Values can range from 0.00 to 1.00 (sometimes expressed as 0 to 100), with high values indicating that the examination is likely to correlate with alternate forms (a desirable characteristic). The KR-20 may be affected by difficulty of the test, the spread in scores and the length of the examination.
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).
The formula for KR-20 for a test with K test items numbered i=1 to K is
where pi is the proportion of correct responses to test item i, qi is the proportion of incorrect responses to test item i (so that pi +
qi = 1), and the variance for the denominator is
where n is the total sample size.
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