Can we disregard the whole model? Omnibus non-inferiority testing for R2 in multi-variable linear regression and η^2 in ANOVA

Harlan Campbell (Corresponding author), Daniël Lakens

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

Determining a lack of association between an outcome variable and a number of different explanatory variables is frequently necessary in order to disregard a proposed model (i.e., to confirm the lack of a meaningful association between an outcome and predictors). Despite this, the literature rarely offers information about, or technical recommendations concerning, the appropriate statistical methodology to be used to accomplish this task. This paper introduces non-inferiority tests for ANOVA and linear regression analyses, which correspond to the standard widely used F test for η ^ 2 and R 2 , respectively. A simulation study is conducted to examine the Type I error rates and statistical power of the tests, and a comparison is made with an alternative Bayesian testing approach. The results indicate that the proposed non-inferiority test is a potentially useful tool for 'testing the null'.

Original languageEnglish
Pages (from-to)64-89
Number of pages26
JournalBritish Journal of Mathematical and Statistical Psychology
Volume74
Issue number1
Early online date13 Feb 2020
DOIs
Publication statusPublished - Feb 2021

Keywords

  • ANOVA
  • equivalence testing
  • F test
  • linear regression
  • non-inferiority testing

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