The Kuder-Richardson Formula 20, often abbreviated KR-20, is used to measure the internal consistency reliability of a test in which each question only has two answers: right or wrong.
The Kuder-Richardson Formula 20 is as follows:
KR-20 = (k / (k-1)) * (1 – Σpjqj / σ2)
- k: Total number of questions
- pj: Proportion of individuals who answered question j correctly
- qj: Proportion of individuals who answered question j incorrectly
- σ2: Variance of scores for all individuals who took the test
The value for KR-20 ranges from 0 to 1, with higher values indicating higher reliability.
The following example shows how to calculate the value for KR-20 in practice.
Example: Calculating Kuder-Richardson Formula 20
Suppose we administer a test with 7 questions to 10 students.
The results of the test are listed below in Excel, with 1 indicating a correct answer and 0 indicating an incorrect answer:
The following screenshot shows how to calculate the KR-20 value for this test:
Here are the formulas used in various cells:
- B13: =SUM(B2:B11) / 10
- B14: =1-B13
- B15: =B13*B14
- B17: =COUNTA(B1:H1)
- B18: =SUM(B15:H15)
- B19: =VAR.S(I2:I11)
- B20: =(B17/(B17-1))*(1-B18/B19)
The KR-20 value turns out to be 0.0603.
Since this value is extremely low, this indicates that the test has low reliability.
This means the questions may need to be re-written or re-phrased in such a way that the reliability of the test can be increased.
The following tutorials provide explanations of terms commonly used when assessing the validity of tests and questionnaires: