THE NORMAL SCORES TEST FOR THE <i>c</i>‐SAMPLE PROBLEM

McSweeney, Maryellen; Penfield, Douglas A.

doi:10.1111/j.2044-8317.1969.tb00429.x

Cited by 18 publications

(8 citation statements)

References 6 publications

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“…For example, Pratt (1964) showed that the Mann–Whitney U and the expected normal scores test (Hájek and Sidák 1967) resulted in nonrobust Type I error rates. Feir-Walsh and Toothaker (1974) and Keselman, et al (1977) found the Kruskal–Wallis test (Kruskal and Wallis 1952) and expected normal scores test (McSweeney and Penfield 1969) to be substantially affected by heterogeneity of variance.…”

Section: Issues Concerning Intsmentioning

confidence: 99%

Rank-Based Inverse Normal Transformations are Increasingly Used, But are They Merited?

2009

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Many complex traits studied in genetics have markedly non-normal distributions. This often implies that the assumption of normally distributed residuals has been violated. Recently, inverse normal transformations (INTs) have gained popularity among genetics researchers and are implemented as an option in several software packages. Despite this increasing use, we are unaware of extensive simulations or mathematical proofs showing that INTs have desirable statistical properties in the context of genetic studies. We show that INTs do not necessarily maintain proper Type 1 error control and can also reduce statistical power in some circumstances. Many alternatives to INTs exist. Therefore, we contend that there is a lack of justification for performing parametric statistical procedures on INTs with the exceptions of simple designs with moderate to large sample sizes, which makes permutation testing computationally infeasible and where maximum likelihood testing is used. Rigorous research evaluating the utility of INTs seems warranted.

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Section: Issues Concerning Intsmentioning

confidence: 99%

Rank-Based Inverse Normal Transformations are Increasingly Used, But are They Merited?

2009

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“…Bradstreet (1997) found the rank transform test (Conover & Iman, 1982) to result in severely inflated Type I error rates. For the case of k > 2, Feir-Walsh and Toothaker (1974) and Keselman, Rogan, and FeirWalsh (1977) found the Kruskal-Wallis test (Kruskal & Wallis, 1952) and expected normal scores test (McSweeney & Penfield, 1969) to be "substantially affected by inhomogeneity of variance" (p. 220).…”

Section: Robustness With Respect To Unequal N's and Population Normalitymentioning

confidence: 99%

Fermat, Schubert, Einstein, and Behrens-Fisher: The Probable Difference Between Two Means When σ_1^2≠σ_2^2

Sawilowsky

2002

J. Mod. App. Stat. Meth.

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The history of the Behrens-Fisher problem and some approximate solutions are reviewed. In outlining relevant statistical hypotheses on the probable difference between two means, the importance of the BehrensFisher problem from a theoretical perspective is acknowledged, but it is concluded that this problem is irrelevant for applied research in psychology, education, and related disciplines. The focus is better placed on "shift in location" and, more importantly, "shift in location and change in scale" treatment alternatives.

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“…McSweeney and Penfield (1969) have presented a review of the literature, as well as rationale for and derivation of the k-sample case. The Terry-Hoeffding form of the k-sample normal scores test requires the use of special tables (Harter, 1961 ) n; = the number of observations in the ith sample, N = ~ n ;, the number of observations in all samples combined, Wii = the jth expected normal order statistic in the ith sample.…”

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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

106

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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.

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THE NORMAL SCORES TEST FOR THE c‐SAMPLE PROBLEM

Cited by 18 publications

References 6 publications

Rank-Based Inverse Normal Transformations are Increasingly Used, But are They Merited?

Rank-Based Inverse Normal Transformations are Increasingly Used, But are They Merited?

Fermat, Schubert, Einstein, and Behrens-Fisher: The Probable Difference Between Two Means When σ_1^2≠σ_2^2

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

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