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

Frontiers in Psychology

Frontiers Media S.A.

effect sizes, power analysis, cohen's d, eta-squared, sample size planning

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      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.

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      Most cited references 27

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      Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses.

      G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.
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        Using confidence intervals in within-subject designs.

        We argue that to best comprehend many data sets, plotting judiciously selected sample statistics with associated confidence intervals can usefully supplement, or even replace, standard hypothesis-testing procedures. We note that most social science statistics textbooks limit discussion of confidence intervals to their use in between-subject designs. Our central purpose in this article is to describe how to compute an analogous confidence interval that can be used in within-subject designs. This confidence interval rests on the reasoning that because between-subject variance typically plays no role in statistical analyses of within-subject designs, it can legitimately be ignored; hence, an appropriate confidence interval can be based on the standard within-subject error term-that is, on the variability due to the subject × condition interaction. Computation of such a confidence interval is simple and is embodied in Equation 2 on p. 482 of this article. This confidence interval has two useful properties. First, it is based on the same error term as is the corresponding analysis of variance, and hence leads to comparable conclusions. Second, it is related by a known factor (√2) to a confidence interval of the difference between sample means; accordingly, it can be used to infer the faith one can put in some pattern of sample means as a reflection of the underlying pattern of population means. These two properties correspond to analogous properties of the more widely used between-subject confidence interval.
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          Combining effect size estimates in meta-analysis with repeated measures and independent-groups designs.

          When a meta-analysis on results from experimental studies is conducted, differences in the study design must be taken into consideration. A method for combining results across independent-groups and repeated measures designs is described, and the conditions under which such an analysis is appropriate are discussed. Combining results across designs requires that (a) all effect sizes be transformed into a common metric, (b) effect sizes from each design estimate the same treatment effect, and (c) meta-analysis procedures use design-specific estimates of sampling variance to reflect the precision of the effect size estimates.
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            Author and article information

            Affiliations
            Human Technology Interaction Group, Eindhoven University of Technology Eindhoven, Netherlands
            Author notes

            Edited by: Bernhard Hommel, Leiden University, Netherlands

            Reviewed by: Marjan Bakker, University of Amsterdam, Netherlands; Bruno Bocanegra, Erasmus University Rotterdam, Netherlands

            *Correspondence: Daniël Lakens, Human Technology Interaction Group, Eindhoven University of Technology, IPO 1.24, PO Box 513, 5600MB Eindhoven, Netherlands e-mail: d.lakens@ 123456tue.nl

            This article was submitted to Cognition, a section of the journal Frontiers in Psychology.

            Journal
            Front Psychol
            Front Psychol
            Front. Psychol.
            Frontiers in Psychology
            Frontiers Media S.A.
            1664-1078
            26 November 2013
            2013
            : 4
            3840331
            10.3389/fpsyg.2013.00863
            Copyright © 2013 Lakens.

            This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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            Figures: 0, Tables: 3, Equations: 26, References: 45, Pages: 12, Words: 10635
            Categories
            Psychology
            Review Article

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