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A comparison of the efficiencies of the c ‐sample normal scores and the Kruskal‐Wallis tests in the case of grouped data
Author(s) -
Padmanabhan A. R.
Publication year - 1977
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1977.tb00743.x
Subject(s) - mathematics , cauchy distribution , statistics , homogeneity (statistics) , exponential function , exponential distribution , decimal , normal distribution , sample size determination , goodness of fit , test (biology) , combinatorics , mathematical analysis , arithmetic , paleontology , biology
The problems of using the Kruskal‐Wallis (KW) test and two equivalent forms of the normal scores (NS) test in analysing data arising from a continuous distribution are discussed for the cases where the data have been rounded to the nearest integer and first decimal place respectively. When the distribution function G is normal, the NS test is asymptotically slightly more efficient than the KW test, whereas when G is double exponential, Cauchy or logistic, the KW test is somewhat more efficient. Even when G is exponential or rectangular, the NS test is only slightly more efficient than the KW test. This is quite surprising by comparison with the continuous case where the NS test is infinitely more efficient than the KW test. Nor do these conclusions need modification for the cases where the populations differ both in location and in scale and where the differences among the location parameters and among the scale parameters tend to zero as the sample sizes tend to infinity, provided G is normal, double exponential, Cauchy or logistic. When homogeneity of variances obtains, the results follow from those of Conover (1973), but with heterogeneous variances his techniques have to be modified as in Goldsmith & Padmanabhan (1976). The limitations of these results and problems for further investigation are explained.