KR20

Kuder-Richardson Formula 20 (KR-20) is a measure of internal consistency reliability for tests with dichotomous items, such as true/false or correct/incorrect questions. It was developed by Kuder and Richardson in 1937 and is used to assess whether the items on a test consistently measure the same underlying construct.

The formula for KR-20 is: KR-20 = (k / (k - 1)) * [1 - (sum p_i q_i) / s^2], where k is the number of items, p_i is the proportion of examinees who answered item i correctly, q_i = 1 - p_i, and s^2 is the variance of the total test scores across examinees. The term p_i q_i represents the variance of item i.

Interpretation of KR-20 values is similar to other reliability coefficients: larger values (closer to 1) indicate greater internal consistency among the items, while smaller values indicate less reliable measurement. Values can theoretically be negative in unusual circumstances, which suggests problematic item characteristics or scoring practices. In practice, a higher KR-20 implies that the test items function coherently as a scale.

KR-20 is a special case of Cronbach's alpha for dichotomous data; Cronbach's alpha generalizes to tests with items that have more than two scoring categories. Because it assumes that items are intended to measure a single underlying construct, KR-20 is most appropriate for unidimensional tests with uniform item difficulty and scoring.