One way to test the reliability of a test is to repeat the test. This is not always possible. Another approach, which is applicable to questionnaires, is to divide the test into even and odd questions and compare the results.

**Example 1**: 12 students take a test with 50 questions. For each student the total score is recorded along with the sum of the scores for the even questions and the sum of the scores for the odd question as shown in Figure 1. Determine whether the test is reliable by using the split-half methodology.

**Figure 1 – Split-half methodology for Example 1**

The statistical test consists of looking at the correlation coefficient (cell G3 of Figure 1). If it is high then the questionnaire is considered to be reliable.

*r* = CORREL(C4:C15,D4:D15) = 0.667277

One problem with the split-half reliability coefficient is that since only half the number of items is used the reliability coefficient is reduced. To get a better estimate of the reliability of the full test, we apply the **Spearman-Brown correction**, namely:

This result shows that the test is quite reliable.

**Real Statistics Functions**: The Real Statistics Resource Pack contains the following supplemental functions:

**SPLIT_HALF**(R1, R2) = split half coefficient (after Spearman-Brown correction) for data in ranges R1 and R2

**SPLITHALF**(R1, *type*) = split-half measure for or the scores in the first half of the items in R1 vs. the second half of the items if *type* = 0 and the odd items in R1 vs. the even items if *type* = 1.

The SPLIT_HALF function ignores any empty cells and cells with non-numeric values. This is no so for the SPLITHALF function.

For Example 1, SPLIT_HALF(C4:C15, D4:D15) = .800439.

**Example 2**: Calculate the split half coefficient of the ten question questionnaire using a Likert scale (1 to 7) given to 15 people whose results are shown in Figure 2.

**Figure 2 – Data for Example 2**

We first split the questions into the two halves: Q1-Q5 and Q6-Q10, as shown in Figure 3.

**Figure 3 – Split-half coefficient (Q1-Q5 v. Q6-Q10)**

E.g. the formula in cell B23 is =SUM(B4:F4) and the formula in cell C23 is =SUM(G4:K4). The coefficient 0.64451 (cell H24) can be calculated as in Example 1. Alternatively, the coefficient can be calculated by the worksheet formula =SPLIT_HALF(B23,B37,C23:C37) or =SPLITHALF(B4:K18,0).

We can also split the questionnaire into odd and even questions, as shown in Figure 4.

**Figure 4 – Split-half coefficient (odd v. even)**

E.g. the formula in cell L23 is =B4+D4+F4+H4+J4 and the formula in cell M23 is =C4+E4+G4+I4+K4. The coefficient 0.698813 (cell R24) can be calculated as in Example 1. Alternatively, the coefficient can be calculated by the supplemental formula =SPLIT_HALF(L23,L37,M23:M37) or =SPLITHALF(B4:K18,1).

There are many ways to determine reliability as internal consistency, repeat test, split-half,….. .

Do the reliability coefficient are the same with all?

No, the tests can generate different results. See Figure 8 of the webpage Cronbach’s Alpha

Charles

after splitting the items into 2. can we use pearson r to get d correlation coefficient before stepping it up with spearman brown correction formula? thank u.

Please explain what you mean by “d correlation coefficient”.

Charles

hi, i have the problem on finding the spearman brown when the correlation coefficient is negative number

If your correlation coefficient is negative, then you already know that reliability is very low and so you really don’t need to bother with spearman brown.

Using spearman brown without any sort of correction will result in a correlation less than -1, which is not very desirable. I would guess that the correct calculation is to apply spearman brown to the absolute value of the correlation coefficient and then negate the result, but I have not seen this done before.

Charles

I am analyzing data from subjective scoresheets (10 questions regarding performance and scoring against performance). I am feeling that the questions are subjective and being scored differently by different scorers. How can I measure the reliability. I used Spearman Brown (.065)& Pearsons (.12) but am questioning this. Please assist

Jane,

Please describe the scoring used in a little more detail. Are people rating some characteristics using a Likert scale (say 1 to 5) or is this a typical multiple choice question test or something else?

Charles

Dear Sir,

I would like assess the reliability of a questionnaire in an experimental study. I have done pre and post test among 15 samples as my main study will be 150. How do I calculate reliability?

The usual approach is to use Cronbach’s Alpha. Although this measurement has a number of flaws, it is the commonly used measurement.

Charles

Thank You! big help. I have 2 questions though. What if the correlation coefficient’s equation was (0/0), is that considered to be 0.00 for that matter? What is the interpretation of a 0.00 for correlation coefficient and spearman-brown correction? Thank You!

Denise,

A correlation coefficient of zero means there is no correlation, which in this case indicates very poor reliability. Spearman-Brown is undefined (can’t divide by zero), but there is no need to calculate it since the zero value tells you all you need to know.

Charles

Dear sir,

Do I need to test the reliability of a likert-type 5 point scale with the data from a pilot study before applying the instrument for the final study? I am new in statistics please answer.

Alam

Alam,

You don’t have to do this, but it is commonly done.

Charles

Dear Sir,

If I use without testing the reliability of the instrument and it is discovered during analysis that the instrument was not reliable then I have to do the research again. That is my understanding, I might be wrong. That why is it not right to check the reliability of the instrument through a pilot study?

I am expecting your clarification of the matter so that, I can get a clear idea.

Regards,

Nabiul

Alam,

It is best to find out if there are problems early (e.g. with a pilot with say 30 subjects) rather than for the full experiment (e.g. after you have given the questionnaire to say 2,000 people). If reliability is a problem you can fix the questionnaire and then repeat the pilot. If you only check reliability after giving the questionnaire to 2,000 people you will need to repeat the questionnaire with all 2,000 people if you find there is a problem.

Charles

Thanks lot sir for your clear answer!!

Thank you. The information is extremely helpful. Can I use the split half methodology with a test that has two sections – Multiple Choice and Essay? Can I, instead of using odd vs even , use multiple choice vs essay?

Claudette,

The idea of the Split-Half Method is to make a random split of the test items. Odd/even is just one way to do this. However, multiple choice vs essay may not be a random split, and so I would be a bit cautious of using such a split.

Charles

Thank you.

Dear Sir,

I’ve been searching for some one who could explain Cronbach’s alpha and Spearman-Brown split-half. You have done a wonderful job. Thanks a million. I have a doubt though. Plz do forgive me if itz undiluted stupidity (I’m new to Statistics). Do they (Cronbach’s alpha and Spearman-Brown split-half) test both reliability and validity or just one and not the other? I’ve seen a study where the researcher used Spearman-Brown split-half to test reliability and Cronbach’s alpha for validity. Hence the question.

Meera.

Meera,

Reliability only.

Charles

Thank you Sir. How then can we measure validity?

Meera.

Meera,

Most of the tests that you find in this website can be viewed as tests for validity. The actual test used depends on what you are trying to determine.

Charles

Thanks

Thanks a lot. It’s a very nice presentation for the researcher. May Allah bless u. You may present all of the methods of reliability and validity test with formula and indications for excel or SPSS. You may also present directions regarding test of hypotheses.

best regards

can we use split half for 15 item tool

Yes, but you need to leave one item out. Probably it is better to use Cronbach’s alpha.

Charles

I have another question…So if I am giving my survey to 430 students, do I need to conduct the split half test on a small number of the sample to see if its reliable before I give it to all of the students?

Karisa,

That is the usual approach. Note that you can use Cronbach’s Alpha instead of split half.

Charles

Great information! Is it possible to get a reliable score using the split half method with just a 10 questions survey?

Karisa,

Yes, you will get a reliable score for the split half method with just 10 questions. The real question is whether the 10 question survey is reliable (i.e. internally consistent). I don’t have a simple answer for this question. All I can say is that, in general, more questions increases reliability. However, if you add a question which is poorly worded, tricky and/or testing something different from the other questions, then reliability can decrease.

Charles

Thanks for the response. It’s a student survey for elementary students so I was worried that more questions would prompt false responses. Decisions….Decisions….

sir, is this a tool used for item analysis? the reliability of an item?

asap reply is much appreciated.

THANK U

Please see the webpage Item Analysis for a description of the available item analysis capabilities.

Charles

I seem confused. So, this can’t be used to compute the reliability of the test items you’ve created? I meant the Item-Reliability Index in Item Analysis.

Pls help sir.

Thank you.

The Split-Half Methodology can be used as an item reliability index.

Charles

Thank u sir. I have been benifited. I m ever heart to u sir

Thank you very much for giving very much clear concept! i got the idea about split- half reliability.

CAN YOU HELP ME WITH THIS QUESTION PLZ?

COMPUTE RANK ORDER CO-ORELATION FOR THE FOLLOWING

R1 : 1, 8, 3, 7, 5, 10, 4, 6, 2, 9

R2 : 1, 8, 4, 7, 5, 9, 3, 6, 2, 10

If I understand your question correctly you are looking for what is called Spearman’s rho. See webpage http://www.real-statistics.com/correlation/spearmans-rank-correlation/ for details about how to calculate this.

Charles

Thanks for this clear and concise explanation. Can I use the rank order method to calculate the r ? Is it good enough to establish the reliability of a structured knowledge questionnaire?

I would guess that it depends on the motivation you have for using the rank order correlation (i.e. Spearman’s rho) instead of the Pearson’s r.

Charles

Consice and clear. It is a great help for me. Thank you very much.

Hi Charles,

Any thoughts how to calculate Spearmann-brown for Likert 5 point scale answers? How to split the answers?

Thank you very much

Groover,

The calculation is exactly the same as described in the referenced page. You can split the questions by odd-even as described on the referenced webpage or first half of the questions vs. second half of the questions. It is important to decide on which approach to use in advance and not after you have seen the results (which are likely to be different); alternatively you can report on both approaches.

Charles

Hi, Thank you very much for a very helpful article. I have downloaded The Real Statistics Resource Pack to my Excel. However, it doesn`t have SPLIT_HALF function. Any suggestions?

Thanks and kind regards

Hi Parto,

You are correct. The Real Statistics Resource Pack does not contain a SPLIT_HALF function at present, but the referenced webpage does contain an example of how to calculate the split half method in Excel (namely Example 1). You can find the worksheet that carries out the calculations for Example 1 in the Examples Workbook. You can download the Example Workbook for free at http://www.real-statistics.com/free-download/real-statistics-examples-workbook/.

Charles

Thanks very much for your prompt answer. I have it now.

Big help, thank you!