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Understanding Effect Size in One-Way BG ANOVA: Importance and Measurement

This presentation delves into the concept of effect size in the context of One-Way Between-Groups ANOVA. It highlights the significance of mean differences, error variance, and practical utility of effects. It also explains raw and standardized effect sizes, such as Cohen's d, and their categories: small, moderate, and large. The discussion includes Eta Squared and Omega Squared metrics for measuring the amount of variance accounted for by effects, emphasizing their importance in interpreting statistical results in behavioral sciences.

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Understanding Effect Size in One-Way BG ANOVA: Importance and Measurement

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  1. One-Way BG ANOVA Andrew Ainsworth Psy 420 Obtained from www.csun.edu/~ata20315/psy420/One-Way%20BG%20ANOVA.ppt

  2. Effect Size • A significant effect depends: • Size of the mean differences (effect) • Size of the error variance • Degrees of freedom • Practical Significance • Is the effect useful? Meaningful? • Does the effect have any real utility?

  3. Effect Size • Raw Effect size – • Just looking at the raw difference between the groups • Can be illustrated as the largest group difference or smallest (depending) • Can’t be compared across samples or experiments

  4. Effect Size • Standardized Effect Size • Expresses raw mean differences in standard deviation units • Usually referred to as Cohen’s d

  5. Effect Size • Standardized Effect Size • Cohen established effect size categories • .2 = small effect • .5 = moderate effect • .8 = large effect

  6. Effect Size • Percent of Overlap • There are many effect size measures that indicate the amount of total variance that is accounted for by the effect

  7. Effect Size • Percent of Overlap • Eta Squared • simply a descriptive statistic • Often overestimates the degree of overlap in the population

  8. Effect Size • Omega Squared • This is a better estimate of the percent of overlap in the population • Corrects for the size of error and the number of groups

  9. Our Example EPRS8540 • Eta Squared • Small .01 • Medium .06 • Large .14 Cohen (1977) • Omega Squared • Small < .06 • Medium .06 - .15 • Large > .15 Cohen (1977)

  10. Our Example EPRS8540 • There was no significant price difference among the three store types (F2, 9 = 3.12, P > .05, ).

  11. References • Cohen, J. (1977). Statistical power analysis for the behavioral sciences. NY: Academic Press. Cited with regard to intepretation of omega-square. • Cohen, J. (1988). Statistical power analysis for the behavioral sciences . Second ed., Hillsdale, NJ: Erlbaum. • Olejnik, S., & Algina, J. (2003). Generalized eta and omega statistics: Measured for effect size for some common research designs, Psychological Methods, 8, 434 – 447.

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