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).

Big help, thank you!

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.

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

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

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