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Should we calculate Cronbach's alpha instead of KR20/KR21 for measuring the reliability of an achievement test, or a test with dichotomous data?

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KR 20 is an algebraic simplification of alpha for dichotomous data. If your data are dichotomous then you can use either one -- they will give the same result.

KR 21 is an approximation that is of historical interest only. Don't use it.

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