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 *x*_{1}*, …, x _{k}* and

*x*

_{0}= and

**Cronbach’s alpha**is defined to be

**Property 1**: Let *x _{j} = t_{j} + e_{j}* where each

*e*is independent of

_{j}*t*and all the

_{j}*e*are independent of each other. Also let

_{j}*x*

_{0}= and

*t*

_{0}= . Then the reliability of

*x*

_{0}≥

*α*where

*α*is Cronbach’s alpha.

Here we view the *x _{j}* as the measured values, the

*t*as the true values and the

_{j}*e*as the measurement error values. Click here for a proof of Property 1.

_{j}**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).

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**

Since the questions only have two answers, Cronbach’s alpha .73082 We see that this is the same as the We see that this is the same as the KR20 reliability calculated for Example 1 of Kuder and Richardson Formula 20.

**Observation**: If the variances of the *x _{j}* vary widely, the

*x*can be standardized to obtain a standard deviation of 1 prior to calculating Cronbach’s alpha.

_{j}**Observation**: To determine how each question on a test impacts the reliability, Cronbach’s alpha can be calculated after deleting the *i*th variable, for each *i ≤ k.* Thus for a test with *k* questions, each with score *x _{j}*, Cronbach’s alpha is calculated for for all

*i*where = .

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.

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 2.

**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.

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 *k*th 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.

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). Note too that the split-half measures are also shown in N12 and N13.

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

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

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 ?

Dear Hammad,

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

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?

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

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

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

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

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.

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

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

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

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

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.

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

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

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

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.

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 dataandsingle subject consistency statistics, including the following:http://www.physther.net/content/74/8/768.full.pdf

http://www.u.arizona.edu/~dusana/psych290Bpresession06/notes/Ch%2014%20Single-Subejct%20Research%20Designs.ppt

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

Charles

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

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

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

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!

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.

Hadia,

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?

Joseph,

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

Charles

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?

Karen,

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

Charles

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?

Krisliz,

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

Charles

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

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

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?

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

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.

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

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 ?

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.

http://www.ctbassessments.com/assessment_insights/february_2011/research_insights.html

http://psychweb.psy.umt.edu/denis/datadecision/front/cortina_alpha.pdf

Charles

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

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

Dee,

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

Charles

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

I’m not sure what you mean by “run cronbach on each item”. You run cronbach on all the items. You can also run cronbach on all the items except one (as in Example 2). In any case, how you calculate cronbach is described on the referenced webpage and you can get more information by looking at the example worksheet which you can download for free at webpage http://www.real-statistics.com/free-download/real-statistics-examples-workbook/.

Charles

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

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

Thanks so much indeed Charles. I got it.

You have a Blessed day.

Best,

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

Arin,

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

Charles

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.

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

Hello Charles,

I really need your help.

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.

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

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

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

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

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

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

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

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

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

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

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

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??

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

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?

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

Thank you very much charles:)

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

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

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

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

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.

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

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

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 Rangedata analysis tool andExtractColfunction).Many of the statistical functions ignore any rows with missing data, but the

CRONALPHAdoesn’t have this capability. You need to first remove any missing data (e,g, by using the Real Statistics functionDELROWBLANKorDELROWNonNumor via theReformatting a Data Range by Rowsdata analysis tool) and then apply theCRONALPHAfunction to the reduced data range.Charles

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

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

Hi, I am currently working on my research. I face problem when i generating Cronbach Alpha. My questionnaire contains such question :

If yes,please answer Section B.

If no, please answer Section C.

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.

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

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

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

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?

Appreciate your advice.

Debbie

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

Dear Charles,

Thank you so much! Much appreciated.

Debbie

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

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.

.

please, how do I compute the correlation

between a particular item and the

sum of the rest of the items.

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.

Sadhna,

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.

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?

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

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?

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

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.

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

i need draw backs of cronbach alpha test.

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

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

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

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

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

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

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

Thank you again!

Cheers

Giacomo

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.

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

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).

Please advise

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

Charles

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.

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

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.

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.