Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s 'F'-test instead of the Classical 'F'-test in One-Way ANOVA
Student’s 't'-test and classical 'F'-test ANOVA rely on the assumptions that two or more samples are independent, and that independent and identically distributed residuals are normal and have equal variances between groups. We focus on the assumptions of normality and equality o...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Ubiquity Press
2019-08-01
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| Series: | International Review of Social Psychology |
| Subjects: | |
| Online Access: | https://www.rips-irsp.com/articles/198 |
| _version_ | 1811264130522284032 |
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| author | Marie Delacre Christophe Leys Youri L. Mora Daniël Lakens |
| author_facet | Marie Delacre Christophe Leys Youri L. Mora Daniël Lakens |
| author_sort | Marie Delacre |
| collection | DOAJ |
| description | Student’s 't'-test and classical 'F'-test ANOVA rely on the assumptions that two or more samples are independent, and that independent and identically distributed residuals are normal and have equal variances between groups. We focus on the assumptions of normality and equality of variances, and argue that these assumptions are often unrealistic in the field of psychology. We underline the current lack of attention to these assumptions through an analysis of researchers’ practices. Through Monte Carlo simulations, we illustrate the consequences of performing the classic parametric 'F'-test for ANOVA when the test assumptions are not met on the Type I error rate and statistical power. Under realistic deviations from the assumption of equal variances, the classic 'F'-test can yield severely biased results and lead to invalid statistical inferences. We examine two common alternatives to the 'F'-test, namely the Welch’s ANOVA ('W'-test) and the Brown-Forsythe test ('F'*-test). Our simulations show that under a range of realistic scenarios, the 'W'-test is a better alternative and we therefore recommend using the 'W'-test by default when comparing means. We provide a detailed example explaining how to perform the 'W'-test in SPSS and R. We summarize our conclusions in practical recommendations that researchers can use to improve their statistical practices. |
| first_indexed | 2024-04-12T19:57:26Z |
| format | Article |
| id | doaj.art-258fa30b5d304f3d9900c7b6b93b37f9 |
| institution | Directory Open Access Journal |
| issn | 2397-8570 |
| language | English |
| last_indexed | 2024-04-12T19:57:26Z |
| publishDate | 2019-08-01 |
| publisher | Ubiquity Press |
| record_format | Article |
| series | International Review of Social Psychology |
| spelling | doaj.art-258fa30b5d304f3d9900c7b6b93b37f92022-12-22T03:18:37ZengUbiquity PressInternational Review of Social Psychology2397-85702019-08-0132110.5334/irsp.19885Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s 'F'-test instead of the Classical 'F'-test in One-Way ANOVAMarie Delacre0Christophe Leys1Youri L. Mora2Daniël Lakens3Université Libre de Bruxelles, Service of Analysis of the Data (SAD), BruxellesUniversité Libre de Bruxelles, Service of Analysis of the Data (SAD), BruxellesUniversité Libre de Bruxelles, Service of Analysis of the Data (SAD), BruxellesEindhoven University of Technology, Human Technology Interaction Group, EindhovenStudent’s 't'-test and classical 'F'-test ANOVA rely on the assumptions that two or more samples are independent, and that independent and identically distributed residuals are normal and have equal variances between groups. We focus on the assumptions of normality and equality of variances, and argue that these assumptions are often unrealistic in the field of psychology. We underline the current lack of attention to these assumptions through an analysis of researchers’ practices. Through Monte Carlo simulations, we illustrate the consequences of performing the classic parametric 'F'-test for ANOVA when the test assumptions are not met on the Type I error rate and statistical power. Under realistic deviations from the assumption of equal variances, the classic 'F'-test can yield severely biased results and lead to invalid statistical inferences. We examine two common alternatives to the 'F'-test, namely the Welch’s ANOVA ('W'-test) and the Brown-Forsythe test ('F'*-test). Our simulations show that under a range of realistic scenarios, the 'W'-test is a better alternative and we therefore recommend using the 'W'-test by default when comparing means. We provide a detailed example explaining how to perform the 'W'-test in SPSS and R. We summarize our conclusions in practical recommendations that researchers can use to improve their statistical practices.https://www.rips-irsp.com/articles/198ANOVAWelch testparametric testparametric assumptionsreplicability crisis |
| spellingShingle | Marie Delacre Christophe Leys Youri L. Mora Daniël Lakens Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s 'F'-test instead of the Classical 'F'-test in One-Way ANOVA International Review of Social Psychology ANOVA Welch test parametric test parametric assumptions replicability crisis |
| title | Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s 'F'-test instead of the Classical 'F'-test in One-Way ANOVA |
| title_full | Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s 'F'-test instead of the Classical 'F'-test in One-Way ANOVA |
| title_fullStr | Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s 'F'-test instead of the Classical 'F'-test in One-Way ANOVA |
| title_full_unstemmed | Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s 'F'-test instead of the Classical 'F'-test in One-Way ANOVA |
| title_short | Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s 'F'-test instead of the Classical 'F'-test in One-Way ANOVA |
| title_sort | taking parametric assumptions seriously arguments for the use of welch s f test instead of the classical f test in one way anova |
| topic | ANOVA Welch test parametric test parametric assumptions replicability crisis |
| url | https://www.rips-irsp.com/articles/198 |
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