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Determining a lack of association between an outcome variable and a number ofdifferent explanatory variables is frequently necessary in order to disregard aproposed model (i.e., to confirm the lack of an association between an outcomeand predictors). Despite this, the literature rarely offers information about,or technical recommendations concerning, the appropriate statisticalmethodology to be used to accomplish this task. This paper introducesnon-inferiority tests for ANOVA and linear regression analyses, that correspondto the standard widely used $F$-test for $\hat{\eta}^2$ and $R^{2}$,respectively. A simulation study is conducted to examine the type I error ratesand statistical power of the tests, and a comparison is made with analternative Bayesian testing approach. The results indicate that the proposednon-inferiority test is a potentially useful tool for 'testing the null.'

Can we disregard the whole model? Omnibus non-inferiority testing for $R^{2}$ in multivariable linear regression and $\hat{\eta}^{2}$ in ANOVA