# Kuder-Richardson Formula 20 (Definition & Example)

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)

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.

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.