The Kuder and Richardson Formula 20 test checks the internal consistency of measurements with dichotomous choices. It is equivalent to performing the split half methodology on all combinations of questions and is applicable when each question is either right or wrong. A correct question scores 1 and an incorrect question scores 0. The test statistic is
k = number of questions
pj = number of people in the sample who answered question j correctly
qj = number of people in the sample who didn’t answer question j correctly
σ2 = variance of the total scores of all the people taking the test = VARP(R1) where R1 = array containing the total scores of all the people taking the test.
Values range from 0 to 1. A high value indicates reliability, while too high a value (in excess of .90) indicates a homogeneous test.
Example 1: A questionnaire with 11 questions is administered to 12 students. The results are listed in the upper portion of Figure 1. Determine the reliability of the questionnaire using Kuder and Richardson Formula 20.
The values of p in row 18 are the percentage of students who answered that question correctly – e.g. the formula in cell B18 is =B16/COUNT(B4:B15). The values of q in row 19 are the percentage of students who answered that question incorrectly – e.g. the formula in cell B19 is =1–B18. The values of pq are simply the product of the p and q values, with the sum given in cell M20.
We can calculate ρKR20 as described in Figure 2.