Calcular e apresentar tamanhos do efeito em trabalhos científicos (3): Guia para reportar os tamanhos do efeito para análises de regressão e ANOVAs

Helena Maria Amaral Espirito Santo; Fernanda Daniel

doi:10.31211/rpics.2018.4.1.72

Autores

Helena Maria Amaral Espirito Santo Centro de Investigação Interdisciplinar Psicossocial, Instituto Superior Miguel Torga; Centro de Investigação do Núcleo de Estudos e Intervenção Cognitivo-Comportamental Universidade de Coimbra, Portugal https://orcid.org/0000-0003-2625-3754
Fernanda Daniel Centro de Investigação Interdisciplinar Psicossocial, Instituto Superior Miguel Torga, Coimbra, Portugal

DOI:

https://doi.org/10.31211/rpics.2018.4.1.72

Palavras-chave:

ANOVA, Análise de regressão, Tamanho do efeito, Valor p

Resumo

No primeiro número da Revista Portuguesa de Investigação Comportamental e Social foi revista a importância de calcular, indicar e interpretar os tamanhos do efeito para as diferenças de médias de dois grupos (família d dos tamanhos do efeito). Os tamanhos do efeito são uma métrica comum que permite comparar os resultados das análises estatísticas de diferentes estudos, informando sobre o impacto de um fator na variável em estudo e sobre a associação entre variáveis. Depois de rever os tamanhos do efeito para as diferenças de médias entre dois grupos (Espirito-Santo e Daniel, 2015) e a maior parte da família r (Espirito-Santo e Daniel, 2017), faltava rever os tamanhos do efeito para a análise da variância. A análise da variância pode ser compreendida como uma extensão da família d a mais de dois grupos (ANOVA) ou como uma subfamília r em que a proporção da variabilidade é imputável a um ou mais fatores. Na subfamília r revista neste estudo, analisa-se a mudança na variável dependente que decorre de uma ou mais variáveis independentes. Esta análise debruça-se sobre os modelos lineares gerais, onde se incluem os modelos de regressão e a ANOVA. Este artigo fornece as fórmulas para calcular os tamanhos do efeito mais comuns, revendo os conceitos básicos sobre as estatísticas e facultando exemplos ilustrativos computados no Statistical Package for the Social Sciences (SPSS). As orientações para a interpretação dos tamanhos do efeito são também apresentadas, assim como as cautelas no seu uso. Adicionalmente, o artigo acompanha-se de uma folha de cálculo em Excel para facilitar e agilizar os cálculos aos interessados.

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Referências

American Psychological Association. (2010). Publication manual of the American Psychological Association (6th ed.). Washington, DC: American Psychological Association. [Google Scholar]

Bakeman, R. (2005). Recommended effect size statistics for repeated measures designs. Behavior Research Methods, 37(3), 379-384. [Google Scholar]

Berben, L., Sereika, S. M., & Engberg, S. (2012). Effect size estimation: methods and examples. International Journal of Nursing Studies, 49(8), 1039-1047. [Google Scholar] [CrossRef]

Bewick, V., Cheek, L., & Ball, J. (2003). Statistics review 7: Correlation and regression. Critical Care, 7(6), 451-459. [Google Scholar] [CrossRef]

Bezeau, S., & Graves, R. (2001). Statistical power and effect sizes of clinical neuropsychology research. Journal of Clinical and Experimental Neuropsychology (Neuropsychology, Development and Cognition: Section A), 23(3), 399-406. [Google Scholar]

Carroll, R. M., & Nordholm, L. A. (1975). Sampling characteristics of Kelley“s ε2 and Hays” ω2. Educational and Psychological Measurement, 35(3), 541-554. [Google Scholar] [CrossRef]

Cohen, J. (1973). Eta-squared and partial eta-squared in fixed factor ANOVA designs. Educational and Psychological Measurement, 33, 107-112. [Google Scholar] [CrossRef]

Cohen, J. (1992a). A power primer. Psychological Bulletin, 112(1), 155-159. [Google Scholar] [CrossRef]

Cohen, J. (1992b). Statistical power analysis. Current Directions in Psychological Science, 1(3), 98-101. [Google Scholar] [CrossRef]

Cumming, G. (2012). Understanding the new statistics. New York: Routledge. [Google Scholar]

Ellis, P. D. (2010). The essential guide to effect sizes. Cambridge: Cambridge University Press. [Google Scholar]

Erceg-Hurn, D. M., & Mirosevich, V. M. (2008). Modern robust statistical methods: An easy way to maximize the accuracy and power of your research. The American Psychologist, 63(7), 591-601. [Google Scholar] [CrossRef]

Espirito-Santo, H., & Daniel, F. B. (2015). Calcular e apresentar tamanhos do efeito em trabalhos científicos (1): As limitações do p < 0,05 na análise de diferenças de médias de dois grupos [Calculating and reporting effect sizes on scientific papers (1): p < 0.05 limitations in the analysis of mean differences of two groups]. Revista Portuguesa de Investigação Comportamental e Social, 1(1), 3-16. [Google Scholar] [CrossRef]

Espirito-Santo, H., & Daniel, F. (2017). Calcular e apresentar tamanhos do efeito em trabalhos científicos (2): Guia para reportar a força das relações [Calculating and reporting effect sizes on scientific papers (2): Guide to report the strength of relationships]. Revista Portuguesa de Investigação Comportamental e Social, 3(1), 53-64. [Google Scholar] [CrossRef]

Ferguson, C. J. (2009). An effect size primer: A guide for clinicians and researchers. Professional Psychology: Research and Practice, 40(5), 532-538. [Google Scholar] [CrossRef]

Field, A. (2005). Effect sizes. [PDF]

Field, A., Miles, J., & Field, Z. (2012). Discovering statistics using R. London: Sage. [Google Scholar]

Fisher, R. A. (1925). Statistical methods for research workers. Edinburgh: Oliver & Boyd. [Google Scholar]

Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: Current use, calculations, and interpretation. Journal of Experimental Psychology: General, 141(1), 2-18. [Google Scholar] [CrossRef]

Glass, G. V., & Hakstian, A. R. (1969). Measures of association in comparative experiments: Their development and interpretation. American Educational Research Journal, 6(3), 403-414. [Google Scholar] [CrossRef]

Haase, R. F., Waechter, D. M., & Solomon, G. S. (1982). How significant is a significant difference? Average effect size of research in counseling psychology. Journal of Counseling Psychology, 29(1), 58-65. [Google Scholar] [CrossRef]

Hair, J., Black, B., Babin, B., & Anderson, R. (2009). Multivariate data analysis (7th ed.). Upper Saddle River: Pearson Higher Ed. [Google Scholar]

Hays, W. L. (1963). Statistics for psychologists. New York: Holt, Rinehart and Winston. [Google Scholar]

Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational and Behavioral Statistics, 6(2), 107-128. [Google Scholar] [CrossRef]

Herzberg, P. A. (1969). The parameters of cross-validation. Richmond, VA: William Byrd Press. [Google Scholar]

Ialongo, C. (2016). Understanding the effect size and its measures. Biochemia Medica, 26(2), 150-163. [Google Scholar] [CrossRef]

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1-24. [Google Scholar] [CrossRef]

Kelley, T. L. (1935). An unbiased correlation ratio measure. Proceedings of the National Academy of Sciences of the United States of America, 21(9), 554-559. [Google Scholar] [PMC]

Kennedy, J. J. (1970). The eta coefficient in complex ANOVA designs. Educational and Psychological Measurement, 30(4), 885-889. [Google Scholar] [CrossRef]

Keppel, G., & Wickens, T. D. (2004). Design and analysis: A researcher's handbook (4th ed.). New Jersey: Pearson. [Google Scholar]

Keren, G., & Lewis, C. (1969). Partial omega squared for ANOVA designs. Educational and Psychological Measurement, 39(1), 119-128. [Google Scholar] [CrossRef]

Keselman, H. J. (1975). A Monte Carlo investigation of three estimates of treatment magnitude: Epsilon squared, eta squared, and omega squared. Canadian Psychological Review/Psychologie Canadienne, 16(1), 44-48. [Google Scholar] [CrossRef]

Keselman, H. J., Algina, J., Lix, L. M., Wilcox, R. R., & Deering, K. N. (2008). A generally robust approach for testing hypotheses and setting confidence intervals for effect sizes. Psychological Methods, 13(2), 110-129. [Google Scholar] [CrossRef]

Kirk, R. E. (1996). Practical significance: A concept whose time has come. Educational and Psychological Measurement, 56(5), 746-759. [Google Scholar] [CrossRef]

Kline, R. B. (2013). Beyond significance testing: Reforming data analysis methods in behavioral research (2nd ed.). Washington, DC: American Psychological Association. [Google Scholar]

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4(863), 1-12. [Google Scholar] [CrossRef]

Lenhard, W., & Lenhard, A. (2016). Calculation of effect sizes. [Google Scholar] [CrossRef]

Levine, T. R., & Hullett, C. R. (2002). Eta squared, partial eta squared, and misreporting of effect size in communication research. Human Communication Research, 28(4), 612-625. [Google Scholar] [CrossRef]

Lipsey, M. W., Puzio, K., Yun, C., Hebert, M. A., Steinka-Fry, K., Cole, M. W., . . . Busick, M. D. (2012). Translating the statistical representation of the effects of education interventions into more readily interpretable forms. National Center for Special Education Research, Institute of Education Sciences. [Google Scholar] [URL]

Lipsey, M. W., & Wilson, D. B. (2001). Practical meta-analysis. New York: Sage Publications, Inc. [Google Scholar]

Lyons, L. C., & Morris, W. A. (2018). The meta analysis calculator. [Google Scholar] [URL]

Okada, K. (2013). Is omega squared less biased? A comparison of three major effect size indices in one-way anova. Behaviormetrika, 40(2), 129-147. [Google Scholar] [CrossRef]

Olejnik, S., & Algina, J. (2000). Measures of effect size for comparative studies: Applications, interpretations, and limitations. Contemporary Educational Psychology, 25(3), 241-286. [Google Scholar] [CrossRef]

Olejnik, S., & Algina, J. (2003). Generalized eta and omega squared statistics: Measures of effect size for some common research designs. Psychological Methods, 8(4), 434-447. [Google Scholar] [CrossRef]

Pallant, J. (2011). SPSS: Survival manual (4th ed.). Crows Nest, NSW: Allen & Unwin. [Google Scholar]

Pampel, F. C. (2000). Logistic regression: A primer. Thousand Oaks: SAGE Publications. [Google Scholar]

Pearson, K. (1905). Mathematical contributions to the theory of evolution. XIV. On the general theory of skew correlation and non-linear regression. London: Dulau. [Google Scholar]

Pierce, C. A., Block, R. A., & Aguinis, H. (2004). Cautionary note on reporting eta-squared values from multifactor ANOVA designs. Educational and Psychological Measurement, 64(6), 916-924. [Google Scholar] [CrossRef]

Richardson, J. T. E. (2011). Eta squared and partial eta squared as measures of effect size in educational research. Educational Research Review, 6(2), 135-147. [Google Scholar] [CrossRef]

Roberts, J. K., & Henson, R. K. (2002). Correction for bias in estimating effect sizes. Educational and Psychological Measurement, 62(2), 241-253. [Google Scholar] [CrossRef]

Rosenthal, R. (1991). Meta-analytic procedures for social research (Revised). Newbury Park: Sage. [Google Scholar]

Rosenthal, R. (1994). Science and ethics in conducting, analyzing, and reporting psychological research. Psychological Science, 5(3), 127-134. [Google Scholar] [CrossRef]

Rosnow, R. L., & Rosenthal, R. (1989). Statistical procedures and the justification of knowledge in psychological science. The American Psychologist, 44(10), 1276-1284. [Google Scholar] [CrossRef]

Rosnow, R. L., Rosenthal, R., & Rubin, D. B. (2000). Contrasts and correlations in effect-size estimation. Psychological Science, 11(6), 446-453. [Google Scholar] [CrossRef]

Sechrest, L., & Yeaton, W. H. (2016). Magnitudes of experimental effects in social science research. Evaluation Review, 6(5), 579-600. [Google Scholar] [CrossRef]

Smithson, M. (2003). Confidence intervals. Thousand Oaks, CA: Sage. [Google Scholar]

Snyder, P., & Lawson, S. (1993). Evaluating results using corrected and uncorrected effect size estimates. The Journal of Experimental Education, 61(4), 334-349. [Google Scholar] [JSTOR]

Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9(2), 164-182. [Google Scholar]

Steiger, J. H., & Fouladi, R. T. (2016). Noncentrality interval estimation and the evaluation of statistical models. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.), What if there were no significance tests? (pp. 197-229). Routledge: Routledge. [Google Scholar]

Stevens, J. P. (2007). Intermediate statistics (3rd ed.). New York: Lawrence Erlbaum Associates. [Google Scholar]

Steyn, H. S. Jr., & Ellis, S. M. (2009). Estimating an effect size in one-way multivariate analysis of variance (MANOVA). Multivariate Behavioral Research, 44(1), 106-129. [Google Scholar] [CrossRef]

Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (5th ed.). Boston: Pearson Education. [Google Scholar]

Thompson, B. (2002). "Statistical,” “practical,” and “clinical”: How many kinds of significance do counselors need to consider?. Journal of Counseling & Development, 80(1), 64-71. [Google Scholar] [CrossRef]

Thompson, B. (2007). Effect sizes, confidence intervals, and confidence intervals for effect sizes. Psychology in the Schools, 44(5), 423-432. [Google Scholar] [CrossRef]

Vacha-Haase, T., & Thompson, B. (2004). How to estimate and interpret various effect sizes. Journal of Counseling Psychology, 51(4), 473-481. [Google Scholar] [CrossRef]

Vaughan, G. M., & Corballis, M. C. (1969). Beyond tests of significance: Estimating strength of effects in selected ANOVA designs. Psychological Bulletin, 72(3), 204-213. [Google Scholar] [CrossRef]

Wherry, R. J. (1931). A new formula for predicting the shrinkage of the coefficient of multiple correlation. The Annals of Mathematical Statistics, 2(4), 440-457. [Google Scholar] [CrossRef]

Wilkinson, L., & Task Force on Statistical Inference., (1999). Statistical methods in psychology journals: Guidelines and explanations. The American Psychologist, 54(8), 594-604. [Google Scholar]

Wilson, D. B. (2010). Meta-analysis stuff. [Google Scholar] [URL]

Wilson, D. B. (2018). Practical meta-analysis effect size calculator. [Google Scholar] [URL]

Zhang, G., & Algina, J. (2011). A robust Root Mean Square Standardized Effect Size in one-way fixed-effects ANOVA. Journal of Modern Applied Statistical Methods, 10(1), 77-96. [Google Scholar] [CrossRef]