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
See Basic Concepts of Correlation for more information about the correlation coefficient r.
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).