Comparing measures of the ‘typical’ score across treatment groups

Othman, Abdul Rahim; Keselman, H. J.; Padmanabhan, A. R.; Wilcox, Rand R.; Fradette, Katherine

doi:10.1348/0007110042307159

Cited by 25 publications

(26 citation statements)

References 58 publications

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“…We chose this criterion since it was widely used by most robust statistic researchers (e.g. Keselman et al, 2000;Othman et al, 2004;Syed Yahaya et al, 2004;Wilcox et al, 2000) to judge robustness. Nevertheless, for Guo and Luh (2000), if the empirical Type I error rate do not exceed the 0.075 level, it is considered robust.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Progress has been made in terms of finding better methods for controlling the Type I error and the power of the test that detects treatment effects in one-way independent group designs (Babu, Padmanabhan & Puri, 1999;Othman et al, 2004;. Through a combination of impressive theoretical developments, more flexible statistical methods, and faster computers, serious practical problems that seemed insurmountable only a few years ago can now be addressed.…”

Section: Introductionmentioning

confidence: 99%

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A Robust Alternative to the t - Test

Yusof¹,

Abdullah²,

Yahaya³

et al. 2012

MAS

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Abstractt-test is a classical test statistics for testing the equality of two groups. However, this test is very sensitive to non-normality as well as variance heterogeneity. To overcome these problems, robust method such as F t and S 1 tests statistics can be used. This study proposed the use of a robust estimator that is trimmed mean as the central tendency measure in F t test and median as the central tendency measure in S 1 test when comparing the equality of two groups. The performance of the S 1 test with MAD n was able to give the most convincing result than the other methods. The F t with MAD n showed comparable results with the conventional methods. This study has shown some improvement in the statistical solution of detecting differences between location parameters. These modified methods may serve as alternatives to some other robust statistical methods which are unable to handle either the problem of non-normality, variance heterogeneity or unbalanced design.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Robust Alternative to the t - Test

Yusof¹,

Abdullah²,

Yahaya³

et al. 2012

MAS

View full text Add to dashboard Cite

show abstract

“…Unbalanced designs (i.e., unequal sample sizes across the groups) that are paired with unequal variances can severely affect Type I and Type II error control of ANOVAtype procedures (Keselman et al, 1998;Othman et al, 2004). Thus, the current study Table 1.…”

Section: Methodsmentioning

confidence: 97%

Equivalence of Population Variances: Synchronizing the Objective and Analysis

Mara

Cribbie

2017

The Journal of Experimental Education

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Researchers are often interested in testing for the equivalence of population variances.Traditional difference-based procedures are appropriate to answer questions about differences in some statistic (e.g., variances, etc.). However, if a researcher is interested in evaluating the equivalence of population variances, it is more appropriate to use a procedure specifically designed to determine equivalence. A simulation study was used to compare newly developed equivalence-based tests to difference-based variance homogeneity tests under common data conditions. Results demonstrated that traditional difference-based tests assess equality of variances from the wrong perspective, and that the proposed Levene-Wellek-Welch test for equivalence of group variances using the absolute deviations from the median was the best performing test for detectingequivalence. An R function is provided in order to facilitate use of this test for equivalence of population variances. keywords: equivalence testing, homogeneity of variances, ANOVA, dispersion 3 Equivalence of Population Variances: Synchronizing the Objective and AnalysisHomogeneity of variances occurs when population distributions have similar dispersion. Researchers are becoming increasingly interested in the properties of their data aside from central tendency, such as dispersion. For instance, Borkenau, Hrebícková, Kuppens, Realo, and Allik (2013) hypothesized that self-reported personality scores would have similar variability across males and females. Salgado (1995) examined whether the variability in validity coefficients in self-report tests for a specific construct was equivalent to the variability in validity coefficients in psychomotor tests evaluated by an external rater of the same construct. A more well-known reason for exploring variances is to verify the homogeneity of variances assumption related to traditional parametric tests of mean differences. Regardless of the reason, researchers need a valid test for assessing questions related to variability.There has been substantial research on different tests that can be used to test for differences in variances. This paper discusses whether traditional tests of variance homogeneity address the problem of variance equality from the wrong perspective. We argue that to test for variance homogeneity, one should use equivalence tests because the research hypothesis of variance equality is properly aligned with the alternate hypothesis, not the null hypothesis. To that end, we first situate a test for equality of group variances within the equivalence testing framework. Even though difference-based procedures are appropriate to answer questions about differences in some statistic (e.g., means, variances, etc.), these procedures are not appropriate to address questions related to equivalence. Then, the main goal of this paper is to compare our newly developed tests 4 for equivalence of group variances to currently recommended variance homogeneity tests under data conditions common in educational and psychologic...

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“…This ratio was chosen as it reflects extreme variance heterogeneity. This variance ratio was used by a number of researchers in their study for two groups case (Keselman, Wilcox, Lix, Algina & Fradette, 2007;Othman, Keselman, Padmanabhan, Wilcox & Fradette, 2004;Luh & Guo, 1999).…”

Section: Design Specificationsmentioning

confidence: 99%

“…On the other hand, a negative pairing referred to the case in which the largest group size is paired with the smallest group variance and the smallest group size is paired with the largest group variance. These conditions were chosen since the test for equality of central tendency parameters typically produces conservative results for the positive pairings and liberal results for the negative pairings (Syed Yahaya et al, 2004;Othman et al, 2004;Keselman et al, 2004). According to Cribbie and Keselman (2003), when variance and sample size are directly paired, Type I error estimates can be conservative and power correspondingly will be deflated.…”

Section: Design Specificationsmentioning

confidence: 99%

Comparative Performance of Pseudo-Median Procedure, Welch’s Test and Mann-Whitney-Wilcoxon at Specific Pairing

Ahad¹,

Othman²,

Yahaya³

2011

MAS

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The objective of this study is to investigate the performance of two-sample pseudo-median based procedure in testing differences between groups. The procedure is the modification of one-sample Wilcoxon procedure using pseudo-median of differences between group values as the central measure of location. The test was conducted on two groups setting with moderate sample sizes of symmetric and asymmetric distributions. The performance of the procedure was measured and evaluated in terms of Type I error and power rates obtained via Monte Carlo methods. Type I error and power rates of the procedure were then compared with the alternative parametric and nonparametric procedures namely the Welch's test and Mann-Whitney-Wilcoxon test. The findings revealed that the pseudo-median procedure is capable in controlling its Type I error close to the nominal level when heterogeneity of variances exists. In terms of robustness, the pseudo-median procedure outperforms the Welch's and Mann Whitney Wilcoxon tests when distributions are skewed. The pseudo-median procedure is also capable in maintaining high power rates especially for negative pairing.

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Comparing measures of the ‘typical’ score across treatment groups

Cited by 25 publications

References 58 publications

A Robust Alternative to the t - Test

A Robust Alternative to the t - Test

Equivalence of Population Variances: Synchronizing the Objective and Analysis

Comparative Performance of Pseudo-Median Procedure, Welch’s Test and Mann-Whitney-Wilcoxon at Specific Pairing

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