Calcular e apresentar tamanhos do efeito em trabalhos científicos (2): Guia para reportar a força das relações

Palavras-chave: Tamanho do efeito, Coeficientes de correlação, Apresentação estatística, Interpretação estatística

Resumo

No primeiro número da Revista Portuguesa de Investigação Comportamental e Social foi descrita a importância de calcular, indicar e interpretar os tamanhos do efeito para as diferenças de médias de dois grupos. A RPICS pretende continuar a alertar para a importância de reportar os tamanhos do efeito para outros testes estatísticos. A magnitude da força das relações não foi indicada no artigo prévio e talvez não se saiba que a correlação é um tamanho do efeito. Assim, este artigo pretende fornecer algumas diretrizes aos autores sobre os procedimentos de cálculo do coeficiente de correlação de Pearson e alguns coeficientes de correlação para dados especiais (Ró de Spearman, Tau de Kendall, Ponto-bisserial e bisserial, Fi, V de Cramér e Eta).

Com esse objetivo, serão apresentadas as fórmulas, os passos no SPSS (Statistical Package for the Social Sciences), pressupostos e precauções, classificação dos valores e sua interpretação. Uma vez que o SPSS não computa todos os coeficientes referidos, nos suplementos ao artigo são incluídas cinco folhas de cálculo (3 formas de comparar correlações, correlações ponto-bisserial e bisserial e correção de correlações para amostras < 60).

Downloads

Não há dados estatísticos.

Biografias Autor

Helena Espírito Santo, Instituto Superior Miguel Torga
Professora do Instituto Superior Miguel TorgaCoordenadora do Departamento de Investigação & Desenvolvimento do ISMT 
Fernanda Daniel, Instituto Superior Miguel Torga, Coimbra, Portugal Centro de Estudos e Investigação em Saúde da Universidade de Coimbra
Professora Auxiliar do Instituto Superior Miguel Torga

Referências

Abrami, P. C., Cholmsky, P., & Gordon, R. (2001). Statistical analysis for the social sciences: An interactive approach. Boston: Allyn and Bacon. [Google Scholar]

Bartlett, J. W., Seaman, S. R., White, I. R., & Carpenter, J. R. (2015). Multiple imputation of covariates by fully conditional specification: Accommodating the substantive model. Statistical Methods in Medical Research, 24(4), 462-487. [Google Scholar] [CrossRef]

Beranuy, M., Oberst, U., Carbonell, X., & Chamarro, A. (2009). Problematic Internet and mobile phone use and clinical symptoms in college students: The role of emotional intelligence. Computers in Human Behavior, 25(5), 1182-1187. [Google Scholar] [CrossRef]

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]

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

Breaugh, J. A. (2003). Effect size estimation: Factors to consider and mistakes to avoid. Journal of Management, 29(1), 79-97. [Google Scholar] [CrossRef]

Brogden, H. E. (1949). A new coefficient: Application to biserial correlation and to estimation of selective efficiency. Psychometrika, 14(3), 169-182. [Google Scholar] [CrossRef]

Butters, M. A., Young, J. B., Lopez, O., Aizenstein, H. J., Mulsant, B. H., Reynolds, C. F., . . . Becker, J. T. (2008). Pathways linking late-life depression to persistent cognitive impairment and dementia. Dialogues in Clinical Neuroscience, 10(3), 345-357. [Google Scholar] [PMC]

Carroll, J. B. (1961). The nature of the data, or how to choose a correlation coefficient. Psychometrika, 26(4), 347-372. [Google Scholar] [CrossRef]

Chiu, S. I., Hong, F. Y., & Chiu, S. L. (2013). An analysis on the correlation and gender difference between college students' internet addiction and mobile phone addiction in Taiwan. ISRN Addiction, 2013, 10-1155. [Google Scholar] [CrossRef]

Cohen, B. H. (2001). Explaining psychological statistics (2nd ed.). New York, NY: Wiley. [Google Scholar]

Cohen, J. (1983). The cost of dichotomization. Applied Psychological Measurement, 7(3), 249-253. [Google Scholar] [CrossRef]

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). New York, NY: Lawrence Erlbaum Associates. [Google Scholar]

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

Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum Associates. [Google Scholar]

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple correlation/regression analysis for the behavioral sciences. Mahwah, NJ: Lawrence Erlbaum Associates. [Google Scholar]

Costa, M. D., Espirito-Santo, H., Simões, S. C., Correia, A. R., Almeida, R., Ferreira, L., Conde, Â., . . . Lemos, L. (2013). 1549 - Correlates of elderly loneliness [Abstract]. European Psychiatry, 28(1), 1-6. [Google Scholar] [CrossRef]

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

Durlak, J. A. (2009). How to select, calculate, and interpret effect sizes. Journal of Pediatric Psychology, 34(9), 917-928. [Google Scholar] [CrossRef]

Ellis, P. D. (2010). The essential guide to effect sizes: Statistical power, meta-analysis, and the interpretation of research results. Cambridge: Cambridge University Press. [Google Scholar] [CrossRef]

Enders, W. (2015). Applied econometric time series (4th ed.). Hoboken, NJ: Wiley & Sons, Inc. [Google Scholar]

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]

Ezekiel, M. (1929). The application of the theory of error to multiple and curvilinear correlation. Journal of the American Statistical Association, 24(165A), 99-104. [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]

Fermino, S., Espirito-Santo, H., Matreno, J., Daniel, F., Pena, I., Maia, S., . . . Gaspar, A. (2012). Diferenças sintomáticas, neuropsicológicas e sociodemográficas entre idosos com doença de Alzheimer e idosos com depressão [Symptomatic, neuropsychological, and sociodemographic differences between older people with Alzheimer's disease and older people with depression]. In Asociación Española de Psicología Conductual. (Ed.), Libro de Resúmenes de los Trabajos Aceptados en el V Congreso Internacional Y X Nacional de Psicología Clínica (p. 551). [Google Scholar] [Handle]

Fisher, R. A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10(4), 507-521. [Google Scholar] [CrossRef]

Fisher, R. A. (1921). On the “probable error” of a coefficient of correlation deduced from a small sample. Metron, 1, 3-32. [Google Scholar] [Handle]

Fisher, R. A. (1924). The distribution of the partial correlation coefficient. Metron, 3, 329-332. [Google Scholar] [Handle]

Fortenbaugh, F. C., DeGutis, J., Germine, L., Wilmer, J. B., Grosso, M., Russo, K., & Esterman, M. (2015). Sustained attention across the life span in a sample of 10000: Dissociating ability and strategy. Psychological Science, 26(9), 1497-1510. [Google Scholar] [CrossRef]

Glass, G. V., & Hopkins, K. D. (1995). Statistical methods in education and psychology (3rd ed.). Needham Heights, MA: Allyn & Bacon. [Google Scholar]

Goodwin, L. D., & Leech, N. L. (2006). Understanding correlation: Factors that affect the size of r. The Journal of Experimental Education, 74(3), 251-266. [Google Scholar] [CrossRef]

Granger, C. W. J., & Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2(2), 111-120. [Google Scholar] [CrossRef]

Gravetter, F. J., & Wallnau, L. B. (2013). Statistics for the behavioral sciences (9th ed.). Belmont, CA: Cengage Learning. [Google Scholar]

Gupta, D. S. (1960). Point biserial correlation coefficient and its generalization. Psychometrika, 25(4), 393-408. [Google Scholar] [CrossRef]

He, Y., Zaslavsky, A. M., Landrum, M. B., Harrington, D. P., & Catalano, P. (2010). Multiple imputation in a large-scale complex survey: A practical guide. Statistical Methods in Medical Research, 19(6), 653-670. [Google Scholar] [CrossRef]

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]

Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2002). Applied statistics for the behavioral sciences (5th ed.). Boston: Houghton Mifflin. [Google Scholar]

Horton, N. J., & Kleinman, K. P. (2007). Much ado about nothing. The American Statistician, 61(1), 79-90. [Google Scholar] [CrossRef]

Huff, D. (1993). How to lie with statistics. New York, NY: W. W. Norton & Company. [Google Scholar] [PDF]

IBM. (2013). IBM SPSS modeler 16 algorithms guide. IBM Corporation. [URL]

Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81-93. [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]

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]

MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7(1), 19-40. [Google Scholar] [CrossRef]

Matthews, R. (2000). Storks deliver babies (p = 0.008. Teaching Statistics, 22(2), 36-38. [Google Scholar] [CrossRef]

Mendonca, J. D., & Holden, R. R. (1996). Are all suicidal ideas closely linked to hopelessness?. Acta Psychiatrica Scandinavica, 93(4), 246-251. [Google Scholar] [CrossRef]

Nakagawa, S., & Freckleton, R. P. (2008). Missing inaction: The dangers of ignoring missing data. Trends in Ecology and Evolution, 23(11), 592-596. [Google Scholar] [CrossRef]

Napoleão, M., Monteiro, B., & Espirito-Santo, H. (2016). Qualidade subjetiva do sono, sintomas depressivos, sentimentos de solidão e institucionalização em pessoas idosas [Subjective sleep quality, depressive symptoms, feelings of loneliness, and institutionalization in elderly people]. Revista Portuguesa de Investigação Comportamental e Social, 2(2), 12-24. [Google Scholar] [CrossRef]

Nelsen, R. B. (2012). Kendall tau metric. In M. Hazewinkel (Ed.), Encyclopedia of mathematics. [Google Scholar] [URL]

Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York, NY: McGraw-Hill. [Google Scholar]

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]

Pallant, J. (2011). SPSS survival manual: A step by step guide to data analysis using SPSS for Windows (4th ed.). Crows Nest, NSW: Allen and Unwin. [Google Scholar]

Pearson, K. (1904). Report on certain enteric fever inoculation statistics. British Medical Journal, 2(2288), 1243-1246. [Google Scholar] [CrossRef]

Pearson, K. (1905). Mathematical contributions to the theory of evolution XIV: On the general theory of skew correlation and non-linear regression. Draper’s Company Research Memoirs, Biometric Series II. London: Dulau & Co. [Google Scholar] [URL]

Pituch, K. A., & Stevens, J. P. (2015). Applied multivariate statistics for the social sciences (6th ed.). New York, NY: Routledge. [Google Scholar]

Rodgers, J. L., & Nicewander, W. A. (1988). Thirteen ways to look at the correlation coefficient. The American Statistician, 42(1), 59-66. [Google Scholar] [CrossRef]

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

Rosenthal, R., & DiMatteo, M. R. (2001). Meta-analysis: Recent developments in quantitative methods for literature reviews. Annual Review of Psychology, 52(1), 59-82. [Google Scholar] [CrossRef]

Rosenthal, R., & Rubin, D. B. (1982). A simple, general purpose display of magnitude of experimental effect. Journal of Educational Psychology, 74(2), 166-169. [Google Scholar] [CrossRef]

Rosnow, R. L., & Rosenthal, R. (1996). Computing contrasts, effect sizes, and counternulls on other people's published data: General procedures for research consumers. Psychological Methods, 1(4), 331-340. [Google Scholar] [CrossRef]

Rovine, M. J., & Von Eye, A. (1997). A 14th way to look at a correlation coefficient: Correlation as the proportion of matches. The American Statistician, 51(1), 42-46. [Google Scholar] [CrossRef]

Rubin, D. B. (1996). Multiple imputation after 18+ Years. Journal of the American Statistical Association, 91(434), 473-489. [Google Scholar] [CrossRef]

Shieh, G. (2010). Estimation of the simple correlation coefficient. Behavior Research Methods, 42(4), 906-917. [Google Scholar] [CrossRef]

Simões, S., Ferreira, J. J., Braga, S., & Vicente, H. T. (2015). Bullying, vinculação e estilos educativos parentais em adolescentes do 3º ciclo do ensino básico [Bullying, attachment and parental rearing styles in adolescents from the 3rd cycle of basic school]. Revista Portuguesa de Investigação Comportamental e Social, 1(1), 30-41. [Google Scholar] [CrossRef]

Smith, B. B. (1923). Handbook of statistical terms and methods. Bureau of Agricultural Economics. [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] [CrossRef]

Sprinthall, R. C. (2003). Basic statistical analysis (7th ed.). Boston: Pearson Allyn & Bacon. [Google Scholar]

Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87(2), 245-251. [Google Scholar] [CrossRef]

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

Templeton, G. F. (2011). A two-step approach for transforming continuous variables to normal: Implications and recommendations for IS research (Vol. 28, pp. 41–58). Paper presented at the Communications of the Association for Information. [Google Scholar] [URL]

Thompson, B. (2006). Research synthesis: Effect sizes. In J. Green, G. Camilli & P. B. Elmore (Eds.), Handbook of complementary methods in education research (pp. 583-603). Washington, DC: Routledge. [Google Scholar]

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

Vogt, W. P. (1999). Dictionary of statistics and methodology: A nontechnical guide for the social sciences (2nd ed.). Thousand Oaks, CA: Sage. [Google Scholar]

Wang, Z., & Thompson, B. (2007). Is the Pearson r2 biased, and if so, what is the best correction formula?. The Journal of Experimental Education, 75(2), 109-125. [Google Scholar] [CrossRef]

Publicado
2017-02-28
Como Citar
Espírito Santo, H., & Daniel, F. (2017). Calcular e apresentar tamanhos do efeito em trabalhos científicos (2): Guia para reportar a força das relações. Revista Portuguesa De Investigação Comportamental E Social, 3(1), 53-64. https://doi.org/10.7342/ismt.rpics.2017.3.1.48
Secção
Artigo de Revisão