RANK AND PRODUCT-MOMENT CORRELATION
成果类型：
Article
署名作者：
KENDALL, MG
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.2307/2332540
发表日期：
1949
页码：
177193
关键词：
摘要：
The effect of non-normality on the known relations between Kendall''s [image] and Spearman''s [rho]s rank correlation coeffs. on the one hand and the product moment coeff. [rho] on the other, is investigated. Non-normality is introduced through the Gram-Charlier A series. It is found that the expressions for E(t) and E(rs) in terms of [rho] are independent of odd order product moments and hence, of skewness in the parent population. Corrections to the usual formulas for mean and variance of both coeffs. are given for non-normality to cumulants of 5th order (neglecting powers higher than first of cumulants of 4th order). An error in K. Pearson''s computation of var (rs) is corrected. The effectiveness of sin (1/2) [pi]t and 2 sin (1/6) [pi]r rs as estimators of [rho] is examined in six non-normal examples. When dichotomization is close to the two medians, the first is no more than fair, the second is much worse and tetrachoric r is impossibly bad, the last seeming to be extremely sensitive to departure from normality. An example of computation of t from a 4 x 4 table is given.
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