Relative Variation, Variance Heterogeneity, and Effect Size

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## Relative Variation, Variance Heterogeneity, and Effect Size

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**by**Relative Variation, Variance Heterogeneity, and Effect Size Andrew R. Gilpin & Helen C. Harton Number Crunchers, April 7, 1998**Homogeneity of Variance as Assumption for Tests on Means**Robustness of t, F Unequal n’s, non-normal data are troublesome**Variance as Dependent Variable**Selection bias Differential influences between groups Learning Attitudinal shifts**Tests on Homogeneity of Variance**Fisher’s F Levene’s ANOVA procedure (ANOVA on transformed scores) Miscellaneous other approaches Box Cochran Hartley O’Brien**Experimental Effect Size**Cohen’s d Glass’s g Hedges’ h Pooled Variance Issue**Relative Variation**Pearson’s Coefficient of Variation Means are often proportional to standard deviations Psychophysics research (Weber/Fechner Law) Physical size**Implications of Homogeneity of Relative Variation for h vs.**g Pooled variance estimate based on smaller variance (and mean) will underestimate actual variance; pooled variance estimate based on larger variance (and mean) will overestimate actual variance. Distorted pooled variance will cause h to depart from g**Simulation Design**10,000 simulated experiments per cell 9 Populations (normal, 8 real radically non-normal) 9 Sample sizes (5,5), (25,25), (100,100), (5,25), (5,100), (25,100), (25,5), (100,5), (100,25) 3 Coefficient of Variation (V=.1, V=.2, V=.3) 6 Nominal g sizes: 0.0, 0.5, 1.0, 1.5, 2.0, 2.5**Simulation: Dependent variables**Mean observed h Proportion (of 10,000) significant for =.05 Fisher’s F for variance heterogeneity Levene’s F (t) for variance heterogeneity**Observed h (100,100, Normal Population)**Mean h Observed Nominal g**Power Curve for Levene’s Test (100,100, Normal Population)**Proportion Significant Nominal g**Projected Sample Sizes Are Distorted**Noncentrality parameter for independent-groups, equal N t-test For power (1-) = .80, =2.80 and N=15.68/d2 Estimated distortion from Normal population, (25,25)**Comparison of Estimated Sample Sizes**Assumes N1=N2=N, Power=.80**Variance heterogeneity is implied by homogeneity of relative**variation Use g rather than h if means are related to standard deviations General Conclusions**Suggestions, Anyone?**How common is variance heterogeneity? How common is proportionality of means and standard deviations? Other?