Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs

Abstract

Effect sizes are the most important outcome of empirical studies. Most articles on effect sizes highlight their importance to communicate the practical significance of results. For scientists themselves, effect sizes are most useful because they facilitate cumulative science. Effect sizes can be used to determine the sample size for follow-up studies, or examining effects across studies. This article aims to provide a practical primer on how to calculate and report effect sizes for t-tests and ANOVA's such that effect sizes can be used in a-priori power analyses and meta-analyses. Whereas many articles about effect sizes focus on between-subjects designs and address within-subjects designs only briefly, I provide a detailed overview of the similarities and differences between within- and between-subjects designs. I suggest that some research questions in experimental psychology examine inherently intra-individual effects, which makes effect sizes that incorporate the correlation between measures the best summary of the results. Finally, a supplementary spreadsheet is provided to make it as easy as possible for researchers to incorporate effect size calculations into their workflow.

A trauma-focused approach for patients with tinnitus: the effectiveness of eye movement desensitization and reprocessing – a multicentre pilot trial

“…Lakens (2013) states that Cohen’s d z is an accurate description of effect size in within-group designed research as it takes the correlation between measurements into account, whereas Cohen’s d is used to describe the standardized mean difference of an effect between independent groups. Interpretations of effect sizes of d and d z are equivalent: small ( d  = .2), medium ( d  = .5) and large ( d  = .8).…”

A three-dimensional spatial characterization of the crossed-hands deficit

“…To quantify the magnitude of the effects we report, we provide partial eta squared values for F-tests, which assesses the proportion of variance accounted for by that effect, partialling out the effects of other main effects and interactions. For t-tests, we provide Cohen's dz, which givens the standardized mean difference between conditions (Lakens, 2013).…”

Hand selection in a preferential reaching task: The effects of object location, orientation, and task intention in preadolescent children

“…Only significant results with large effect sizes (${\eta }_p^2$ ≥ 0.14; Lakens, 2013) will be discussed in detail. All other nonsignificant effects and significant effects with small and medium effect sizes can be found in Table 1.…”