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### Reliability, Kuder-Richardson Formula[Page 1418]

The Kuder-Richarson Formula 20, often abbreviated as KR-20, and the Kuder-Richardson Formula 21, abbreviated KR-21, are measures of internal consistency for measures that feature dichotomous items. As these are measures of internal consistency, they measure the extent to which all the items measure the same characteristic. This entry covers the formulas for both the KR-20 and KR-21, as well as when to use them, what they are used for, how to interpret their outputs, the limitations of these procedures, and some possible alternatives.

### Formulas

The formula for KR20 is

$\mathrm{KR}20=n/n-1\phantom{\rule{0.25em}{0ex}}×\phantom{\rule{0.25em}{0ex}}\left[1-\left(\left(pq\right)/\mathrm{Var}\right)\right]$

In this formula, KR20 is the output and is the score that serves as an estimation of the internal reliability of the measure. n is simply the number of items that the researcher has; p is the proportion of ...