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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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          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 references19

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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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            Generalized eta and omega squared statistics: measures of effect size for some common research designs.

            The editorial policies of several prominent educational and psychological journals require that researchers report some measure of effect size along with tests for statistical significance. In analysis of variance contexts, this requirement might be met by using eta squared or omega squared statistics. Current procedures for computing these measures of effect often do not consider the effect that design features of the study have on the size of these statistics. Because research-design features can have a large effect on the estimated proportion of explained variance, the use of partial eta or omega squared can be misleading. The present article provides formulas for computing generalized eta and omega squared statistics, which provide estimates of effect size that are comparable across a variety of research designs.
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              Inference by eye: confidence intervals and how to read pictures of data.

              Wider use in psychology of confidence intervals (CIs), especially as error bars in figures, is a desirable development. However, psychologists seldom use CIs and may not understand them well. The authors discuss the interpretation of figures with error bars and analyze the relationship between CIs and statistical significance testing. They propose 7 rules of eye to guide the inferential use of figures with error bars. These include general principles: Seek bars that relate directly to effects of interest, be sensitive to experimental design, and interpret the intervals. They also include guidelines for inferential interpretation of the overlap of CIs on independent group means. Wider use of interval estimation in psychology has the potential to improve research communication substantially. ((c) 2005 APA, all rights reserved).

                Author and article information

                Front Psychol
                Front Psychol
                Front. Psychol.
                Frontiers in Psychology
                Frontiers Media S.A.
                26 November 2013
                : 4
                : 863
                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.

                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.

                : 13 July 2013
                : 30 October 2013
                Page count
                Figures: 0, Tables: 3, Equations: 26, References: 45, Pages: 12, Words: 10635
                Review Article

                Clinical Psychology & Psychiatry
                cohen's d,eta-squared,effect sizes,sample size planning,power analysis


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