Kuder–Richardson Formula 20

The Kuder -Richardson formula is a measure of multivariate statistics, which determines the extent to which a group of test items as measuring a single latent can be viewed ( from the outside is not directly observable ) variables. That is, it indicates the extent to which different items measure the same thing basically.

The measure is used primarily in the social sciences or in psychology, especially in test construction and evaluation. It is used to estimate the reliability of a psychometric instrument.

The formula is considered the forerunner of the measure, Cronbach's alpha and differs only slightly from this measure. In contrast Cronbach's alpha, the Kuder -Richardson formula is applied to items with only two possible answers. One speaks here of dichotomous items.

By the formula, the scale is divided into as many test halves as items are present. Accordingly, correlations between this test halves calculated and the obtained values ​​are " extrapolated " to the respective length of the scale ( see also Spearman - Brown formula ).

The formula will automatically be used for SPSS for dichotomous data when selecting the item " Coefficient Alpha".

There are various formulas for the calculation, depending on which data is given. So there is the KR- 8 Formula, Formula KR- 20, KR - 21 Formula

K- R- 8 Formula

K- R- 20 Formula

  • : Result of the KR formula, as the average correlation
  • : Number of questions
  • : Variance of the Testrohwerte
  • : Difficulty P/100
  • 1 -p
  • : Selectivity
Psychometrics Dichotomy Spearman–Brown prediction formula
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