Testing Statistical Hypotheses of Equivalence and Noninferiority

Wellek, Stefan

doi:10.1201/ebk1439808184

Cited by 470 publications

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“…For example, equivalence testing may be used to reject the hypothesis that a meaningfully large effect exist (e.g., Wellek, 2010) or researchers may check for the sign of expected effects (Gelman and Tuerlinckx, 2000). However, because typically only statistically significant data is published, published studies most probably exaggerate effect sizes.…”

Section: Used Analysis Ofmentioning

confidence: 99%

When null hypothesis significance testing is unsuitable for research: a reassessment

Szűcs

Ioannidis

2016

Preprint

107

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Null hypothesis significance testing (NHST) has several shortcomings that are likely contributing factors behind the widely debated replication crisis of (cognitive) neuroscience, psychology, and biomedical science in general. We review these shortcomings and suggest that, after sustained negative experience, NHST should no longer be the default, dominant statistical practice of all biomedical and psychological research. If theoretical predictions are weak we should not rely on all or nothing hypothesis tests. Different inferential methods may be most suitable for different types of research questions. Whenever researchers use NHST they should justify its use, and publish pre-study power calculations and effect sizes, including negative findings. Hypothesis-testing studies should be pre-registered and optimally raw data published. The current statistics lite educational approach for students that has sustained the widespread, spurious use of NHST should be phased out.

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Section: Used Analysis Ofmentioning

confidence: 99%

When null hypothesis significance testing is unsuitable for research: a reassessment

Szűcs

Ioannidis

2016

Preprint

107

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“…The summary of the conditions tested in this study can be found in Table 1. For the equivalence-based tests, the conservative and liberal equivalence limits of ε = .25 and ε = .50, respectively, were used (Wellek, 2010). However, the pattern of results for both equivalence limits were similar, so only the results for ε = .50 are presented.…”

Section: Methodsmentioning

confidence: 99%

“…Previously, Wellek (2010) developed an approach for assessing the equivalence of variances for two groups that utilizes the ratio of the largest to smallest variance, which, as suggested by an anonymous reviewer, is similar in nature to the F max test developed by Hartley (1950). The current research explores an alternative approach that uses the raw difference rather than the ratio and is suitable for two or more independent groups.…”

Section: Studymentioning

confidence: 99%

“…For example, a researcher may be interested in demonstrating that the means of groups are equivalent, that no relationship exists between two variables, or that variables do not interact (e.g., Cribbie, Gruman, & Arpin-Cribbie, 2004;Cribbie, Ragoonanan & Counsell, in press;Goertzen & Cribbie, 2010;Robinson, Duursma, & Marshall, 2005;Rogers, Howard, & Vessey, 1993, Schuirmann, 1987Wellek, 2010), or that the variances of two or more populations are equal (as proposed in the current study).…”

Section: Equivalence Testingmentioning

confidence: 99%

“…Specifically, if one is using a traditional test for homogeneity of variances, the goal is to fail to reject the null hypothesis for these tests, & Vessey, 1993, Schuirmann, 1987Wellek, 2010), or that the variances of two or more populations are equal (as proposed in the current study).…”

Section: Problems With Traditional Tests For Equivalence Of Variancesmentioning

confidence: 99%

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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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Methods of Determining Sample Sizes

2013

Wiley Series in Probability and Statistics

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Testing Statistical Hypotheses of Equivalence and Noninferiority

Cited by 470 publications

References 0 publications

When null hypothesis significance testing is unsuitable for research: a reassessment

When null hypothesis significance testing is unsuitable for research: a reassessment

Equivalence of Population Variances: Synchronizing the Objective and Analysis

Methods of Determining Sample Sizes

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