have run the Cronbach’s alpha for 2 of the individual manager’s sets of results for one of the scales and a set of data I would have thought should have shown far lower inter correlation than the other came out the other way round. Is it because I only have about 6 individuals results – which is too low?

• Charles says:

Yvonne,
It is difficult to answer your question without seeing the data, but as I said in my previous response it doesn’t sound like Cronbach’s alpha is the correct measurement to use in any case.
Charles

63. Karen Monaghan says:

Thank you, thank you, thank you for this clear and logical explanation of how to apply Cronbach’s Alpha to a Likert scale.

64. nasir mirza says:

what about sample size shoud be taken to test reliability having 20 questions with 7 piont scale likert type

• Charles says:

Nasir,
To answer this question you need to spply additional information such as the expected/minimum value of Cronbach’s alpha, minimum power, etc.
Charles

65. terry says:

love the info. thanks so much.
so nice to have experts share their knowledge on the net.

66. Mark Campbell says:

I am trying to determine the reliability of an exam in which there are 25 multiple choice exams with a variable number of response choices (4, 5 or 10). Blank answers are given 1/4 credit. What is the most appropriate way to measure the exam reliability?

• Mark Campbell says:

• Charles says:

Mark,
The number of response choices shouldn’t really matter since each question is scored 1 for correct or 0 for incorrect. However things are more complicated with 1/4 credit for a blank answer. Perhaps one way to address this is to assign a score of 0 for incorrect, 4 for correct and 1 for blank and then use Cronbach’s alpha.
Charles

67. Kent says:

Hi Charles,

Hope you can help. We did a survey on identifying comparison in students’ attitude towards a list of 10 sub-factors (5 point Likert scale) on advantages of using a tool. The Cronbach alpha for each of the 2 colleges (A and B) with 2 columns (A and B) is over .9 which should reflect good reliability. My question is, if we then look into overall gender comparison analysis on students of the same two colleges using the same sub-factors with 2 columns (male and female), is it necessary to evaluate the Cronbach’s alpha for the gender comparison or can we assume that the reliability is the same?

• Charles says:

Kent,

If you suspect there is a gender bias to one of the questions, then I would evaluate Cronbach’s alpha for each gender. If one question seems to lower the score for one gender, then I would either reword or eliminate that question. If your goal is to compare the results by gender then you want to use a different test (e.g. t test, Mann-Whitney, etc.).

One other comment. The value you obtained for Cronbach’s alpha was high, but since it is over .9 it may be too high, meaning that the questions may be too similar and are just testing the same things.

Charles

• Kent says:

Yes, we do conduct the t-test for comparison. I wonder if it is necessary to provide Cronbach’s alpha value to indicate good reliability and internal consistency when we are using the same set of questions for college and gender comparisons. Is it a necessity to provide Cronbach’s alpha value to validate good reliability before doing a comparison between colleges or gender?

• Charles says:

Kent,
If you have gotten high values of Cronbach’s alpha in your test sample it is not necessary to repeat Cronbach’s alpha for new samples, unless you suspect there is something different about the new sample. As I stated in my previous response, if you suspect there is a gender bias, not in the responses per se, but in the internal consistency (perhaps because one question is misinterpreted by men or women), then you should repeat Cronbach’s alpha. In any case, since you will be testing the data anyway you probably should run CRonbach’s alpha just to make sure there is nothing strange going on.
Charles

• Kent says:

Tqvm, Charles.
You have been a great help.
Take care.

68. Azili says:

Hi Charles,
I want to ask you about cronbach alpha.I have questionnaire which in this questionnaire have Likert type scale (1-4) and question yes/no.In questionnaire also have question like gender,marital status etc.How to get the cronbach alpha value using these data?Thank you

• Charles says:

Hi Azili,
The idea of Cronbach’s alpha is to measure the internal consistency of the questionnaire. If the yes/no questions are measuring something different from the Likert questions (e.g. the yes/no questions are testing the subject’s knowledge and the Likert scale questions are determining their satisfaction) then there may be no point in calculating one Cronbach’s alpha; better to calculate two or more values.
If instead the yes/no questions are measuring something similar to the Likert questions then perhaps you can decide to treat the yes/no questions in a manner similar to the Likert scale questions. E.g. if the Likert scale questions measure satisfaction (with 0 very dissatisfied and 4 very satisfied) and yes = satisfied and no = not satisfied, then perhaps a coding like yes = 3 and no = 1 will work. In most cases, I suspect that the yes/no questions are measuring something different from the Likert scale questions and so you need to calculate multiple Cronbach alphas.
Charles

69. Raman says:

Hi Charles,

My querry regarding Cronbach’s alpha values. No of respondand =100, The questionaire having 5 point scale ans consisit of 22 input and 4 output facors. I used the procedure expalined by you in figure 1. I got value. But some researcher are showing Cronbach’s alpha values for every input and output factors. If there need to compute the value if Cronbach’s alpha for for every input and output factors. If yes then how.. Kindly do needfull

• Charles says:

Raman,
I don’t know what you mean by input and output factors in the context of Cronbach’s alpha.
Charles

70. Sammie says:

For example 1, can you explain why cells B20 and B21 do not have the same value? I’m trying to follow the formulas, but it seems like M17 in B20 would have the same value as the result of the formula for B21. Thank you!

• Charles says:

Sammie,
B21 contains the variance of the row sums, i.e. VARP(M4:M15), while B20 contains the sum of the variances of the column sums, i.e. SUM(B17:L17). There is no reason why these should be equal.
Charles

71. Raman says:

Thanks Charles for ur kind reply. I want to check the influence of input parameres on the output parameters of a system. for this questionnaire study was performed.

the data collected table has 100 rows and 15 column.
I got the single value of Cronbach’s alpha. If there need to compute the value if Cronbach’s alpha for every column. If yes then how.. Kindly do needfull

• Charles says:

Raman,
In the examples I have given on the referenced webpage, the columns correspond to “items” in a questionnaire (these are variables). Not only don’t you need to compute Cronbach’s alpha for each column, but such a calculation would yield an error since Cronbach’s alpha requires more than one item. On the website, however, Cronbach’s alpha on one column corresponds to Cronbach’s alpha on all the item leaving out that one column. This tells you the influence that specific item has on the entire questionnaire.
Charles

• Raman says:

Thanks a lot

72. Brenda says:

Hello,
Thank you for this very helpful site! I am curious about the use of Excel’s VarS function (instead of VarP). I notice you use VarP above, and I’m wondering why that is. If I understand Excel’s explanation, VarS would be used for a sample whereas VarP is used for a population. Wouldn’t most, if not all, of the scales we may develop require the formula for sample variance? Can you help me understand your choice to use VarP so that I can distinguish it’s use in my application of Cronbach’s Alpha for scales I am creating?
Brenda

• Charles says:

Brenda,
This is more of a mathematical issue. If you replace Var.P by Var.S throughout you will get the very same answer (since the n or n-1 terms in the denominator cancel out).
Charles

• Brenda says:

Oh yes, of course! Thank you!

73. Raman Kumar says:

Hello Sir,

Firstly i want to say thanks for helping me to compute Cronbach’s alpha Value.

I go through almost all study material provided by you. But still in confusion which more statistical tools can be implement on my questionnaire data.

There are 22 input and 4 output.

I collected data for every input with respect to every output on likert scale

Q1 Rate the effect of Input 1 on Output 1

(Importance scale for every question)
(Extremely (Very Neither Imp (Very (Extremely
Important) Important) Nor UnImp. Unimportant) Unimportant)
1 2 3 4 5

Q2 Rate the effect of Input 1 on Output 2

Q3 Rate the effect of Input 1 on Output 3

Q4 Rate the effect of Input 1 on Output 4

Q5 Rate the effect of Input 2 on Output 1

Q6 Rate the effect of Input 2 on Output 2

Q7 Rate the effect of Input 2 on Output 3

Q8 Rate the effect of Input 2 on Output 4

Q9 Rate the effect of Input 3 on Output 1
………… and so on
Q85 Rate the effect of Input 22 on Output 1
Q86 Rate the effect of Input 22 on Output 2
Q 87 Rate the effect of Input 22 on Output 3
Q88 Rate the effect of Input 22 on Output 4

The no of respondent : 100

Thanking you in anticipation

• Charles says:

Raman,
If I understand correctly, you have 88 questions using a Likert scale of 1 to 5 and 100 subjects. This is just like Example 4 of the referenced webpage but with 100 rows and 88 columns. You can use the CRONALPHA function or the Reliability data analysis tool to calculate Cronbach’s alpha.
Charles

• Raman Kumar says:

Sir,

I have computed the value of Cronbach alpha.

But my query is now let me know which more tools such as Z test, correlaion, regression, factors could be used. The objective of my survey is to examine the impact of input factor in output.

• Charles says:

Raman,
The phrase “examine the impact of input factor in output” is too vague. You need to create a hypothesis and then decide which test best tests this hypothesis.
Charles

• Raman Kumar says:

Sir,
i want to know how many input parameters significantly influence output1; how many parameters significantly influence output2,parameters significantly influence output3, parameters significantly influence output4.

• Charles says:

Raman,
What do you mean by “significantly influence”?
Charles

74. Raman says:

Sir,

I want to know which input or inputs (out of 22) has more impact on output 1
which input/ inputs (out of 22) has more impact on output 2
which input/ inputs (out of 22) has more impact on output 3
which input/inputs (out of 22) has more impact on output 4

• Charles says:

Raman,
Sorry, but the term “more impact” is unclear to me.
Charles

75. K says:

Good day sir.

In my experiment survey of Y/N(1-0) questions, where all 3 questions got a perfect score of 1 from 15 respondents, I was not able to compute the alpha. The value of all the variances is 0.
The final result is k=3, eVar=0, var=0.

What could it mean?
Is it also possible to get a perfect score of 1 or 0 for the alpha? What would each result mean?

Thank you.
-K

• Charles says:

K,
Unfortunately, in these circumstances Cronbach’s alpha is undefined because of division by zero. The good news is that all the respondents answered the same way, it is pretty easy to make evaluate the effectiveness of the survey even without using Cronbach’s alpha.
If on each of the three questions the subjects didn’t have identical scores, but if each subject got the same score on all three questions, then Cronbach’s alpha would be 1.
If you assign all scores of 0 or 1 at random, then Cronbach’s alpha is likely to be low (even negative).
Charles

76. AriesMW says:

Hi Charles,

I am so glad to find your website. Your demonstration of how to calculate Cronbach alpha is very relevant to my research. May I ask you one question?

I used a spelling test from a published study for my own research and I want to report the internal consistency reliability of this test based on the data I have collected. The spelling test examines how students spell four English vowel sounds. In such case, do I need to calculate Cronbach alpha for each target vowel sound? Is it appropriate to calculate Cronbach alpha for all items (all sounds) and report internal consistency reliability of the whole test?

Thank you so much for helping me.

• Charles says:

If the test is for spelling of vowel sounds then one Cronbach’s alpha should be sufficient, but if you suspect there may be differences between vowels then I would compute separate Cronbach’s alphas for each vowel sound. I would do both and explain the results.
Charles

• AriesMW says:

Thank you very much for answering my question.

• AriesMW says:

Hi Charles,

Sorry I have one more question. I have four groups of participants (who have different characteristics) in my study and the same spelling test was administered to all groups. Do I need to calculate Cronbach’s alpha of the test for each group?

Thank you for helping me again.

• Charles says:

I would do both. If the difference in the characteristics of the participants changes the reliability of the test, then this should become evident in the Cronbach’s alpha values.
Charles

• AriesMW says:

Thank you!

77. watan says:

Dear sir,
I want to use a test with high zero frequency in scoring , if the answer is rarely or sometimes or never then the score is equal zero (represent the same number) ?! so Cronbach’s alpha is low ?! but if I insert the data as, never represent=6 , rarely=5, sometimes=4,usually=3, often=2, always=1 then Cronbach’s alpha will increase !!
can I do that only to calculate Cronbach’s alpha ?! I mean changing the scoring only for the pilot study?!
Best,,

• Charles says:

I just recalculated Example 4 on the referenced webpage using a Likert coding of 0 to 6 (instead of 1 to 7) by reducing each code by 1. The calculated value of Cronbach’s alpha did not change. Is this the sort of thing you are referring to?
Charles

78. Tushar says:

I am research scholar. I need to know when to calculate Alpha. E.g For testing reliability, can I go with 10 sample units and the value of Alpha is 0.897. Would it be fine???

• Charles says:

I don’t completely understand your question, but if you are using Cronbach’s alpha to test the reliability of a questionnaire based on 10 subjects, an alpha of .897 would generally indicate a high level of reliability.
Charles

79. Vince says:

does anyone know what the lower bound for the number of observations using the alpha is? i’ve heard it’s about ten times the number of items, however can’t be sure at all… many thanks!

80. Godspower says:

Pls sir how did you calculate variances in row 17 and 21. will you mind using Figures from the table?
I really want to know this cronbach alpha

• Charles says:

This is already explained in Figure 2 and the text between Figures 1 and 2. What else are you looking for?
Charles

Dear sir,
i had done a survey on questionnaire which contain 3 parts (A,B,C). I’m using cronbach alpha for my questionnaire. I had calculated those 3 parts and only part A and C are reliable, whereby the value part A ( 0.798), Part B ( 0.642) ,Part C (0.857). So what should I do with those result and are they reliable?

• Charles says:

The reliability ratings for Part A and C are quite good. Even Part B is not bad. The typical approach now is to see how Cronbach’s alpha changes by removing one question (as described on the referenced webpage). If say removing question Q4 from Part B increases the reliability for Part B to .7, then you should consider eliminating this question from Part B or changing it.
Charles

TQ sir for answering my question. I would like to remove the question but most of the score of all the questions in Part B are around 0.6. So should i remove all the questions?

• Charles says:

You probably don’t want to remove all the questions. You might want to think about changing the wording of all the questions a little. Alternatively, you can do nothing since .6 is a little on the low side, but acceptable to some.
Charles

hello. I am writing from Mongolia. First of all, thanks for your help. I have been doing the survey that has 5 foint likert scale. the survey is Student satisfaction for teachers. my university has 3000 students and all students give answer to 130 teachers. How to calculate cronbach’s alpha?

• Charles says:

Good to communicate with someone from Mongolia.
Enter the Likert scores in a range with 130 columns and 3000 rows and then either follow the approach from Example 4 or use Real Statistics’ CRONALPHA function or the Cronbach’s alpha option from the Reliability data analysis tool.
Charles

Thank you very much for answering my question.

Excuse me sir. can I use average score of each teacher.

• Charles says:

It depends on what you are measuring. If each student makes multiple evaluations of each teacher, you can use the average score (or total score) by each student of each teacher.
Charles

thank you for your response. I have one more question. Can I do ANOVA by three schools? Is it possible to do ANOVA when you have ordinal data?

• Charles says:

I don’t exactly know what you mean by doing ANOVA by three schools. You can do ANOVA with ordinal data, but I would not recommend it. You should use a non-parametric test instead (e.g. Kruskal-Wallis).
Charles

85. Nana says:

Hello Charles
I’m phd student and using questionnaire in my thesis .
I have 4 variable as independent and one dependent variable , each variable had 7-6 question. I tested Cronbach’s alpha for each variable in my pilot and remove and delete 3 to 4 question to increase my Cronbach’s alpha to .8 or .9 ,
and continue my data collection with 4-5 question for each variable.
now
i should analyses my main data with PLS,
but now, my Cronbach’s alpha decrease a gain and are less than .7 for each variable, and now i can not delete some question again.
what should i do now?
i really confuse.
thank
Nana

• Charles says:

Is PLS partial least squares regression? Are the revised values for Cronbach’s alpha based on the latent variables (after applying PLS)?
If this is the situation, then I am not sure what the best approach is. If Cronbach’s alpha is just slightly less than .7 then I would worry about it too much.
Charles

86. Negar says:

Hi Charles,
I would like to know what kinds of questions could increase my Cronbach alpha? I did some readings to increase the quality of my questions in my questionnaire and after some piloting I have added 5 more items to the questionnaire but my alpha is still below 0.7 and I should delete some which are really critical questions. Do you have any suggestions? I feel so desperate.
Best,
Negar

• Charles says:

Negar,
It is possible that your questionnaire is measuring more than one thing. In such cases, Cronbach’s alpha will be reduced. Instead of deleting questions, for the purposes of computing Cronbach’s alpha, you may need to split the questionnaire into two (or more) parts, one part for each group of questions that are measuring the same thing. In this way, you might be able to bring Cronbach’s alpha up to 0.7 on each part of the questionnaire.
If necessary, factor analysis can be used to figure out how to do the splitting of the questionnaire.
Charles

• Negar says:

87. Justin says:

Hi! How do you conduct cronbach alpha when the variables are income, consumption,a likert scale, and a dummy variable?

• Charles says:

Justin,
Are using Cronbach’s alpha for a questionnaire? What do you mean by there are two variables? Do you mean two questions or two types of questions: those relating to income and those relating to consumption?
Charles

• Justin says:

Yes, there are separate questions for income and consumption and we also have a question where it is answerable by 1 or 0 (dummy variable). We dont know how to do the cronbachs alpha for that dummy variable. 🙁

• Charles says:

Justin,
Cronbach’s alpha can be used even when the questions take a value 1 (say for correct) and 0 (say for incorrect). This would cover True/False and multiple choice questions. The problem is that you can’t use Cronbach’s alpha with only one question. After all, Cronbach’s alpha measures internal consistency, but withonly one question there is no internal consistency to measure. The same is true for Kuder and Richardson.
Charles

88. Joseph Kosure says:

Dear Charles
This is a wonderful website.
Kindly assist I am administering a questionnaire in a census survey of 86 target respondents. The questionnaire has a total of 23 questions some of which have sub items. How many sample respondents should I use for calculating cronbach alpha in the pre-test?
Joseph

• Charles says:

Joseph,
You can use the Statistical Power and Sample Size data analysis tool. Choose the Cronbach’s Alpha and Sample Size options.
Charles

89. Kristine says:

Hi! I want to know the reliability of a 4o-item Math Test. How would I do that in SPSS? What data am I going to enter?

• Charles says:

Kristine,
Sorry, but I am not familiar with SPSS. The Real Statistics Resource Pack provides such capabilities.
Charles

90. Kristine says:

Can I find the reliability of a test using excel?

• Charles says:

Kristine,
One approach may be to use Cronbach’s alpha as described on the referenced webpage.
Charles

91. JIHYE says:

You are my lifesaver!
I have trouble with calculate cronbach alpha until I saw this page.
I finally got my cronbach alpha answer through Excel which is written by you.
Thank you!

• Charles says:

Good to hear that the information was helpful.
Charles

92. Sherif says:

Hi Charles,
Thank you for the description of Cronbach’s alfa, I really found it the best from several references, I reviewed in the past week.
I’m a PHD student conducted a questionnaire on 50 participants asking them 30 questions, each question has 3 multiple choices. Each choice support one of three leadership approaches from different perspectives (reordered randomly).
Because my thesis is only interested in the middle approach between two extremes; when I tried to calculate Cronbach’s alfa I considered the vote to the middle approach to be 1 and any vote to the other two approaches to be 0. Is this correct? The middle approach got 89% of the total votes (1500). I was expecting alfa to be very high because of that but when I calculated alfa it was very low (0.164). Please advice.
Many thanks.

• Charles says:

Sherif,

The approach of 1 for the “correct” answer and 0 for an incorrect answer is the usual approach. I can’t say why the alpha value was so low, but usually this a sign of a problem showing low value for many call internal consistency, possibly because the test is measuring more than one thing (“factor”).

Care must also be taken with reverse coded questions (as described on the referenced website), although with 89% correct answers perhaps this is a less likely cause for concern in your case.

Another possible reason for a low alpha value is that the assumption for using this measure is violated (namely what is called “tau-equivalence”). Cronbach’s alpha is commonly used despite violations of this assumption. For this and many other reasons a lot of people don’t believe that Cronbach’s alpha is really a measure of reliability, despite the fact that it is commonly used and insisted on by many journals.

The fact that 89% of all the responses were correct seems very high. I can’t say whether this is contributing to the low alpha or not.

Charles

93. natasha says:

hi,
i want to test the reliability of a multiple choice test. how do i code the responses and how do i find the reliability using cronbach alpha

• Charles says:

Natasha,
The simplest way to code the response is 1 for a correct answer and 0 for an incorrect answer. You can then calculate Cronbach’s alpha using any of the approaches described on the referenced webpage.
Charles

94. lila says:

hello !
I would like to do a Cronbach for my test but somehow i am not sure it is pertinent.
I’m not confident in doing this kind of work so i will explain detailfully.
Actually, there is a question and 7 possibilities of answer but only one is the good one.
So i wrote 1 if succeed, and 0 if didn’t succeed.
Then i did the cronbach test. 28 questions. 11 persons.
So it means (k/(k-1)) = 28/27 = 1,04. Isn’t it ?
Then i should calculate the variance for each question, one by one
(so it means if i get only 1 for all the answer, variance will be 0). Then i add them.

And then , this is where i have difficulties : i should calculate the variance between the total of the the 28 questions ? Or variance between each person ?

If i do it between each person i get -0,77
If i do it between the questions i get 0,46
And if i fake to have almost always good answer, i get 1,03 for example. Is it normal ?

Also I tried to do it question per question to find out which of the questions put the level so down. Is there a special formula for this ? Or should i apply it 28 times without one item.

• Charles says:

Lilla,

I wasn’t able to follow all the steps you listed, but in any case you have the following options for computing Cronbach’s alpha

1. Use any of the techniques described on the referenced webpage
2. View the Excel worksheets that carry out the various techniques described on the referenced webpage. You can download these worksheets for free from the webpage Examples Workbooks.
3. Use the Real Statistics CRONALPHA function or the Cronbach’s Alpha option on the Real Statistics Reliability data analysis tool.

Charles

95. Dani says:

Hi, I have problem with cronbach’s alpha. I only have 3 questions for one variable, in which the alpha is only 0.372. However, when I deleted one question, it is still low as 0.4978. Is it still possible to use the data for regression, while the alpha is only 0.4978? thanks

• Charles says:

Dani,
I would think that you could still use regression in this case. But you should make sure that the model has a good fit.
Charles

96. Manasi says:

Hi
My questionnaire was administered four times with 15 subjects on two days. How do I calculate cronbachs’ alpha? Should I take average of all four times for day 1 and day 2 and then average for the two days? Which values should I consider?

• Charles says:

When you say that your “questionnaire was administered four times with 15 subjects on two days” does this mean
(1) that in total you have 15 subjects who answered the questionnaire, each subject answering the questionnaire one time, or
(2) as in (1) except that you had 15 subjects four times, and so you had 60 subjects in total answering the questionnaire, or
(3) 15 subjects answered the same questionnaire four times?

If the situation is (1) or (2), you can simply apply Cronbach’s alpha on all 15 (or 60) subjects, ignoring the day that they answered the questionnaire (unless you think that for some reason this is relevant).

If the situation is (3), then you should probably report four different Cronbach’s alpha values, one for each time the 15 subjects answered the questionnaire. I might give a different answer if I knew why they needed to answer the same questionnaire four times in two days.

Charles

• Manasi says:

They answered the same questionnaire four times on each of the two days. this was done to see any significant difference in subjective responses before and after a rest period.
so we had following experimental design:
day 1 (1) day 1 (2) day 1 (3) day 1 (4)
s1-s15 s1-s15 s1-s15 s1-s15

day 2 (1) day 2 (2) day 3 (3) day 4 (4)
s1-s15 s1-s15 s1-s15 s1-s15

• Charles says:

You can use repeated measures ANOVA to determine whether there is a significant difference between the test results.

You can use Cronbach’s alpha to measure the reliability of the test, but in this case, I would calculate four separate Cronbach alphas.

Charles

97. Lubna Alharbi says:

Hello

require your assistance to calculate the Cronbach’s alpha for my questionnaire
it consists 4 Section and in each section there are a number of questions and the last section two open questions
it is measured as well
when I calculate the number of items
how I do it
I count the number of question or what
if you have an email I want to send the result for you please
regards

• Charles says:

Charles

98. Christian says:

Dear Charles,
first of all: Thanks for this awesome website. It already helped a lot!

My question: I already made all the calculations to get to the point of Figure 3 (Example 2). Now I need to figure out, which of my items can be omitted. You wrote that the one with the lowest alpha value affects the result the most. So it’s better to remove items with the highest alpha values? In the next step the omission of one item changes the alpha value of the others, right? Does this influence order?

Thanks a lot!
Christian

• Charles says:

Dear Christian,

Which item to remove really depends on what your objective is. If you objective is to increase reliability then you would want to remove the one with the lowest alpha value.

Removal of one item will change the values of the others. I don’t know how it impacts the order, but I suspect that the order can change.

Charles

• Christian says:

Dear Charles,
As I already have about 20 items and due to this a high alpha (~0,95) I want to remove several items.
That’s why I’m wondering, which items would be best to keep and which items I can remove from my list.

Christian

• Christian says:

Excuse me Charles,
just to get things clear:
Would you, in my case, recommend to delete the items with the lowest alphas until I only have a few items (say about 5) left, but still have an acceptable overall alpha for the scale?

Christian

• Charles says:

Christian,
It is hard for me to say since I don’t know your objective. If you would prefer an example with fewer questions, then I would probably choose the course of action that you have described, especially since your Cronbach’s Alpha is 95% (which is quite high), and so it seems that all the questions are pretty much testing the same thing.
Charles

99. Ben says:

Hi,
Can i use cronbachs alpha for satisfaction questions on a scale 1 to 100, with 100 being the most satisfied?

• Charles says:

Ben,
Yes, you can use Cronbach’s alpha in this cazse.
Charles

100. Dan says:

Hi,

I created and performed an attitudinal survey regarding how people believe that are being treated in a particular company. I am looking at factors correlated with and/or those that predict work-life balance. I have extracted a number of factors from the literature which are associated with work life satisfaction, and I have adapted questions accordingly. I have administered the survey and now am trying to make sure it is a reliable and valid indicator. I used your (awesome) tool and have a high Cronbach alpha (>.90). What type of test should I run for validity? It may be that I publish this, so I want to make sure I can at least comment on some psychometric properties. Is Cronbach enough and, if not, what would you recommend? I am not going for the most robust analysis in the world, just something that provides that this is a reasonably credible instrument. Thanks!

Dan

• Charles says:

Dan,
Here is a response to a similar question that I found on another site. I hope that you find it useful.
Charles

Julia B. Smith · 41.59 · 90.86 · Oakland University
If this is too basic, I apologize, but…

Reliability examines whether you are getting consistent information. Validity examines whether the information you are getting measures what you think it measures. My basic example is a scale – I can get on the scale 15 times in a row, get the same information each time, and that is reliable. But if I want to use the scale to tell me how tall I am, that is not valid.

Consequently, using a statistical tool to examine validity is entirely anchored in what it is you think is being measured, and what other source of information you have to compare it to. If I have a survey that I think measures depression, I am going to want to compare the results on that survey to results on an instrument that is already known to measure depression. That statistical analysis would require correlation, but the basis of the validity argument rests on the other source of information (and what is known about it).

Recall that there are several types of validity (content validity, construct validity, outcome validity, etc.), and each requires a different kind of examination. I have attached an article that does a nice job of discussing the problem of testing validity applied to student evaluation of college instructors.

Onwuegbuzie_et_al2007.pdf

101. Gabe says:

Dear Charles,

Thanks for the crystal clear explanation, it was very helpful.

I have one question that I’ve been struggling with lately.

Suppose I have 6 items (i.e. questions), that 100 participants (i.e. cases) answered on a continuous scrolling bar yielding valued between -350 and 350. I’d like to know whether these 6 items are “internally consistent” so I proceed to computing Chronbach’s alpha. However, should I, or should I not mean-center the 6 responses of each subject before computing the alpha?

The reason of my question is this: I noticed that subjects have very consistent spatial biases in the way the use my scale, so I tried mean-centering the scores by subject. As a result, the magnitude of alpha was strongly decreased.

This seems to derive from the fact that mean-centering by subject decreases the “total variance” component of the alpha formula, more than it does the (sum of the) within-item variance. However, intuitively, I don’t understand why differences in the way subjects use the scale (independently of what items the scale represent) should affect a measure of its internal reliability.

Surely, I’m getting something wrong, though I don’t quite know what.
Any ideas?

Thanks!
gabe

• Charles says:

Gabe,
It depends on what you mean by “mean centering”. If you calculate the mean for each question and then for each participant and each question you subtract the mean for that question from the score of that participant for that question, Cronbach’s alpha will be the same.
Charles

102. Pallavi says:

Thank you for this Charles.
Can I please ask you to clarify my problem with a reliability test that I carried out pre and post survey. The cronbach’s alpha values were in the range of 0.73 to 0.90 for the pilot tests on 10 responses, deeming the scale to be reliable. However, when I ran a reliability test post survey with 82 responses, the cronbach’s alpha’s ranged from 0.57 to 0.83. The cronbach alpha values had decreased for some of the constructs and since as per the literature, constructs with values below 0.70 are said to have poor reliability, I am not sure what kind of inference I can make out of this situation for my research. Also , at this stage I cannot delete any items off the questionnaire because it is post survey. Can you please suggest an explanation for the constructs with lower alpha values and how I can defend their reliability for my research.

• Charles says:

Unfortunately, a pilot test of 10 responses is not so much, and so it is entirely possible that the actual Cronbach’s alpha is different from what you found; in fact if you set the significance level to 95% (alpha = .05), you should assume that one out of 20 times you could get surprised in this way.

The .70 value is only a guideline. I have read others saying that .60 is also acceptable. This sort of problem happens. The only thing that I can suggest is to report your findings as they are. Clearly some of the alpha values are higher than .70, which is good. For the ones that are much lower, you can explain what you might do in the future differently.

Charles

• Pallavi says:

Thank you for this Charles.

103. Kim says:

Help pls! We have rows of necessities such as food, etc. and column of value like very important, important, etc. the total is always 50. And we have computed the alpha which resulted to -2.something. What does it interpret?

• Kim says:

50 because 50 is our total respondents. This is a research our adviser told us to use cronbach but we dont know how to interpret it on our study. Our study is about minimum wage earners

• Charles says:

Kim,
I am sorry, but I don’t completely understand the situation that you are describing. Are you saying that the alpha value is a negative value less than -2? This is a very unlikely result (sic).
Charles

104. Pree says:

Hi,
For my thesis I have made two sections first is a multiple choice questionnaire and second is a 5 point likert scale. May I use split half method for the questionnaire and cronbach alpha for the rating scale? Please help.

• Charles says:

You can use Cronbach’s alpha for the Likert scale. You can use either Cronbach’s alpha or split half for multiple choice questions.
Charles

105. Kelly says:

Hi there,
I have a very basic question. I am doing exploratory research with 500+ participants in predicting risk and thriving behaviours. My problem is that some of my outcome variables have only two items, thus my Cronbach alphas are always .50-.65 range. I’ve been reading that it is not even acceptable to run alpha analysis when you only have two items. Any thoughts for or against this practice?

• Charles says:

There really isn’t much point in running Cronbach’s alpha with only two items, but you can calculate a result. Although I haven’t really thought it through, you might try using Cohen’s kappa to see whether there is agreement among the participants between the two items.
Charles

• Kelly says:

The variables are all continuous , and as I understand Cohen’s kappa is for inter-rater agreement on categorical variables.

• Charles says:

Good point.
Charles

106. applefabela says:

Can’t you help me about kuder richard formula 20
I need exact explenation about kuder richard formula 20
thanks.

• Charles says:

Sorry, but I don’t have anything else to add to what I responded earlier.
Charles

107. Tiffany says:

Hi Charles , I have a question here…

I am doing single subject. Questionnaire (Scale 1- 4) was administered 15 times with 3 subjects on 15 days which meant
1. 5 time baseline
2. 5 time intervention
3. 5 time withdrawn
My question here is how do I calculate cronbachs’ alpha with 15 time different phase?

• Charles says:

Tiffany,
You would typically run Cronbach’s alpha multiple times, once per each of the time periods. This is of course impossible if you only have one subject (although you also say that you have three subjects).
Charles

108. Marc says:

Dear Sir,
Thanks for the further explanations. What if every student answered every question correctly? That’ll result in 11 for all cells M4-M15, correct? And therefore, the variance in the totals would be 0 (cell B21). How would you interpret such a result with respect to the alpha, please?
Thank you,
Marc

• Charles says:

Marc,
If everyone answers the question correctly, in some sense the reliability would be perfect, i.e. 1, but not particularly interesting. For many of the reliability measurements, the mathematical result in extreme situation, such as this one, is counter-intuitive or not very helpful. Often because the variance is zero.
Charles

• Marc says:

Charles,
Thank you very much indeed. That really helps my discussion and is a good contra argument
Marc

109. Maria says:

First of all, you are doing a really great job here. Thank you very much.

My question is: Can someone use Cronbach’s alpha in order to come up with conclusions about the reliability of a questionnare that includes only open-ended questions? These open-ended questions are supposed to elicit critical thinking skills from the respondents and they are coded per skill as “insufficient”, “low”, “middle” and “high”.

• Charles says:

Maria,
You can use Cronbach’s alpha as long as you have an objective way to code the responses as “insufficient”, “low”, “middle” and “high”, and you can assign numeric values to these responses (e.g. as 0, 1, 2, 3).
Charles

• Maria says:

110. Maria says:

1. If someone has a pre-post design with 60 students and wants to compare the significance of the pre-post differences (per critical thinking skill let’s say), why would they choose to do the comparison by performing z-tests with students’ percentages per skill before and after the intervention? Couldn’t they have just estimated the pre/post-means and run a t-test or a non parametric equivalent?

2. If they already had their z-tests for comparing separately whether the number (percentages) of students at each level of each skill has increased or decreased significantly, why would they continue with contigency tables and chi-square for checking whether students transition from skill-level to skill-level (low…high..etc) for each skill separeately, is significant or not? I mean do you think that this info really adds to their argument about the efficacy of their intervention regarding the target-skills?

Thank you very much.

• Charles says:

Maria,

1. If you are trying to compare before and after data, the usual approach is to use a paired t-test of a paired Wilcoxon signed ranks test. Both are described on the website.

2. I don’t completely understand this question.

Charles

• Maria says:

Thank you very much, Charles.

Let me clarify my 2nd question: if someone does find a significant gain in the learning outcomes of their interst by comparing pre-post data, is there actually a reason for them to search with chi-square whether the transition of students from “low to middle” or from “middle to high” level responses is significant too? Do you think that this info can really strengthen the argument about the efficacy of the intervention which was already shown, or it is practically useless?

• Charles says:

Maria,
I don’t know what chi-square test you are referring to in the question “is there actually a reason for them to search with chi-square whether the transition of students from “low to middle” or from “middle to high” level responses is significant too?”
Charles

111. Pam says:

Hi!

I would like to know if I can conduct cronbachs alpha on my own questionnaire?
For example, my questionnaire would be like this:

2.Internet marketing creates brand awareness.

Then this would be in the form of a likert scale. 5-strongly agree then 1-strongly disagree.

Thanks for the help!

• Charles says:

Pam,
Sure, you can use Cronbach’s alpha to test such things. It is important that if you are testing multiple concepts that you create a Cronbach’s alpha score for each concept based on the questions that relate to that concept.
Charles

• Pam says:

For example,

there would be concepts about advertising, personal selling, sales promotion, and public relations. But this would be in just one questionnaire. Should i conduct cronbachs alpha separately for each concept?

Thanks!

• Charles says:

Yes, you should conduct a separate Cronbach’s alpha for each concept.
Charles

112. Marilyn says:

I designed a 7th grade science test with 30 multiple choice items as part of an experimental investigation. Each question has four alternatives. Part I consists of 10 questions about the scientific method; Part II consists of 15 questions on the structure and organization of organisms, and; Part III consists of 5 questions about taxonomy. My question is: When I calculate reliability, should I calculate three separate Cronbach alphas (one for each part), or only one overall Cronbach’s alpha for the entire test? Also, is using the 0/1 coding (incorrect/correct) the correct procedure?

I appreciate your input and guidance.

• Charles says:

Marilyn,
Since it looks like you are testing three different concepts, you should calculate three separate Cronbach alphas. The 0/1 coding (incorrect/correct) is correct.
Charles

113. Tobias says:

Hi Charles,

I’m using a likert scale 1 to 5, 15 questions as feedback about facebook and moodle. Same set of questions apply to both facebook and moodle given to the same students (21 students). What is the best and proper approach? Seems like I cannot use the 0/1 coding. Please advice.

• Charles says:

Depending on what you are measuring, you might need to compute two Cronbach’s alphas, one for moodle and the other for facebook. You can use the Likert scale as input to Cronbach’s alpha.
Charles

• Tobias says:

Hi Charles,

If the response is 1/0 the formula is …=(k/(k-1)…

if the response is 1, 2, 3, 4, 5…what would be the formula?

• Charles says:

Tobias,
Sorry, but I don’t know which formula you are referring to. The formula that I use for Cronbach’s alpha is the same for dichotomous values as for Likert values.
Charles

114. Kate says:

Hi Charles,

I am looking for some guidance – – I have administered a pre-/post- survey, using a 5 point likert scale. Response prediction was a one-tailed shift, and this was true. Sample size was only 32, and most respondents shifted from a ‘3’ to a ‘2’ or ‘1’, so not a huge shift, but one that was pretty uniform. There were about 6 that did not shift at all. Although the shift was evident, my paired sample ttest returns a very high p-value, indicating no statistical significance. I am wondering if I should use a different analysis approach?? little out of my depth…

• Charles says:

Kate,
Can you send me the data so that I can understand the situation better? See Contact Us for my email address.
Charles

115. Pat says:

Hi Charles,

I am questioning if I did my Cronbach’s Alpha test correct. I have one cell with a score of -7.113. The rest of the scores fall between 2.25 and 0.22.

Should/can there be negative numbers? And should I be concerned about my one cell that has a score of 7?

I realize this may be an impossible question for you to answer without my work (most questions are a Likert scale with a range of 1 – 7).

• Charles says:

Pat,
Yes, I would need to see your data to understand your question. You can send me an Excel file to my email address, as shown on Contact Us.
Charles

116. Mayza says:

Hi charles,
im doing an experiment about voice perception.. i use likert scale in in 5 question. There are five voices. The questions are do u find the voice trusthworthy dominant aggressive etc. Can this method help me solve this?pls. A student from philippines

• Charles says:

It depends on what you mean by “Can this method help me solve this?”. What is it that you want to solve?
You can certainly use Cronbach’s alpha with a Likert scale.
Charles

117. Richard Batamwita M says:

I am new to this site/blog but it is exciting.
I am involved in HIV research at operation level. So at time we wonder how to measure internal consistence. For example we have this question:
In the last 12 months, have you experienced any of the following feelings because you are living with or affected by HIV? (Tick as many boxes as apply ) (read out)

1. I feel ashamed
2. I feel guilty
3. I blame others
4. I blame my self
5. I have low self esteem
6. I feel i should be punished etc.

All these are items that measure what is termed as Internal HIV stigma.
Kindly help guide me how to measure the internal consistency. This will guide whether I should drop some items.

• Charles says:

Essentially you have 6 questions with a response of ticked or not ticked. You can assign the code 1 for the ticked items and 0 for non ticked items. This is the coding assuming that all the ticked items represent Internal HIV stigma; if some of the items are reverse coded (i.e. not ticked represents Internal HIV stigma) then simply interchange the roles of 0 and 1 for those items. You then calculate Cronbach’s alpha as described on the referenced webpage.
Charles

118. Sarthak says:

Hi Charles,

I want to know the minimum sample size required to safely calculate the test reliability (cronbach alpha) in a 4 choice mcq test consisting of 3 sections with 20 questions in each section. Each section measures different skills.

Also, kindly explain the method so I can determine the same for different variants of the test.

Regards

119. menaka says:

I would like to know the answer for this question. Anyone who knows answer this.
Question: If you are provided with questionnaire consisting of 20 questions and you have the response in the form of a likert scale value(1 to 5) obtained form 25 respondents, then how will you find the factor loadings value?

• Charles says:

If you are looking for factor loading values, you are probably referring to Factor Analysis, See the following webpage:
Factor Analysis
Charles

120. Shri says:

I have two groups of questions; First is Functional form of question (Positive side) , for example: If a door is closing how do you feel. One answer be selected by the user 1. I like 2. It must be that way, 3. I am Neutral, 4. I can live that way, 5. I dislike it that way
Second question: Dysfunctional (negative): If a door is not closing how do you feel. The answer be selected by the user 1. I like 2. It must be that way, 3. I am Neutral, 4. I can live that way, 5. I dislike it that way. How to can I certainly use Cronbach’s alpha

• Charles says:

Shri,
If some of the questions reverse the scale then you should reverse the coding (i.e. 1 becomes 5, 2 becomes 4, 4 becomes 2 and 5 becomes 1), but I can’t tell from your example whether this is really a case of reverse coding or not.
Charles

121. Flasha says:

Hello,
I know that if you have several dimensions, you calculate Cronbach alpha for each dimension. But can you calculate it for the whole test? In case you want to know reliability for the test as whole. Or do you rather conclude on the whole reliability based on reliability of each dimension?
Thank you very much

• Charles says:

If there are several dimensions you should use the Cronbach’s alpha for each dimension. Cronbach’s for the whole test won’t be that meaningful. If you need one value, you could use the smallest of the Cronbach’s alpha values, but it is better to simply use Cronbach’s for each dimension.
Charles

122. Alina says:

Hello Charles

could you explain to me how I create a table with 5 separately calculated alpha-coefficients in SPSS?

Thank you

• Charles says:

Sorry Alina, but I don’t use SPSS.
Charles

123. Nayers says:

I have spent all day reading psychometric testing books and this is the most helpful thing I’ve read on Cronbach’s alpha. Thank you so much – very clear.

124. Learner says:

Can we use Cronbach’s Alpha to see if there is an agreement in the ratings (of features of some products) of two groups (gender groups or age groups for example)? If yes, how much sample size is enough for 6 features (rating 1 to 5).

• Charles says:

Learner,
Cronbach’s alpha is not used for this purpose. To determine whether there is agreement in rating, you could use Cohen’s kappa, Fleiss’s kappa, ICC, Kendall’s W, etc., depending on the specifics of what you are trying to do. I suggest that you look at the website for more details about each of these approaches and see which one best fits with your needs. See the webpage
Reliability
Charles

• Learner says:

Many thanks Professor. Earlier I found use of kappa coefficient and I’ve tried different measures like Cohen’s kappa, Fleiss’s kappa and Krippendorff’s Alpha, Kendall’s tau etc. using R, all gave me similar results regarding agreement in the ratings (of features of some products) of two groups (gender groups or age groups for example).
But I was wondering, what is the fundamental difference (difference between Cohen’s kappa, Fleiss’s kappa is clear to me). How to choose between these coefficient?
I found your way of explaining things is the best.

• Charles says:

Learner,
A key difference relates to the type of input data. E.g. Cohen’s kappa supports two raters with categorical ratings, Fleiss’s kappa supports two or more raters with categorical ratings, Weighted kappa supports two raters with ordered ratings, ICC supports any number of raters with interval/continuous ratings.
Charles

• Learner says:

Thanks a ton Professor. So simple explanation!!
What I could understood is that ICC is used to measure internal consistency of the raters (within each group) and the measures mentioned by you (Cohen’s kappa, Fleiss’s kappa and weighted kappa) measures agreement between
two or more group of raters. Please correct, if I am wrong.

• Charles says:

Learner,
Sorry, but I don’t understand what you wrote.
Charles

125. Abimbola says:

pls am doing my project in which I want how to analysis it am having 20 questionnaire and it contains 17 questions each and respondent has to choose from strongly Agree or Agree or strongly disagree or disagree in their responses. how I calculate it using alpha

• Charles says:

Abimbola,
You can calculate Cronbach’s alpha with Likert scale items as shown in Example 4 of the referenced webpage. Alternatively you can use the Real Statistics capabilities described on that webpage.
Charles

Please I want to know if i can check the reliability of a “writing test” using this technique or it is just used for questionnaires!!!

• Charles says:

How will you score the writing test?
Charles

127. Zaizan says:

May I ask, can we run cronbach alpha test before having data in hand (e.g. before pilot study)?

• Charles says:

You can run Cronbach’s alpha using the data from a pilot study.
Charles

128. Sardar Ali says:

I need to know that the Cronbach’s Alpha Test is applied only on the questions of independent variables??? or it include questions both dependent and independent variables?Please reply as soon as possible.

• Charles says:

Sardar,
You can perform Cronbach’s alpha on any data that you like. Whether something is an independent variable or a dependent variable often depends on the context.
The real question is why do you want or need to perform Cronbach’s alpha at all?
Charles

129. Angela says:

Dear Charles,

Thanks for this great explanation. I was actually already familiar with the contant, but I used it to again check my data, because I have a problem I can’t seem to solve. My alpha keeps being 1,01 (which is theoretically impossible, right?). I know it’s very difficult to give advice if you don’t see my dataset and used formulas, but I’ll give it a try: do you have any advice for me on which things to check? I already tried calculating things manually, but I keep coming up with the same number.
(My dataset looks exactly like figure 1 and I used the formulas from figure 2.)

• Angela says:

Btw, my items are not dichotome scored. They’re scored on a scale of 5.

• Charles says:

Angela,
Shouldn’t be a problem since Cronbach’s alpha works with Likert scales.
Charles

• Charles says:

Angela,
If you send me an Excel file with your data and calculations I will try to figure out why you are getting a value bigger than 1.
Charles

130. vahid says:

does Cronbach alpha can be used for YES/NO questions? If yes , please explain

• Charles says:

Vahid,
Yes, Cronbach’s alpha can be used with Yes/No questions. If these questions test someone’s knowledge, then code the question as 1 if the answer is correct and 0 if the answer is incorrect (irrespective of whether it is Yes or No).
Charles

131. Lily says:

Hi Charles,

Thank you so much for this wonderful explanation!
I did have one question, though.

I am doing a questionnaire about purchase intentions of genuine and counterfeit bags with a lot of logos or no logos. If a question had two pictorial choices with one showing preference for a bag with a lot of logos and the other with no logos (I hope this makes sense…), how would you code a question with these two answer choices? Would it be 0 and 1 or 1 and 2? or 1 and 7 (my other questions were 7-point Likert scales)? Would this even be eligible for a Cronbach’s Alpha test?

If you could help me out, that would be greatly appreciated.

Many thanks!
Lily

• Charles says:

Lily,
I believe that you will get the same value for Cronbach’s alpha whether you use a 0-1 coding, a 1-2 coding or a 1-7 coding.
Cronbach’s alpha can handle a 7-point Likert scale, although you will need to be careful about mixing questions from this scale with questions using a 0-1 or 1-2 scale.
Charles

132. RURU says:

Hi
I counted the total number of participation in 5 enrichment activities (piano, art, sport, etc) that are based on yes-no questions (took a lesson = yes, didn’t take that lesson = no). The score ranges from 0 to 5 with more than 50% for 0. Cohen’s alpha is really low like .40. To me, theoretically, it doesn’t seem to make to sense to run cohen’s alpha because internal consistency is not important (a student who takes a piano activity may not take a sport activity, but at the same time, the total number of activities show students’ degrees of engagement in those activities. Should I still run cohen’s alpha? I would really appreciate your advice.

• Charles says:

Hi,
I assume that you are referring to Cronbach’s alpha and not Cohen’s alpha.
You are not forced to run Cronbach’s alpha. If internal consistency is not important then you don’t need to use Cronbach’s alpha.
Charles

133. Pat says:

Hi Charles! What if my questionnaire is a 9-item quiz-type one and for every question, it corresponds to either of the three: easy, average, and difficult, the scoring of which are 1 for easy, 2 for average, and 3 for difficult? Is Cronbach’s alpha applicable to this type of questionnaire? If not, can you suggest other reliability test that I may use to know its validity? Thanks in advance!

• Charles says:

Pat,
You can use Cronbach’s alpha to measure reliability if for each question you use code 1 for the correct answer and 0 for the incorrect answer. I’m not sure how best to integrate this approach with easy, average, difficult. Also, kind in mind that Cronbach’s alpha is used measure reliability, not validity.
Charles

134. tahir says:

I have a construct consist of three items and Cronbach alpha is 0.564, how can I increase reliability coefficient cronbach alpha

• Charles says:

Tahir,
As described on the referenced webpage, first of all make sure that the Cronbach’s alpha value isn’t being reduced due to problems with reverse coding and/or multiple factors. Also check to see what happens if one of the questions is removed (as described on the referenced webpage). If removing one of the questions results in a much higher value for Cronbach’s alpha, then consider rewording or eliminating that question.
Charles

135. Emma says:

Hello, we are trying to measure the reliability of a pain scale, where the nurses valuate 5 different features of the newborns. The problem is that we have different nurses(around 15) that valuate 5 different features(it has to be valuated between 0 and 2) on about 15 newborns. It seems like 3 different variables, how do we write our data into the SPSS and calculate the Cronbach alpha of the whole scale? It would be clear if there was only 1 newborn

• Charles says:

Emma,
I don’t completely understand the scenario you are describing. If there are 5 different features, why are there only 3 variables?
Why have you decided to use Cronbach’s alpha? Are you trying to see whether the nurses agree in their evaluations?
Charles

136. Claire Pan says:

Dear Charlies:
I am working on a study where 224 participants opt for their preferred attitude to 15 questions regarding attitudes towards teacher questioning in class on a Likert Scale (strongly agree, agree….). How can I find the chronbach alpha for all the 15 questions?
Is this also the right measure for me to look at how two raters rated different teacher questions of transcripts of classroom conversations into certain question function to see how they agree on each function they assign to each teacher question?
Thanks l lot.

• Charles says:

Dear Claire,
You can calculate Cronbach’s Alpha for all 15 questions using the approach described for Example 4 on the referenced webpage.
To compare the ratings of two raters you shouldn’t use Cronbach’s alpha. The specific measurement to use depends on the type of rating that is employed. With two raters, likely candidates are Cohen’s kappa, Weighted kappa or ICC.
Charles

• Claire Pan says:

Dear Charles,
If the two raters rate by using numbers (1-14) to assign each teacher question a type of question functions in my study, and the purpose is just to make sure the function assigned to each question is reliable, which exact measure is the right one?
Thank you so much.

• Charles says:

Dear Claire,
If you are comparing the raters then you would use something like ICC or Weighted Kappa.
If you are checking the reliability of the questions, then you could use Cronbach’s alpha. With only two subjects (raters), you shouldn’t expect too much from this measurement.
Charles

137. Susanne says:

Good Evening-I am using an inventory that measures two factors: knowledge of cognition and regulation of cognition. There are 12 items, 6 of which measure knowledge of cognition and 6 which measure regulation of cognition. As long as I know which questions are measuring what factor, can I keep these in one inventory and separate by item number when it comes time to run the Alpha Chronbach? Thank you!

• Charles says:

Susanne,
Yes, but you need to calculate two separate Cronbach alphas, one for the 6 knowledge of cognition questions and another for the other 6 question.
Charles

138. nur hashida says:

hai i am nur hashida

which type of realiability suitable for testing the realibility of parameter estimation method? is it cronbach alpha suitable to use? Tq

• nur hashida says:

i am working with 267 simulated of data to estimate the drift and diffusion parameter for three types of one-dimensional linear stochastic differential equation models. we use three type of parameter estimation method and compare the reliability of method. Can you suggest suitable type of reliability to be used in our master research. Tq so much

• Charles says:

I understand that you have three different methods of estimating parameters. What do you mean by reliability in this case? Do you want to dtermine whether the three methods yield the same results?
Charles

• Susan says:

Dear Charles ,
Thank you so much for this great information. I would like to know if the calculated Cronbach’s Alpha was 1.000 what does it mean? Should I remove some of the questions?

Regards

• Charles says:

Susan,
The measurement indicates 100% reliability/consistency, which is a bit suspect. This indicates either that the questions are somewhat redundant or that the number of people who answered the questionnaire/exam is very small. Removing questions typically increases the value of Cronbach’s alpha (which is not possible in this case) not reduce it.
Charles

• Charles says:

Cronbach’s alpha is not used for parameter estimation.
In this case, you may be looking for “goodness of fit” – e.g. chi-square goodness of fit test. The specific test to use depends on which parameter you are referring to.
Charles

139. Ting says:

hi,
My thesis’ Cronbach alpha is below 0.700, how can I increase reliability coefficient cronbach alpha? i try to remove question or so on..it still under 0.700…what i can do to increase it?may i forward my data to seek you advice..thanks

Thank you

• Charles says:

Ting,
The usual approach to increasing Cronbach’s alpha is to change the wording of some questions before you give out your questionnaire to a large group of respondents.
Just because Cronbach’s alpha is less than .700 doesn’t make the questionnaire bad; some would use a cutoff of .600 anyway. If removing a question substantially increases Cronbach’s alpha then I might remove that question.
Charles

• Ting says:

Thanks, Mr. Charles

My Cronbach’s alpha is lower at 0.409, confuse whether this report can use or not…tq

• Charles says:

Ting,
This value is generally considered to be low. This doesn’t mean that the questionnaire is bad, just that there is some kind of internal inconsistency. The low Cronbach’s value may be caused by many things, including that it is measuring more than one thing — this is not necessarily a bad thing.
Charles

• Ting says:

Thanks, Mr. Charles

• Noma says:

Hello,
I also have the same problem, cronbach alpha value of my data is 0.44, how could it be increased? If i continue with the same data, will it be ok? Or what kind of problems i ll have in regression anaysis?
Thanks

• Charles says:

Noma,
As described on the referenced webpage, you should first make sure that the low value for Cronbach’s alpha isn’t due to one of the following:
1. questionnaire that is measuring more than one concept
2. reverse coding
If not, then you might want to explore the following corrective actions:
1. reword some questions
2. eliminate some questions
Cronbach’s Alpha measures internal consistency, but a low value is not necessary for many statistical tests.
Charles

140. Andrew says:

Hi Sir,
Please how can i get a simulated data for 42 variables with good chronbach alpha as well to satisfy average variance criteria >.7 or =.7.
Thank you Sir.

• Charles says:

Andrew,
This seems like a strange request. Why do you want to do this?
Charles

• Andrew says:

Hi,
For teaching and simulation

• Charles says:

Andrew,
I can probably come up with an example of the type you requested, but I can’t think of a quick way to do this.
Charles

• Andrew says:

Hi,
Alright, an example would be fine.
Thanks

• Charles says:

Andrew,
I just sent you an example. The example consists of a range B2:AO101 containing 0’s and 1’s. The formula for each cell in the first column is =RANDBETWEEN(0,1). The formula in cell C2 (the first cell in the second column) is =IF(RAND()>.2,B2,1-B2). I copied this formula into all the other cells in the range. The result is Cronbach’s alpha of .725515.
I then copied the whole range and pasted values so that the cell values wouldn’t change.
I can’t guarantee that this approach will work in general, but it seemed to make some sense when I did it.
Charles

141. Abbass says:

Hello Sir

I’m thinking of computing Cronbach’s alpha to test the reliability of the multiple choice tests that i prepare for my students’ assessments in the same way you presented in Example 1 ( with the codes: 1 = correct answer and 0 = incorrect answer)
but i was wondering if there is a way to calculate Cronbach’s alpha if i can provide the total number of students who got the correct answer for each question only

best regards

• Charles says:

Abbas,
No, because this wouldn’t capture the variability.
Charles

142. CHRISTY says:

Dear Charles,
I am working with 251 subjects using 32 questions (including 7 questions on the demographic characteristics). The questionnaire is more of rating scale style (agree, strongly agree, disagree and strongly disagree). please, I need assistance on how to calculate the reliabilty (formula) using Half split method

Best Regards.

Christy.

• Charles says:

Christy,
You probably don’t want to include the questions regarding demographic characteristics in the calculation since they are of a completely different nature from the other questions. The referenced webpage shows how to calculate Cronbach’s alpha for questions using Likert scales. Here, for example, you can use the coding 4 = strongly agree, 3 = agree, 2 = disagree and 1 = strongly disagree. Even better is to use the scale 5 = strongly agree, 4 = agree, 3 = neutral, 2 = disagree and 1 = strongly disagree.
You can also perform the split half method using this coding as described on the webpage
Split Half Method
Charles

143. akshini says:

hello sir,
actually i got 0.875 form the cronbach alpha
i want to know if its acceptable

• Charles says:

Hello Akshini,
Generally, this would be considered to be acceptable.
Charles

144. Giorgos says:

Hello. I am using Cronbach’s Alpha in a psychometric study. What kind of figure should i use to illustrate alpha? Maybe a covariance table or covariance 3d figure ? Thanks

• Charles says:

Giorgos,
Sorry, but I don’t understand what you mean by “illustrate alpha”. Generally, alpha is set to 0.05.
Charles

145. Abuhay Misikir says:

One of my dimensions of a scale has 2 items which yielded an internal consistency of .42. How could I solve such a problem? Can I report the inter-item correlation which is .36?

• Charles says:

Sorry, but I don’t understand your question.
Charles

146. Richard Cockell says:

Dear Charles
On your Example 1 – how do I calculate the EVar in cell M17? Can you please point me in the right direction as to how excel can achieve this?
Regards Richard

• Charles says:

Richard,
As alluded to in Figure 2, cell M17 contains the formula =SUM(B17:L17).
Charles

147. Sanjay says:

Hi Charles,
Thanks for excellent answers that clarify the concepts. My question : “Is it ok to assign 1 for strongly agree and 5- for strongly disagree in a 5-point likert scale? Will the Cronbach alpha value differ if I assign 5-strongly agree and 1- strongly disagree ? Also, for 100 nos. responses to say 36 question parameters, will the cronbach alpha value remain same for either of above mentioned scale designs? Is it sufficient to ensure that cronbach alpha is more than 0.7 to ensure that the questionnaire is both consistent/reliable and construct-valid?”

• Charles says:

Sanjay,
1. I don’t think the value of Cronbach’s alpha will differ, but it is easy enough for you to try it both ways and compare the results.
2. More than 0.7 is often considered to be sufficient to consider the questionnaire to be consistent/reliable. This does not mean that the questionnaire is valid. The threshold of 0.7 is not universally agreed upon.
Charles

• Sanjay says:

Thanks a lot Charles! I have 27 item questionnaire, 5 point likert, all questions in positive mode (e.g eating eggs will strengthen bones. …1, 2,3,4,5), do you think If I take 100 responses on this set will suffice to find the consistency/reliability?

148. Reynel says:

Hi Charles,

Thank you for this. But I have a question, I am testing the reliability of my survey questionnaire, the first 2 parts uses likert scale on the scale of 1 to 5 (Strongly Disagree to Strongly Agree) and one additional question that’s answerable on the scale of 1 to 10 (if your familiar with NPS). Is the process still the same?

Thanks.

• Charles says:

Reynel,
You can calculate two separate Cronbach’s Alpha values, especially if the two parts measure different concepts.If you want one value, perhaps you can map the 1 to 5 Likert values into 1 to 10 values (e.g. by doubling the value).
Charles

• Reynel says:

Got it Charles. Thanks.

My problem now is the 2nd and 3rd part which are single-item scale. Based on my reviews, I need to do a test-retest reliability as SPSS cannot cater these single-item questions.

149. Tanish Mathur says:

Dear Charles,
Thanks for such a good explanation of Cronbach’s coefficient alpha. Request your assistance in resolving my query. As part of my research paper I have developed a questionnaire & this questionnaire was responded by 100 participants. There are around 10 close ended questions where I have asked if a particular factor has influenced participant’s activity. Response is in the form of ‘Yes’ or ‘No’ which has been coded with 1=Yes & 2=No. Kindly have a look at the sample Q –

Q. Which of the following factors influence your xxxxx…activity?
Factor 1 Yes/No
Factor 2 Yes/No
Factor 3 Yes/No
Factor 4 Yes/No

All these are independent factors & I have received response as Yes or No for these factors from 100 participants.

My problem is when I am running Cronbach alpha on this I am getting negative alpha.
Request your assistance on below mentioned queries –
Q. – Can I use Cronbach alpha on such data? Primarily I want to check consistency & reliability of my response data?
Q. If Cronbach alpha is not correct measure which one I can use for such a data?

Tanish

• Charles says:

Tanish,
Getting a low value (and a negative value is clearly a low value) for Cronbach’s Alpha may indicate that the reliability/consistency of your questionnaire is low, but it also can mean that you are testing multiple concepts. Cronbach’s Alpha is only meaningful when the questions are all testing the same concept. If not you need to partition your questionnaire based on the concepts being tested and calculate a separate Cronbach’s Alpha for each group of questions. You can use Factor Analysis to discover the underlying concepts being tested and to partition the questionnaire.
Charles

150. Tanish Mathur says:

Thanks for the explanation Charles !!!

151. prathyusha says:

hi
I am doing project on assessment of QOL. For measuring QOL Iam taking yes and no options for each question.Can I use cronbachs alpha score for my project.

• Charles says:

You can use Cronbach’s Alpha for yes/no questions. If there is a correct answer, you should use 1 for correct and 0 for incorrect.
Charles

• jyoti dave says:

Hello Charles, I would like to know whether the sample size affects the Cronbach’s alpha ? I had done a pilot survey for my research and i got alpha as.82 which is considered good, but later when I carried my final survey after my final data collection it reduced. forpilot survey my sample size was 80 and now the sample size is 320? I have used likert 5 point scale.

• Charles says:

Jyoti,
It is also possible that it would have increased. In any case, see the following webpage regarding sample size requirements:
Cronbach’s Alpha Continued
Charlesd

152. Shafaq says:

Hi Charles,

I’ve read over the remedy for negative cronbach’s alpha. However, for some reason I am still ending up with a negative alpha. I even reverse coded the relevant items but I still end up with a negative. My question is “Regarding project objectives; to what extent does your organisation consider the following project objectives important to the success of construction projects?” I used a five point Likert Scale. Each of the items or objectives in the questionnaire are relevant to one another and are testing importance of objective to success of a construction project. What can I do? It’s really throwing off the results for my dissertation

• Charles says:

Hi Shafaq,
One possible issue is that the questions are not measuring the same concept. If you are measuring different concepts, then you need to perform Cronbach’s Alpha separately on each group of questions which correspond to one of these concepts. In this case, you may have a very low value of Cronbach’s Alpha for the whole questionnaire, but perfectly acceptable values for each subgroup of questions.
Charles

153. Kay says:

Hi Charles,

I’ve conducted a pretest with only 13 responses that asks about categories like knowledge, behaviors, experience, etc. I have a 5-point Likert scale (strongly disagree to strongly agree) for each category, while each category only has about 5 to 7 statements. I grouped all of these together to compute Cronbach alpha, which yielded 0.725. However, if I calculated each category separately, I got a Cronbach alpha of -1.268 for one of the categories alone, for instance. Am I doing this right? Am I able to group all categories together or do I have to compute each category separately? If so, what does the negative mean?

Thanks,

Kay

• Charles says:

Kay,
This sounds strange. Cronbach’s alpha for all questions should be lower than for some subset of these questions. If you send me an Excel file with your data and calcualtions I will try to figure out what is going on. You can find my email address at Contact Us.
Charles

154. Hey there,
great tutorial. Not many good ones around otherwise.
I did stumble over the formulas depicted in Figure 4. For cell B42, which is supposed to be the variance of totals w/o Q1, you use a formula that calculated the variance of Q1.
Shouldn’t it be something like “=VARP(M4:M15) – B17”?
Anyway, keep up the great work.
Best,
Sang-Min

• Charles says:

Sang-Min,
The data in column B consists of the totals for all the questions minus the score for Q1, and so the formula in cell B42 doesn’t calculate the variance of Q1.
Also note that var(x-y) is not equal to var(x) – var(y).
Charles

155. Aslina Mohamed Yasin says:

Dear Charles,

Great information.
I have 3 questions:
1. May I know if there any difference of the Cronbach’s alpha using excel and using SPSS in terms of result?

2. If using observation questionnaire by assessor/researcher, can the Cronbach’s alpha is applied to check the reliability of the item?

3. If the questionnaire on knowledge with 4 scales likert (1 Strongly not agree to 4 Strongly agree) and with positive and negative items, should I apply a reverse coding?
(5 minus a recorded score?)

Thank you.

Lynn

• Charles says:

Lynn,
1. I don’t use SPSS and so I can’t comment about SPSS, although it is very likely that the results from SPSS are the same as those calculated using the Real Statistics Excel software.
2. Cronbach’s Alpha is used to check the reliability in terms of internal consistency of the whole questionnaire, not individual items. It can be used to test whether dropping any particular item dramatically increases internal consistency.
3.You don’t need to apply reverse coding as long as all the questions use the same coding (with the same meaning). In fact, you should get the same value for Cronbach’s alpha if you reverse code all the questions.
Charles

156. Lee says:

Hi, wanna ask. How should i do if my cronbach’s alpa value is 0.192? any solution?

• Charles says:

Lee,
As described on the referenced webpage, you should first make sure that the low value for Cronbach’s alpha isn’t due to one of the following:
1. questionnaire that is measuring more than one concept
2. reverse coding
If not, then you might want to explore the following corrective actions:
1. reword some questions
2. eliminate some questions
Charles

157. Imran Butt says:

I asked 05 questions with rating from 1-5. I entered 413 responses.
My Alpha is -0.245.
I used Example-2 and its individual question Alphas is as under:-
-0.41, -0.30, -0.17, -0.10, -0.07 and -0.18
What i should to do to set alpha .7?

• Charles says:

Imran,
Obviously, the values for Cronbach’s alpha are far from acceptable. How to address this is described on the referenced webpage. In particular by
1. Making sure that you are testing one concept only, and if not then you should create separate Cronbach alphas for questions that are associated with different concepts
2. Correcting for reverse coding
3. Rephrasing questions to eliminate ambiguity
Charles

158. Mayra says:

Hi,
Thanks for the information on this page. I´m new to the subject and have some rather basic questions to ask, hope it´s ok…

Which formula did you use to calculate the Var in Figure 1? It seems like there´re some different options on Excel and I´m not quite sure which one applies to my case. I tried using VARP (in row 17) but then it would be the same as the calculation done in B21, so might be wrong?

Did you use the formula SUM() to calculate the Total in Figure 1?

Our questionnaire has some empty rows (that were not filled out). Is it necessary to exclude empty rows?

Thank you.
Mayra

• Charles says:

Myra,
I used VARP (or VAR.P) for the variance in row 17 as well as in cell B21. You can use VAR (or VAR.S) instead, as long as you use this function in all the variance cells.
Yes, I used SUM(…) in cells M16 and M17.
Yes, you should exclude any row that contains one or more cells.
Charles

159. Arsalan says:

let suppose one construct have four dimensions, and all four dimensions reliability reported separately, and overall construct reliability is missing? so how we calculate construct reliability. Same is for R value? I face this problem while reporting data in meta analysis.

• Charles says:

Sorry, but I don’t understand your question.
Charles

160. Jelena says:

Hi Charles,

In example 4 you calculated Cronbach Alpha for whole survey, which I understand how to do it. But I don’t understand how to calculate alpha for each question in Excel (for example, Q1, Q2, Q3…). Please, help me understand it, I need that for my Master asap.

Thank you a lot!

• Charles says:

Jelena,
You calculate it exactly as for Cronbach’s alpha for the whole survey except that you delete one question from the survey. Nothing complicated.
Charles

161. syahril says:

hi charles..
i have question regarding Cronbach’s alpha.. in my pilot study, one construct revealed that the value was 0.385 but in real study showed that theCronbach’s alpha value was 0.745.. should i continue the instrument due to the value of Cronbach’s alpha was showed acceptable rate in real study.. tq in advance

• Charles says:

Syahril,
After getting such a low value (.385) in the pilot, you probably should have made some changes to your questionnaire, but if during the real study you are getting a reasonably high value (.745), it looks like your questionnaire has an acceptable level of consistency/reliability.
Charles

162. Anthony Cooling says:

Sir,

Thanks for your efforts! I have a question about missing data and Cronbach’s alpha. I was getting lowish Cronbach’s Alpha scores, around .5, on some scales I created with GSS data. I had converted the qualitative responses to the equivalent of a Likert type of numerical scale. But when I drop all the zeros (which I were the “not applicable,” and “no answer” responses) from my dataset, leaving them blank in the columns, I am getting scores about .7 when Real Stats w/Excel computes Cronbach’s Alpha. Is this an acceptable route to take with missing data?

• Charles says:

Anthony,
Any row with a empty cell is simply eliminated from the analysis (listwise deletion), which means that all subjects who had one or more N/A responses are dropped. If this is what you want then, the approach should be ok. I would be very cautious, however, if this results in eliminating a substantial percentage of the subjects (i.e. you need to understand why so many are making this response. If one question results in a very high number of N/A, it might be better to eliminate this question from the analysis.
Charles

• Anthony Cooling says:

Thank you. The responses that are removed are from subjects who were not asked the question. Off the 1700 or so subjects in each GSS, only 800 or so are asked the specific questions that I am using for my scales. When you download the GSS data from their website, you get ALL respondents, not just the ones who answered your subset.

163. Mar says:

Hello,
I’m writing a paper that elaborate the result of 36 questions, however my professor would like to eliminate most of them and only take 7 most reliable questions. Can I do that by: trying manually to delete one of the question that result in a higher Cornbach’s alpha ? thanks a lot

Regards
Mar

• Charles says:

That seems like a reasonable approach.
Charles

164. vivian says:

hi charles,
can u help mi validate a survey questionnaire?
i dont have the cronbachs s-alpha copy.

• Charles says:

Hi Vivian,
Charles

165. riya says:

can a tool have crohnbach alpha of 0.61 aand splithalf reliablity of of 0.74

• Charles says:

Riya,
I have not investigated this, but probably it is possible.
Charles

166. riya says:

can split half reliablity of a tool be greater than crohnbach’s alpha?

• Charles says:

Riya,
I have not investigated this, but probably it is possible.
Charles

167. VENKAT says:

Excellent! Charles, for your good job!

Could you plz. kindly explain how to find Factor Loading for each item in a questionnaire…

168. Siti Azreena says:

Hi,
My variances is all zero since all respondents for my pilot study answered 1 (I am using yes/no type answers). I have 5 respondents. How can I fix this? My alpha given this #DIV/0!

My questionnaire is more like a checklist (to check whether my prototype is designed accordingly or not).

• Charles says:

Siti,
There is nothing to fix; with all 1’s the variance will be 0 and therefore Cronbach’s alpha will be undefined. If you are happy with the checklist you don’t really need to perform Cronbach’s alpha on it; if not then all the answers being the same tells you there is a problem.
Charles

169. Yize says:

Dear Charles,

I have one problem which I need your support. I made one survey which has 6 factors, each factors I designed two items(questions), actually the designed questions I referred to a matured questionnaire but with adaptation for my research purpose. But I did test for my questionnaire (invited only two friends to participate the questionnaire), but unfortunately alpha value calculated for 5 factors was 0, and only one alpha value is about 0,8.
I really do not understand what is the problem?
1)Is it because tool less test participants?
2)Is it because only two questions for one factor?
3)Or is it because the questions of each factor are too similar?
For example, one question is “do you feel joyful at work?” and second one is “do you feel positive at work?” But actually these questions are used and tested by some other questionnaires. I really confused.
I calculated Alpha by SPSS software. But I will try to use your software to do it once more.

Best regards
Victor

• Charles says:

Victor,
You probably can’t expect too much if you only had two participants.
Using similar questions should increase the value of Cronbach’s alpha.
Charles

170. Is .096 acceptable or not?

• Charles says:

Wesley,
.096 is quite a low value for Cronbach’s alpha and would generally not be viewed as acceptable (unless you meant 0.96, which is just the opposite).
Charles

• Mona says:

I am getting an alpha of -1.6. I didn’t think that was possible. Any ideas on what errors I might have made? (I’ve checked it a few times now already). I used the calculation method in Excel that you describe in the beginning (not reliability stats features).

• Charles says:

Mona,
You can get negative results, but I can’t remember now whether such a high negative value is even possible.
In any case, without seeing your data and analysis, I can’t say for sure why you are getting such a result.
I suggest that you install the Real Statistics software and use the Reliability data analysis tool.
Charles

• Mona says:

ok, thanks. How does one interpret negative results?

• Charles says:

Mona,
A negative result indicates poor internal consistency. Potential causes for this are described on the referenced webpage.
Charles

171. Erik says:

Hi,

first of all thank you for the nice wrap up of Cronbachs Alpha, it did help me a lot! I used your way to calculate it in Excel for my Master Thesis.

However, while it did totally work fine for 3 scales, the fourth scale has an alpha of -6.5. I did rescale “negative” questions (e.g. -2 to 2 in case of “i don’t like..”).

Could you please help me out, which reasons are there for a negative alpha? Thanks a ton!

• Charles says:

Erik,
If you send me an Excel file with your data and calculations, I will try to figure out what has gone wrong.
Charles

172. Dr Pooja Singhania says:

Hi Charles,

Can I use Cronbach’s alpha test to test reliability of a tool wherein responses are simple
“low, moderate, high a” and not ranked on Likert scale

Thanks

Pooja

• Charles says:

Pooja,
Essentially this is a Likert ranking, e.g.: 1 = low, 2 = moderate, 3 = high
Charles

173. Rin says:

Hi ! What if I have 2 questionnaires? Should, I’ll compare the Cronbach’s Alpha of both? And is the Cronbach’s Alpha is the percent of the total number of people?

Is the variance under the questions the percent of the people?

• Charles says:

Rin,
You should create two separate Cronbach’s alphas. You don’t need to compare these alphas to each other.
Alpha is not a percentage of the number of people nor is the variance.
Charles

174. Jamuna says:

Hi…so say if i have a 5 likert scale assessment for 15 questions, i would need atleast 70 to 80 repondents for cronbach 0.70?

• Charles says:

Jamuna,
How did you calculate this? I don’t see how you can guarantee a Cronbach’s alpha of .70.
Charles

175. Med benaou says:

I got these results.

Reliability Statistics
Cronbach’s Alpha N of Items
.420 25
What do you think?

• Charles says:

That is a pretty low value for Cronbach’s alpha.
Charles

• Med benaou says:

I’ve deleted 8 items and i ve got 0.703.
Is this acceptable? and is it ok to delete some items? thanks in advance.

• Charles says:

Yes, it is ok to delete these items, but you need to decide why deleting these items increased Cronbach’s alpha.
It is possible that some of these items were poorly worded or used reverse coding (as explained on the referenced webpage), but it is also possible that these items were on a different topic (or more than one other topic). In fact, it would be interesting to calculate Cronbach’s alpha just on the 8 items that you removed.
Charles

• Med benaou says:

That’s what i got

Reliability Statistics
Cronbach’s Alphaa
-.143
N of Items
8
??

176. sravya says:

while doing cronbach alpha test for reliability,do questions regarding to all factors can be tested in one test?

• Charles says:

You should calculate separate Cronbach alphas for each factor. Obviously you can calculate one value, but it won’t provide a good measurement of the questions.
Charles

177. Romain says:

Hi Charles,

I’ve got an issue with my Cronbach’s Alpha which is negative !!
I do not know where is the problem as it can’t be a calculation error because I did it with SPSS… If you have any idea keep me informed

Thanks

• Charles says:

Romain,
It is entirely possible for Cronbach’s alpha to be negative. This shows very poor interval consistency.
Charles

178. Ripudaman says:

Hi Charles, Firstly I would really like to thank you for responses above as they are of great help for beginners.
Now my query. I have two scales of 30 statements​ each with FOUR constrcts in first scale and only one constrct in second sacle. Do I need to calculate cronbach alpha value for each constrct. What should I do with negative statement s in each scale

• Charles says:

Ripuhaman,
Sorry, but I don’t understand what you mean by “constricts”. Perhaps by four constricts you mean a Likert scale of form 1,2,3,4, but in this case I don’t know what you mean by “only one constrict”.
Also, if by “negative statements” you mean “reverse coding”, then this is explained on the referenced webpage.
Charles

• Ripudaman says:

By constructs I mean factors which are further explained in the likert scale by various statements ( items).

• Charles says:

Ripudaman,
You need to calculate a separate Cronbach’s alpha for each construct.
Charles

• Ripudaman says:

Hi Charles,
Thanks for the reply. Now I have calculated the alpha value . Both ways separately for each constrct as well as for complex scale values are .90 for scale n for each constrct it is .76,.70,.68,.61 respectively . Are these values ok and acceptable. Should I go by the scale . ? Plz suggest what is to be done.

• Charles says:

Ripudaman,
There is no agreed upon criteria for acceptable values of Cronbach’s alpha. Some would say that a value higher than .7 is acceptable; some would accept slightly lower values.
I don’t know what you mean by “Should I go by the scale?”
Charles

179. Naz says:

Hello Charles, I have a construct of 5 items in which one item is negatively worded. I recoded the negative item. However when i run my reliability analysis thru spss, I got the Cronbach Alpha of .275 after I reverse the negative score. If I run all 5 items without the reverse score, I got Cronbach Alpha of .604. What should I do?

• Charles says:

Naz,
If you recoded the negative item properly, then you should accept .275 as the correct value for Cronbach’s alpha.
Charles

180. B Brown says:

Thanks for this; very helpful. I have calculated alpha using the ANOVA w/o replication model but I need help understanding your equation alpha = 1 – (MSe / MSb). What does MSrows (MSb) represent? I understand that MSe is the mean squared error for the sample? (Sorry for the novice question.)

181. RAKTIM DASGUPTA says:

I want to quantify vendor quality rating by using this cronbachs alpha method considering several parameters on quality delivery price services on likert scale.is this method is effective to calculate the vendor is reliable or not?

• Charles says:

I don’t know what you mean by vendor quality, but I don-t see how Cronbach’s alpha can be used to quantify vendor quality based on how I would define the term.
Charles

182. Sophia says:

Hi Charles,
I have a questions, I have a survey with likert-scale (12 questions for one construct) with only two respondents, and I tried to do the Cronbach Alpha using the formula =cronalpha from realstats, but it gives an error (#VALUE!). Please advice how can I do the cronbach alpha with only two respondents.

• Charles says:

Sophia,
I just tried using the formula =CRONALPHA(A1:J2) to calculate Cronbach’s alpha with only two respondents and 12 questions. It worked fine.
If you send me an Excel file with your data and use of the CRONALPHA formula, I will try to figure out what is going on.
Charles

• Sophia says:

I just figured out that the error is not because of only two respondents. can you please help me how to calculate the cronbach alpha for this data below then. I tried using formula, or using the data analysis tool, or the calculation, but nothing gives the cronbach alpha without error.

Respondent 1: 5 5 5 2 6 5 5 1 1 7 7 7
Respondent 2: 4 6 6 6 6 6 3 4 2 2 4 7

Thank you!

• Charles says:

Sophia,
Unfortunately, Cronbach’s alpha is undefined for this example since the sum of the scores for respondent 1 = 56 = the sum of the scores for respondent 2. Thus, the variance for these sums is zero. This is the value var(x_0) in Definition 1 on the referenced webpage, and so the calculation of Cronbach’s alpha involves division by zero.
Charles

• Sophia says:

Hi Charles,

So what does it mean if the variance is 0? Can I conclude that the response is highly reliable and consistent then as the variance is 0? Please advice. Thank you.

• Charles says:

Sophia,
I am not really sure how to interpret the result in this case. I can see that if I change any single value slightly (e.g. changing 4 to 4.0001), I get a large negative value for Cronbach’s alpha.
Charles

183. susan says:

hi,
how to calculate cronbach’s alpha n coefficient as there’s 150 respondents n 6 questions are likert scale n 5 questions are option one (like tick one) . No of items means no of respondents or what.

• Charles says:

Susan,
This is explained on the referenced webpage. Do you have a specific question?
Charles

184. Chris says:

Hello! Mr Charles, Im conducting research using likert five scale, Sample size 87 with 10 question. Pls how do calculate the cronbach Alpha?

• Charles says:

Chris,
The referenced webpage explains how to calculate Cronbach’s alpha. Do you have a specific question?
Charles

185. BB says:

Hi, I want to insert Multiple Response Questions (MRQ) in the exist data in SPSS to calculate its realibility using Cronbanch’s alpha. Is it possible to do that ? And if yes, how can I insert the MRQ into the exist data in SPSS ?

• Charles says:

Sorry BB, but I don’t use SPSS. This site is about using Excel to perform statistical analysis.
Charles

186. Mr.Ayman says:

Hi Mr.Charles
I faced the negative Cronbach Alpha problem for a 5 Likert scale.
-Do I have to subtract 6 from the negatively phrased questions?
-Can you give me a scientific paper support this ?
Thanks

• Charles says:

If you have some positively phrased questions and some negatively phrased questions, you need to make sure that the 5-point Likert scales agree (e.g. 5 has the same meaning for all the questions, and similarly for the ratings 1, 2, 3 and 4).
Almost any scientific paper on Cronbach’s alpha will support this or it will be implied). The ratings don’t have similar meaning, Cronbach’s alpha is completely meaningless.
Charles

187. Matt says:

Hi Charles,

I have a set of data in which i need to workout alpha for just one variable and its z-score. The variable however is a time measured in seconds. This is for a test that measures 2hand co-ordination. Is there a way to do this?

• Charles says:

Matt,
Why do you want to use Cronbach’s alpha?
Can you give me some idea of what your data looks like?
Charles

188. Matt says:

I’m not sure what else to use to work out the reliability. Basically we have two variables: MeanTime: which is the average time that a candidates takes to complete the task, and ErrorTime which is how much of his run time was spent in an error state. But I’m only considered in the first variable MeanTime. It is measure in seconds so I have 500 lines that looks like this
Person A – 110
Person B – 56
Person C – 89

I’ve computed the Z-scores for this but would like to know the reliability.

• Charles says:

Matt,
What sort of reliability are you looking for? From your description you seem to be looking to see if the three people agree on their measurements for the 500 observations. If that is the case, then Cronbach’s alpha is not the right measurement.
Charles

189. Liza says:

Hi, Would appreciate some help please. I am currently piloting the questionnaire that I am using for my thesis. It is a Protection Motivation Questionnaire, which has 6 sub-constructs (Fear, Self- Efficacy, Response Efficacy, Response Cost, Perceived Sensitivity and Perceived Severity). It is looking at what affects women’s intentions to attend cervical screening. At the end of the questionnaire there is a question (Intention) looking at whether they intend to attend screening or not?

I need to look at the reliability of the scale. So I calculated the cronbach alpha for all 6 sections separately (mostly at =.8 and =.6) and the scale as a whole (=.76). Whenever I calculate the cronbachs alpha, should I be including the intention question? Or just enter the items for each sub construct?

Also my second question is that one of the sub-constructs (Response Efficacy), has low cronbachs alpha and is displaying this error message: The value is negative due to a negative average covariance among items. This violates reliability model assumptions. You may want to check item codings.
There are no reversed item scores, so I am unsure what this error could be caused by.

Liza

• Charles says:

Liza,
Yes, you should calculate Cronbach’s alpha for each of the 6 sections separately. If there is only one question for intention, then you won’t be able to calculate Cronbach’s alpha for that question (nor would its value have any meaning).
The message you are getting isn’t coming from Real Statistics so I don’t know how to comment on it. As far as “reverse coding” is concerned, it is important that all the codes go in the same direction. How to correct this is explained on this webpage.
Charles

• Charles says:

Liza,
Yes, you should calculate Cronbach’s alpha for each of the 6 sections separately. If there is only one question for intention, then you won’t be able to calculate Cronbach’s alpha for that question (nor would its value have any meaning).
The message you are getting isn’t coming from Real Statistics so I don’t know how to comment on it. As far as “reverse coding” is concerned, it is important that all the codes go in the same direction. How to correct this is explained on this webpage.
Charles