[1] It is a special case of Cronbach's α, computed for dichotomous scores.
However, like Cronbach's α, homogeneity (that is, unidimensionality) is actually an assumption, not a conclusion, of reliability coefficients.
In the case when scores are not tau-equivalent (for example when there is not homogeneous but rather examination items of increasing difficulty) then the KR-20 is an indication of the lower bound of internal consistency (reliability).
If it is important to use unbiased operators then the sum of squares should be divided by degrees of freedom (n − 1) and the probabilities are multiplied by
Like KR-20, KR-21 was first set forth as the twenty-first formula discussed in Kuder and Richardson's 1937 paper.