Determining Negligible Associations in Regression

Abstract

Psychological research is rife with inappropriately concluding "no effect" between predictors and outcome in regression models following statistically nonsignificant results. However, this approach is methodologically flawed because failing to reject the null hypothesis using traditional, difference-based tests does not mean the null is true. Using this approach leads to high rates of incorrect conclusions that flood psychological literature. This paper introduces a novel, methodologically sound alternative. In this paper, we demonstrate how an equivalence testing approach can be applied to multiple regression (which we refer to here as "negligible effect testing") to evaluate whether a predictor (measured in standardized or unstandardized units) has a negligible association with the outcome. In the first part of the paper, we evaluate the performance of two equivalence-based techniques and compare them to the traditional, difference-based test via a Monte Carlo simulation study. In the second part of the paper, we use examples from the literature to illustrate how researchers can implement the recommended negligible effect testing methods in their own work using open-access and user-friendly tools (negligible R package and Shiny app). Finally, we discuss how to report and interpret results from negligible effect testing and provide practical recommendations for best research practices based on the simulation results. All materials, including R code, results, and additional resources, are publicly available on the Open Science Framework (OSF): osf.io/w96xe/.

How are gender counter-stereotypical adolescents evaluated by their peers? Investigating the backlash effect in French schools

“…Instead, equivalence testing is required to determine a lack of effect (or rather a negligible effect), which requires selecting a smallest effect size of interest/that is meaningful for the research question (Lakens et al, 2018). Recommendations of best practice for using equivalence testing suggest that the smallest effect size of interest should be chosen before conducting hypotheses tests (Alter & Counsell, 2023). Thus, a future area of research for studies focused on the backlash effect should be to make use of equivalence testing and its ability to make sense of non-significant and/or negligible effects.…”

Simulation-Based Power Analyses for the Smallest Effect Size of Interest: A Confidence-Interval Approach for Minimum-Effect and Equivalence Testing

“…For each raw mean difference, I provide plots with the power for each test for each sample size, as done in previous research (Alter & Counsell, 2023). Simulations for a raw mean difference of 0 showed that the “statistical power” 9 for NHST and minimum-effects testing is .05 and 0, respectively, which is in line with the given Type 1 error rate (see Fig.…”

“…That is, the benefit of simulations and the CI-focused approach is that it can be readily adapted to different areas of research and study designs (Smiley et al, 2023). When using the CI-focused approach, researchers can conduct power analyses for equivalence and minimum-effect tests for any type of study design (e.g., see "negligible" package of Alter & Counsell, 2023). As long as the researchers have an unstandardized SESOI, variation of their measurement procedure, and their study design, they can the simulation-based approach to calculate their sample size based on their justified significance level and desired statistical power.…”

“… 2. For information on why a 90% CI is used, see Alter and Counsell (2023), Metzler (1974), or Seaman and Serlin (1998). …”

Attachment relationship quality with mothers and fathers and child temperament: An individual participant data meta-analysis.

“…We followed guidelines by Judd et al (2017) to compute Cohen’s d effect size derived from mixed-model designs, and calculated 95% confidence intervals (CIs) based on the estimated effects and p values (Altman & Bland, 2011). Given that traditional null hypothesis testing only allows inferences about the presence of effects but not about their absence, we followed nonsignificant temperament predictor estimates with equivalence testing, using the “negligible” package (Alter & Counsell, 2023) in R, with equivalence bounds set for field-specific small effect sizes (Schuengel et al, 2021; −0.20 < d < 0.20) and α of .05. In the current investigation, a significant equivalence test indicates that an absence of a significant association between negative emotionality and the number of attachment relationship classifications is trivially small, allowing us to interpret the observed effect as negligible.…”