COMPARISON OF SOME EFFECT SIZE MEASURES IN SIMPLE AND MULTIPLE LINEAR REGRESSION MODELS

Year 2021, Volume: 22 Issue: 1, 77 - 84, 26.03.2021

Soner Yiğit

https://doi.org/10.18038/estubtda.864226

Cited By: 1

https://izlik.org/JA47TY67CD

Abstract

It is very important that the results of the statistical analysis are understandable. Therefore, while reporting the results of statistical analysis, some effect size measures should be given along with the P-value. In this study, some effect size measure Eta-Squared, Epsilon Squared and Omega-Squared were compared in terms of their performance (bias) in simple and multiple linear regression models. Results of simulation runs showed that the Epsilon and Omega-Squared estimates were quite unbiased when compared to Eta-Squared. Thus, it could be concluded that reporting Epsilon or Omega Squared is more appropriate to evaluate the practical significance along with P-values in simple and multiple linear regression models.

Keywords

practical significance , eta-squared , epsilon-squared , omega-squared , regression analysis , simulation

COMPARISON OF SOME EFFECT SIZE MEASURES IN SIMPLE AND MULTIPLE LINEAR REGRESSION MODELS

https://izlik.org/JA47TY67CD

Abstract

References

• [1] Zar JH. Biostatistical Analysis. 5th ed. New Jersey, USA: Pearson, 2014.
• [2] Cohen J, Cohen P, West SG, Aiken LS. Applied Multiple Regression/Correlation Analysis for The Behavioral Sciences. 3rd ed. New Jersey, USA: Lawrence Erlbaum, 2003.
• [3] Draper NR, Smith H. Applied Regression Analysis. 3rd ed. New York, USA: John Wiley & Sons, 2014.
• [4] Glass GV, Hakstian, AR. Measures of association in comparative experiments: Their development and interpretation. Am Educ Res J 1969; 6: 403–414.
• [5] Cohen J. Things I have learned (so far). Am Psychol 1990; 45: 1304–1312.
• [6] Klein DF. Beyond Significance Testing: Reforming Data Analysis Methods in Behavioral Research. Am J Psychiat 2005; 162: 643-a-644.
• [7] Sullivan GM, Richard F. Using Effect Size-or why the P value is not enough. J Grad Med Educ 2012; 4: 279-282.
• [8] Hays W. Statistics for Psychologists. 1st ed., New York, USA: Rinehart Winston, 1963.
• [9] Thompson B. Editorial policies regarding statistical significance testing: Three suggested reforms. Educ Researcher 1996; 25: 26-30.
• [10] Kelley TL. An unbiased correlation ratio measure. Proc Natl Acad Sci USA 1935; 21: 554– 559.
• [11] Maxwell SE, Camp CJ, Arvey RD. Measures of strength of association: A comparative examination. J Appl Psychol 1981; 6: 525–534.
• [12] Keppel G. Design and Analysis: A Researcher’s Handbook. 1st ed. New Jersey, USA: Prentice Hall, 1982.
• [13] Olejnik S, Algina J. Measures of effect size for comparative studies: Applications, interpretations, and limitations. Contemp Educ Psychol 2000; 25: 241–286.
• [14] Grissom R, Kim J. Effect Sizes for Research: A Broad practical approach. New Jersey, USA: Lawrence Erlbaum, 2005.
• [15] Core R, Team R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. 2018.
• [16] Keselman HJ. A Monte carlo investigation of three estimates of treatment magnitude: Epsilon squared, eta squared, and omega squared. Can Psychol Rev 1975; 16: 44–48.
• [17] Carroll RM, Nordholm LA. Sampling characteristics of Kelley’s epsilon and Hays’ omega. Educ Psychol Meas 1975; 35: 541–554.
• [18] Okada K. Is omega squared less biased? A comparison of three major effect size indices in one-way ANOVA. Behaviormetrika 2013; 40: 129–147.
• [19] Skidmore ST, Thompson B. Bias and precision of some classical ANOVA effect sizes when assumptions are violated. Behav Res Methods 2012; 45: 536–546.
• [20] Yigit S, Mendes M. Which effect size measure is appropriate for one-way and two-way ANOVA models? A Monte Carlo simulation study. Revstat-Stat J 2018; 16: 295-313.
• [21] Schneider A, Hommel G, Blettner M. Linear regression analysis: part 14 of a series on evaluation of scientific publications. Dtsch Arztebl Int 2010; 107: 776-882.
• [22] Doulah MSU. Robust coefficients of determination: A measure of goodness of fit. Int J Eng Res 2013; 4: 1715-1717.