Some Rank Order Tests which are most Powerful Against Specific Parametric Alternatives

Terry, Milton E.

doi:10.1214/aoms/1177729381

Cited by 116 publications

(35 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…developed for the two-sample and the k-sample cases (Hoeffding, 1951;Terry, 1952; Van der Waerden, 1953;Hajek and Sidak, 1967;Puri, 1964). McSweeney and Penfield (1969) have presented a review of the literature, as well as rationale for and derivation of the k-sample case.…”

mentioning

confidence: 99%

An Empirical Comparison of the Anova F-Test, Normal Scores Test and Kruskal-Wallis Test Under Violation of Assumptions

Feir-Walsh

Toothaker

1974

Educational and Psychological Measurement

111

View full text Add to dashboard Cite

The present research compares the ANOVA F-test, the Kruskal-Wallis test, and the normal scores test in terms of empirical alpha and empirical power with samples from the normal distribution and two exponential distributions. Empirical evidence supports the use of the ANOVA F-test even under violation of assumptions when testing hypotheses about means. If the researcher is willing to test hypotheses about medians, the Kruskal-Wallis test was found to be competitive to the F-test. However, in the cases investigated, the normal scores test was not consistently better than the F-test or the Kruskal-Wallis test and could not be recommended on the basis of this research.

show abstract

mentioning

confidence: 99%

An Empirical Comparison of the Anova F-Test, Normal Scores Test and Kruskal-Wallis Test Under Violation of Assumptions

Feir-Walsh

Toothaker

1974

Educational and Psychological Measurement

111

View full text Add to dashboard Cite

show abstract

“…Many authors, such as Barton and David (1958), Terry (1952) and Mood (1954) studied in connections with nonparametric tests on dispersions. The most important procedure for the nonparametric test statistics is to determine null distributions, from which the exact critical values of the test statistics can be calculated.…”

Section: Introductionmentioning

confidence: 99%

Polynomially Adjusted Normal Approximation to the Null Distribution of Ansari-Bradley Statistic

Ha¹,

Yang²

2011

Korean Journal of Applied Statistics

View full text Add to dashboard Cite

The approximation for the distribution functions of nonparametric test statistics is a significant step in statistical inference. A rank sum test for dispersions proposed by Ansari and Bradley (1960), which is widely used to distinguish the variation between two populations, has been considered as one of the most popular nonparametric statistics. In this paper, the statistical tables for the null distribution of the nonparametric Ansari-Bradley statistic is produced by use of polynomially adjusted normal approximation as a semi parametric density approximation technique. Polynomial adjustment can significantly improve approximation precision from normal approximation. The normal-polynomial density approximation for Ansari-Bradley statistic under finite sample sizes is utilized to provide the statistical table for various combination of its sample sizes. In order to find the optimal degree of polynomial adjustment of the proposed technique, the sum of squared probability mass function(PMF) difference between the exact distribution and its approximant is measured. It was observed that the approximation utilizing only two more moments of Ansari-Bradley statistic (in addition to the first two moments for normal approximation provide) more accurate approximations for various combinations of parameters. For instance, four degree polynomially adjusted normal approximant is about 117 times more accurate than normal approximation with respect to the sum of the squared PMF difference.

show abstract

“…Two robust and powerful competitors are the Wilcoxon Rank-Sum test (W) and its normal scores counterpart, the Terry-Hoeffding (NS) (Terry, 1952) counterpart. Both pro cedures are used to test the null hypothesis that samples are from a common population.…”

Section: Introductionmentioning

confidence: 99%

“…However, the normal scores test is at a disadvantage when the populations are heavy-tailed. (For details, see Chemoff and Savage, 1958;Hodges & Lehmann, 1961;Lehmann, 1959;Mikulski, 1963;and Terry, 1952. ) Thus, the purpose of this paper is to present a simple maximum statistic that can be used in lieu of a choice between the Wilcoxon Rank-Sum and Terry-Hoeffding tests.…”

Section: Introductionmentioning

confidence: 99%

Combining two nonparametric tests of location

Blair¹

2002

J. Mod. App. Stat. Meth.

View full text Add to dashboard Cite

A distribution-free test is proposed whose power is similar to that of the Wilcoxon Rank-Sum or Terry-Hoeffding Normal Scores tests depending on which of these two tests is more powerful in a given data analysis situation, regard less of the population. This new statistic is distribution-free, and adds no new assumptions to those associated with the constituent tests. A table of critical values for the new statistic is given and some of its Type I error and power properties are examined.

show abstract

Some Rank Order Tests which are most Powerful Against Specific Parametric Alternatives

Cited by 116 publications

References 11 publications

An Empirical Comparison of the Anova F-Test, Normal Scores Test and Kruskal-Wallis Test Under Violation of Assumptions

An Empirical Comparison of the Anova F-Test, Normal Scores Test and Kruskal-Wallis Test Under Violation of Assumptions

Polynomially Adjusted Normal Approximation to the Null Distribution of Ansari-Bradley Statistic

Combining two nonparametric tests of location

Contact Info

Product

Resources

About