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In psychometrics, the Kuder–Richardson Formula 20 (KR-20) first published in 1937〔Kuder, G. F., & Richardson, M. W. (1937). The theory of the estimation of test reliability. ''Psychometrika, 2''(3), 151–160.〕 is a measure of internal consistency reliability for measures with dichotomous choices. It is analogous to Cronbach's α, except Cronbach's α is also used for non-dichotomous (continuous) measures.〔Cortina, J. M., (1993). What Is Coefficient Alpha? An Examination of Theory and Applications. ''Journal of Applied Psychology, 78''(1), 98–104.〕 It is often claimed that a high KR-20 coefficient (e.g., > 0.90) indicates a homogeneous 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. 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. 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). The formula for KR-20 for a test with ''K'' test items numbered ''i''=1 to ''K'' is : where ''pi'' is the proportion of correct responses to test item ''i'', ''qi'' is the proportion of incorrect responses to test item ''i'' (so that ''pi'' + ''qi'' = 1), and the variance for the denominator is : where ''n'' is the total sample size. If it is important to use unbiased operators then the sum of squares should be divided by degrees of freedom (''n'' − 1) and the probabilities are multiplied by : Since Cronbach's α was published in 1951, there has been no known advantage to KR-20 over Cronbach. KR-20 is seen as a derivative of the Cronbach formula, with the advantage to Cronbach that it can handle both dichotomous and continuous variables. The KR-20 formula can't be used when multiple-choice questions involve partial credit, and it requires detailed item analysis.〔http://chemed.chem.purdue.edu/chemed/stats.html (as of 3/27/2013〕 ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kuder–Richardson Formula 20」の詳細全文を読む スポンサード リンク
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