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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.
533:), is assumed to be the same for each item, however, in practice, KR-21 can be applied by finding the average item difficulty across the entirety of the test. KR-21 tends to be a more conservative estimate of reliability than KR-20, which in turn is a more conservative estimate than Cronbach's
420:
Often discussed in tandem with KR-20, is Kuder–Richardson
Formula 21 (KR-21). KR-21 is a simplified version of KR-20, which can be used when the difficulty of all items on the test are known to be equal. Like KR-20, KR-21 was first set forth as the twenty-first formula discussed in Kuder and
59:
test. However, like
Cronbach's α, homogeneity (that is, unidimensionality) is actually an assumption, not a conclusion, of reliability coefficients. It is possible, for example, to have a high KR-20 with a multidimensional scale, especially with a large number of items.
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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).
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The name of this formula stems from the fact that is the twentieth formula discussed in Kuder and
Richardson's seminal paper on test reliability.
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If it is important to use unbiased operators then the sum of squares should be divided by degrees of freedom (
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Kuder, G. F., & Richardson, M. W. (1937). The theory of the estimation of test reliability.
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Cortina, J. M., (1993). What Is
Coefficient Alpha? An Examination of Theory and Applications.
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349:{\displaystyle \sigma _{X}^{2}={\frac {\sum _{i=1}^{n}(X_{i}-{\bar {X}})^{2}\,{}}{n}}.}
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Similarly to KR-20, K is equal to the number of items. Difficulty level of the items (
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588:. Annual meeting of the Southwest Educational Research Association. New Orleans.
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Quality of assessment chapter in
Illinois State Assessment handbook (1995)
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Understanding a Widely
Misunderstood Statistic: Cronbach's "Alpha"
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24:, first published in 1937, are a measure of internal consistency
603:"Kuder and Richardson Formula 20 | Real Statistics Using Excel"
370: − 1) and the probabilities are multiplied by
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is the proportion of incorrect responses to test item
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519:{\displaystyle r={\frac {K}{K-1}}\left}
198:{\displaystyle r={\frac {K}{K-1}}\left}
582:Ritter, Nicola L. (18 February 2010).
71:The formula for KR-20 for a test with
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416:Kuder–Richardson Formula 21 (KR-21)
44:Kuder–Richardson Formula 20 (KR-20)
424:The formula for KR-21 is as such:
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57:homogeneous
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636:Categories
543:References
38:Richardson
496:σ
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277:∑
256:σ
230:(so that
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608:8 March
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