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Relative Variation, Variance Heterogeneity, and Effect Size PowerPoint PPT Presentation

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

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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


Homogeneity of Relative Variation as a Null Hypothesis


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?


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