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Yet another article giving a formula without explaining all the variables. Pi and Qi would seem to be the proportion of people getting an item correct or incorrect as described here [ [1]] . It might also be helpful to indicate the variance and associated sum of squares are applied to raw scores with N being the number of people in the sample (not number of test items). —Preceding unsigned comment added by 98.231.152.208 ( talk) 15:11, 22 October 2010 (UTC) reply

Rather unusual name - is there some history behind this? What were KR1 to KR19? — Preceding unsigned comment added by 31.221.13.140 ( talk) 09:48, 11 May 2012 (UTC) reply

This article says

The formula for KR-20 for a test with K test items numbered i = 1 to K is

${\displaystyle r={\frac {K}{K-1}}\left[1-{\frac {\sum _{i=1}^{K}p_{i}q_{i}}{\sigma _{X}^{2}}}\right]}$

where p_i is the proportion of correct responses to test item i, q_i is the proportion of incorrect responses to test item i (so that p_i + q_i = 1), and the variance for the denominator is

${\displaystyle \sigma _{X}^{2}={\frac {\sum _{i=1}^{n}(X_{i}-{\bar {X}})^{2}\,{}}{n}}.}$

where n is the total sample size.

It never says what ${\textstyle X_{i}}$ is! Are there people who can read something like that without feeling they're being personally abused? Michael Hardy ( talk) 16:03, 8 July 2023 (UTC) reply