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A quick guide to choice of sample sizes for Cohen's effect sizes

Dunlap and Myers (1997) suggest rules of thumb for sample sizes using Cohen's effect size rules of thumb and equations that they have derived in some simple cases. These are given in the table. The sample sizes guarantee between 80% and 90% power to detect the given effect sizes.

Effect Size

Formula

Small

Medium

Large

Cohen's d unpaired t,

$$\frac{\mbox{16}}{\mbox{d}^text{2}}$$ + 2

0.2

0.5

0.8

equal group sizes

402

66

28

Correlation

8/$$r^text{2}$$

0.1

0.3

0.5

Total sample size

800

88

32

$$\phi$$, 2x2 table

8/$$\phi^text{2}$$

0.1

0.3

0.5

Total sample size

800

88

32

Dunlap and Myers (1997) show in their appendix that for a 2x2 table of proportions of form

Column 1

Column 2

Row 1

$$p_text{11}$$

$$p_text{12}$$

Row 2

$$p_text{21}$$

$$p_text{22}$$

with

A = $$\frac{p_text{11}}{p_text{11}+p_text{12}}$$, B = $$\frac{p_text{21}}{p_text{21}+p_text{22}}$$

C = $$\frac{p_text{11}}{p_text{11}+p_text{21}}$$, D = $$\frac{p_text{12}}{p_text{12}+p_text{22}}$$

then we can define $$\phi = \sqrt{\mbox{abs(A-B)} \mbox{abs(C-D)}}$$

In addition Maxwell (2000) mentions rules of thumb for power to detect the $$R^text{2}$$ of a single predictor with outcome in a multiple regression with a total of p predictors and a type I error of 0.05. These are give below:

Regression on p predictors

Small:$$R^text{2}$$=0.02

Medium:$$R^text{2}$$=0.13

Large:$$R^text{2}$$=0.26

Total sample size

80% Power

392+p

52+p

22+p

Total sample size

90% Power

526+p

70+p

30+p

Reference

Dunlap WP, Myers L. (1997) Approximating power for significance tests with one degree of freedom. Psychological methods 2(2) 186-191.

Maxwell SE (2000) Sample size and multiple regression analysis, Psychological methods 5(4) 434-458.

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