|
Size: 1830
Comment:
|
Size: 2351
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 12: | Line 12: |
| Line 27: | Line 28: |
| then we can define $$\phi = \sqrt{\mbox{abs(A-B)} \mbox{abs(C-D)}}$$ |
|
| Line 28: | Line 31: |
| $$\phi = \sqrt{\frac{\mbox{abs(A-B)}}{\mbox{abs(C-D)}}}$$ | In addition Maxwell (200) mentions rules of thumb for 80% power for a multiple regression with p predictors. These are give below: ||||||||<style="TEXT-ALIGN: center"> Regression on p predictors || || $$R^text{2}$$=0.02 || $$R^text{2}$$=0.13 || $$R^text{2}$$=0.26 || ||||||||<style="TEXT-ALIGN: center"> Regression on p predictors || || '''392+p''' || '''52+p''' || '''22+p''' || |
| Line 33: | Line 41: |
Maxwell SE (2000) Sample size and multiple regression analysis, ''Psychological methods'' '''5(4)''' 434-458. |
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 (200) mentions rules of thumb for 80% power for a multiple regression with p predictors. These are give below:
Regression on p predictors |
|
$$Rtext{2}$$=0.02 || $$Rtext{2}$$=0.13 |
$$R^text{2}$$=0.26 |
||||
Regression on p predictors |
|
392+p |
52+p |
22+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.