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 – Σp _{j}q_{j} / σ^{2})**

where:

**k**: Total number of questions**p**: Proportion of individuals who answered question j correctly_{j}**q**: Proportion of individuals who answered question j incorrectly_{j}**σ**: Variance of scores for all individuals who took the test^{2}

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.

**Additional Resources**

The following tutorials provide explanations of terms commonly used when assessing the validity of tests and questionnaires: