Eta-Squared and Partial Eta-Squared in Fixed Factor Anova Designs:

doi:10.1177/001316447303300111

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Eta-Squared and Partial Eta-Squared in Fixed Factor Anova Designs:

Journal Article•DOI•

Eta-Squared and Partial Eta-Squared in Fixed Factor Anova Designs:

Jacob Cohen¹•Institutions (1)

York University¹

01 Apr 1973-Educational and Psychological Measurement (Sage Publications)-Vol. 33, Iss: 1, pp 107-112

About: This article is published in Educational and Psychological Measurement.The article was published on 1973-04-01. It has received 1104 citations till now. The article focuses on the topics: One-way analysis of variance.

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Journal Article•DOI•

Eta squared and partial eta squared as measures of effect size in educational research

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John T. E. Richardson¹•Institutions (1)

Open University¹

01 Jan 2011-Educational Research Review

TL;DR: In the educational research literature, partial eta squared measures the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable as discussed by the authors.

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1,931 citations

Wisdom of crowds for robust gene network inference

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Daniel Marbach, James C. Costello, Robert Küffner, Nicole M. Vega, Robert J. Prill, Diogo M. Camacho, Kyle R. Allison, Andrej Aderhold, Richard Bonneau, Yukun Chen, James J. Collins, Francesca Cordero, Martin Crane, Frank Dondelinger, Mathias Drton, Roberto Esposito, Rina Foygel, Alberto de la Fuente, Jan Gertheiss, Pierre Geurts, Alex Greenfield, Marco Grzegorczyk, Anne-Claire Haury, Benjamin Holmes, Torsten Hothorn, Dirk Husmeier, Vân Anh Huynh-Thu, Alexandre Irrthum, Manolis Kellis, Guy Karlebach, Sophie Lèbre, Vincenzo De Leo, Aviv Madar, Subramani Mani, Fantine Mordelet, Harry Ostrer, Zhengyu Ouyang, Ravi Pandya, Tobias Petri, Andrea Pinna, Christopher S. Poultney, Serena Rezny, Heather J. Ruskin, Yvan Saeys, Ron Shamir, Alina Sîrbu, Mingzhou Song, Nicola Soranzo, Alexander Statnikov, Gustavo Stolovitzky, Nicci Vega, Paola Vera-Licona, Jean-Philippe Vert, Alessia Visconti, Haizhou Wang, Louis Wehenkel, Lukas Windhager, Yang Zhang, Ralf Zimmer - Show less +55 more

01 Jul 2012

TL;DR: A comprehensive blind assessment of over 30 network inference methods on Escherichia coli, Staphylococcus aureus, Saccharomyces cerevisiae and in silico microarray data defines the performance, data requirements and inherent biases of different inference approaches, and provides guidelines for algorithm application and development.

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Abstract: Reconstructing gene regulatory networks from high-throughput data is a long-standing challenge. Through the Dialogue on Reverse Engineering Assessment and Methods (DREAM) project, we performed a comprehensive blind assessment of over 30 network inference methods on Escherichia coli, Staphylococcus aureus, Saccharomyces cerevisiae and in silico microarray data. We characterize the performance, data requirements and inherent biases of different inference approaches, and we provide guidelines for algorithm application and development. We observed that no single inference method performs optimally across all data sets. In contrast, integration of predictions from multiple inference methods shows robust and high performance across diverse data sets. We thereby constructed high-confidence networks for E. coli and S. aureus, each comprising ∼1,700 transcriptional interactions at a precision of ∼50%. We experimentally tested 53 previously unobserved regulatory interactions in E. coli, of which 23 (43%) were supported. Our results establish community-based methods as a powerful and robust tool for the inference of transcriptional gene regulatory networks.

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1,355 citations

Journal Article•DOI•

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

[...]

Stephen Olejnik¹, James Algina²•Institutions (2)

Georgia College & State University¹, Florida College²

01 Dec 2003-Psychological Methods

TL;DR: In this article, the authors provide formulas for computing generalized eta and omega squared statistics, which provide estimates of effect size that are comparable across a variet yo f research designs, but do not consider the effect that design features of the study have on the size of these statistics.

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Abstract: 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 variet yo f research designs. It is often argued that researchers can enhance the presentation of their research findings by including an effect-size measure along with a test of statistical significance. An effect-size measure is a standardized index and estimates a parameter that is independent of sample size and quantifies the magnitude of the difference between populations or the relationship between explanatory and response variables. Two broad

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1,281 citations

Cites methods from "Eta-Squared and Partial Eta-Squared..."

...Cohen (1973) cautioned however that the use of partial eta squared may be inappropriate and can in fact be misleading when the design includes a blocking factor....
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Journal Article•DOI•

Eta Squared, Partial Eta Squared, and Misreporting of Effect Size in Communication Research

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Timothy R. Levine¹, Craig R. Hullett²•Institutions (2)

Michigan State University¹, University of Wisconsin-Madison²

01 Oct 2002-Human Communication Research

TL;DR: In this paper, a mislabeling problem in the statistical software SPSS (1998) is identified, and a list of suggestions for researchers is then offered, as well as the implications of the reporting errors.

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Abstract: Communication researchers, along with social scientists from a variety of disciplines, are increasingly recognizing the importance of reporting effect sizes to augment significance tests. Serious errors in the reporting of effect sizes, however, have appeared in recently published articles. This article calls for accurate reporting of estimates of effect size. Eta squared (η 2 ) is the most commonly reported estimate of effect sized for the ANOVA. The classical formulation of eta squared (Pearson, 1911; Fisher, 1928) is distinguished from the lesser known partial eta squared (Cohen, 1973), and a mislabeling problem in the statistical software SPSS (1998) is identified. What SPSS reports as eta squared is really partial eta squared. Hence, researchers obtaining estimates of eta squared from SPSS are at risk of reporting incorrect values. Several simulations are reported to demonstrate critical issues. The strengths and limitations of several estimates of effect size used in ANOVA are discussed, as are the implications of the reporting errors. A list of suggestions for researchers is then offered.

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948 citations

Cites background or methods or result from "Eta-Squared and Partial Eta-Squared..."

...For example, Rosenthal and Rosnow (1985, 1991) provide the following formula for eta squared: η2 = SSbetween/SSbetween + SSerror (2) Although these two formulas yield the same result in one-way ANOVAs (where SStotal = SSbetween + SSerror), they produce different results in more complex ANOVAs (Cohen, 1973; Kennedy, 1970; Sechrest &Yeaton, 1982), and can in fact be widely discrepant....
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...Values labeled as eta squared on (at least some) SPSS printouts are really partial eta squared (Cohen, 1973), and consequently, researchers may often be unknowingly reporting partial eta squared values as if they were eta squared....
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...Because partial eta squared values may, in some cases, be widely discrepant from the values of omega squared, epsilon squared, and eta squared, these reporting errors may lead to serious substantive errors in the interpretation of results....
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...Situations such as this led Cohen (1973) to argue that partial eta squared can be more comparable when additional manipulated or control variables are added to a design....
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...Researchers who report partial eta squared should read Cohen (1973) and Kennedy (1970) so they are informed of its proper use, and should report eta squared in addition to partial eta squared....
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Journal Article•DOI•

Functional Brain Networks Are Dominated by Stable Group and Individual Factors, Not Cognitive or Daily Variation

[...]

Caterina Gratton¹, Timothy O. Laumann¹, Ashley N. Nielsen¹, Deanna J. Greene¹, Evan M. Gordon², Evan M. Gordon³, Adrian W. Gilmore¹, Steven M. Nelson, Rebecca S. Coalson¹, Abraham Z. Snyder¹, Bradley L. Schlaggar¹, Nico U.F. Dosenbach¹, Steven E. Petersen¹ - Show less +9 more•Institutions (3)

Washington University in St. Louis¹, University of Texas at Dallas², Baylor University³

18 Apr 2018-Neuron

TL;DR: It is concluded that functional networks are suited to measuring stable individual characteristics, suggesting utility in personalized medicine.

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614 citations

Cites methods from "Eta-Squared and Partial Eta-Squared..."

...We then examined the variance explained (R2) by the full model, as well as the variance explained from each factor (u2, calculated as in Cohen, 1973): u2 = SSeffect dfeffect MSerror MSerror +SStotal Results from each edge are represented in functional network matrices, as well as for each parcel…...
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References

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Book•

Statistical Power Analysis for the Behavioral Sciences

[...]

Jacob Cohen¹•Institutions (1)

University of North Carolina at Chapel Hill¹

01 Dec 1969

TL;DR: The concepts of power analysis are discussed in this paper, where Chi-square Tests for Goodness of Fit and Contingency Tables, t-Test for Means, and Sign Test are used.

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Abstract: Contents: Prefaces. The Concepts of Power Analysis. The t-Test for Means. The Significance of a Product Moment rs (subscript s). Differences Between Correlation Coefficients. The Test That a Proportion is .50 and the Sign Test. Differences Between Proportions. Chi-Square Tests for Goodness of Fit and Contingency Tables. The Analysis of Variance and Covariance. Multiple Regression and Correlation Analysis. Set Correlation and Multivariate Methods. Some Issues in Power Analysis. Computational Procedures.

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115,069 citations

"Eta-Squared and Partial Eta-Squared..." refers background in this paper

...In the recent efforts to raise psychology’s awareness of effect sizes and their measurement by the ptesent author (Cohen, 1965, 1969) and others (Hays, 1963; Kerlinger, 1964; Friedman, 1968), proportion of variance measures have a centrally important role (Cohen, 1968, 1969)....
[...]

Book•

Foundations of Behavioral Research

[...]

Fred N. Kerlinger, Howard B. Lee

01 Jan 1969

TL;DR: In this article, the authors focus on the relationship between the research problems and the design of the research, and emphasize the fundamentals of understanding how to solve a scientific research problem, focusing upon the relationships between the problems and their solutions.

...read moreread less

Abstract: First published in 1964, this text has set the standard for other texts in the field of behavioral research methodology. It emphasises the fundamentals of understanding how to solve a scientific research problem, focusing upon the relationship between the research problems and the design of the research. This edition has more examples from psychology, sociology, and education than the previous edition and places a greater emphasis on multivariate approaches and methods.

...read moreread less

8,931 citations

"Eta-Squared and Partial Eta-Squared..." refers background in this paper

...In the recent efforts to raise psychology’s awareness of effect sizes and their measurement by the ptesent author (Cohen, 1965, 1969) and others (Hays, 1963; Kerlinger, 1964; Friedman, 1968), proportion of variance measures have a centrally important role (Cohen, 1968, 1969)....
[...]

Book•

Statistics for psychologists

[...]

William Lee Hays

01 Jan 1963

2,041 citations

"Eta-Squared and Partial Eta-Squared..." refers background in this paper

...In the recent efforts to raise psychology’s awareness of effect sizes and their measurement by the ptesent author (Cohen, 1965, 1969) and others (Hays, 1963; Kerlinger, 1964; Friedman, 1968), proportion of variance measures have a centrally important role (Cohen, 1968, 1969)....
[...]

Journal Article•DOI•

Multiple regression as a general data-analytic system.

[...]

Jacob Cohen¹•Institutions (1)

York University¹

01 Dec 1968-Psychological Bulletin

TL;DR: In this article, techniques for using multiple regression (MR) as a general variance-accounting procedure of great flexibility, power, and fidelity to research aims in both manipulative and observational psychological research are presented.

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Abstract: Techniques for using multiple regression (MR) as a general variance-accounting procedure of great flexibility, power, and fidelity to research aims in both manipulative and observational psychological research are presented. As a prelude, the identity of MR and fixed-model analysis of variance/covariance (AV/ACV) is sketched. This requires an exposition of means of expressing nominal scale (qualitative) data as independent variables in MR. Attention is given to methods for handling interactions, curvilinearity, missing data, and covariates, for either uncorrelated or correlated independent variables in MR. Finally, the relative roles of AV/ACV and MR in data analysis are described, and the practical advantages of the latter are set forth.

...read moreread less

1,109 citations

"Eta-Squared and Partial Eta-Squared..." refers background in this paper

...In the recent efforts to raise psychology’s awareness of effect sizes and their measurement by the ptesent author (Cohen, 1965, 1969) and others (Hays, 1963; Kerlinger, 1964; Friedman, 1968), proportion of variance measures have a centrally important role (Cohen, 1968, 1969)....
[...]

Journal Article•DOI•

Foundations of Behavioral Research

[...]

Rex Stockton, Fred N. Kerlinger

01 Mar 1965-American Educational Research Journal

542 citations