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Kuder-Richardson Formula 20 is a formula used to measure the internal consistency of a test or assessment. It is a statistical measure that estimates the reliability of a test by calculating the correlation between the items on the test. The Kuder-Richardson Formula 20 is most often used in educational and psychological testing to assess the accuracy of test results.
The Kuder-Richardson Formula 20, often abbreviated KR-20, is used to measure the 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)
where:
- 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.
The following tutorials provide explanations of terms commonly used when assessing the validity of tests and questionnaires: