Tests for mean equality that do not require homogeneity of variances: do they really Work?

Keselman, H. J.; Wilcox, Rand R.; Taylor, J.R.; Kowalchuk, Rhonda K.

doi:10.1080/03610910008813644

Cited by 15 publications

(7 citation statements)

References 24 publications

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“…Many treatises have appeared on the topic of substituting robust measures of central tendency, such as trimmed means or M-estimators, for the usual least squares estimator, that is, the usual least squares means. Indeed, many investigators have demonstrated that one can achieve better control over Type I error and power to detect treatment effects when robust estimators are substituted for least squares estimators (see, for example, Keselman, Wilcox, Taylor, & Kowalchuk, 2000;Wilcox, 1995Wilcox, , 1997Wilcox, Keselman, & Kowalchuk, 1998;Yuen, 1974). In particular, Yuen (1974) demonstrated these benefits in the two-group case and Lix and Keselman (1998) found similar results in the many-group problem.…”

Section: Introductionmentioning

confidence: 99%

Comparing measures of the ‘typical’ score across treatment groups

Othman

Keselman²,

Padmanabhan

et al. 2004

Brit J Math & Statis

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Researchers can adopt one of many different measures of central tendency to examine the effect of a treatment variable across groups. These include least squares means, trimmed means, M-estimators and medians. In addition, some methods begin with a preliminary test to determine the shapes of distributions before adopting a particular estimator of the typical score. We compared a number of recently developed adaptive robust methods with respect to their ability to control Type I error and their sensitivity to detect differences between the groups when data were non-normal and heterogeneous, and the design was unbalanced. In particular, two new approaches to comparing the typical score across treatment groups, due to Babu, Padmanabhan, and Puri, were compared to two new methods presented by Wilcox and by Keselman, Wilcox, Othman, and Fradette. The procedures examined generally resulted in good Type I error control and therefore, on the basis of this critetion, it would be difficult to recommend one method over the other. However, the power results clearly favour one of the methods presented by Wilcox and Keselman; indeed, in the vast majority of the cases investigated, this most favoured approach had substantially larger power values than the other procedures, particularly when there were more than two treatment groups.

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Section: Introductionmentioning

confidence: 99%

Comparing measures of the ‘typical’ score across treatment groups

Othman

Keselman²,

Padmanabhan

et al. 2004

Brit J Math & Statis

Self Cite

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“…These choices of conditions help to show the effect of the heterogeneity and the type of distribution on the power of the pseudo-median procedure. Also, these choices are similar to the choices in previous studies [3,11,12,[23][24][25][26][27] TABLE 1 presents the power values of PM procedure for the three distributions. The first two columns are the effect size values which reflect the shift between the control group and the second (ES1) and third groups (ES2), respectively.…”

Section: Empirical Investigationmentioning

confidence: 53%

Estimated power of a robust method for treatment groups comparison

Alsaggaff¹,

Othman²,

Low³

2012

AIP Conference Proceedings

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Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method Abstract. The pseudo-median procedure is a technique for treatment group comparison which adopts the pseudomedian as a location parameter. The power of this procedure is estimated in various shapes of distributions and different degrees of variation. The bootstrap method is employed to generate the approximate sampling distribution of the statistic. The results show that the power of this procedure is not affected by the shape of the data. However, the power is affected somewhat by the heterogeneity of variances.

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“…To be congruent to the literature of ANOVA studies, we considered five manipulated variables to investigate the performance of the tests being compared: (a) the number of treatments (levels of factor A ), 2 or 3; (b) the number of cells, fully nested or not fully nested; (c) the sample size of each cell, equal or unequal; (d) the variance structure, homogeneous or heterogeneous, within or between treatments, respectively; and (e) the ratio of the standard deviation to the sample size, disproportional or proportional. These simulated conditions were commonly found in applied research studies and were selected to ensure a wide range of observations (Keselman et al , 1998, 2000; Micceri, 1989; Oshima & Algina, 1992; St‐Pierre, 2007). Four schematics of various configurations of sample size and variance for levels of A and of B nested within A are shown in Figures 1–4.…”

Section: The Design Of the Simulation Experimentsmentioning

confidence: 99%

“…Ananda (1995) developed exact tests for unbalanced nested designs under heteroscedasticity, but his methods are very tedious to apply. Approximate tests, such as those due to Welch (1951) and Alexander and Govern (1994), have been recommended by many researchers for dealing with heterogeneous variances (Cai & Hayes, 2008; Keselman, Wilcox, Taylor, & Kowalchuk, 2000; Luh & Guo, 1999; Schneider & Penfield, 1997). These tests compare the means across the levels of one‐factor ( A ) designs when the variances are heterogeneous at the different levels of A ; such designs are clearly non‐nested designs.…”

Section: Introductionmentioning

confidence: 99%

New heterogeneous test statistics for the unbalanced fixed‐effect nested design

Guo

Billard

Luh

2011

Brit J Math & Statis

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When the underlying variances are unknown or/and unequal, using the conventional F test is problematic in the two-factor hierarchical data structure. Prompted by the approximate test statistics (Welch and Alexander-Govern methods), the authors develop four new heterogeneous test statistics to test factor A and factor B nested within A for the unbalanced fixed-effect two-stage nested design under variance heterogeneity. The actual significance levels and statistical power of the test statistics were compared in a simulation study. The results show that the proposed procedures maintain better Type I error rate control and have greater statistical power than those obtained by the conventional F test in various conditions. Therefore, the proposed test statistics are recommended in terms of robustness and easy implementation.

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Tests for mean equality that do not require homogeneity of variances: do they really Work?

Cited by 15 publications

References 24 publications

Comparing measures of the ‘typical’ score across treatment groups

Comparing measures of the ‘typical’ score across treatment groups

Estimated power of a robust method for treatment groups comparison

New heterogeneous test statistics for the unbalanced fixed‐effect nested design

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