Effect Size Measures
Definition of effect size: measure of magnitude of the phenomenon of interest.
Effect size indices:
r, r^{2}(% of variance in one variable explained by variance in other variable)
d
eta^{2,} etc.
d (Cohen)
Definition 1: The Mean difference divided by the population standard deviation.
The larger the difference expected between the two population means, the greater the effect size; the smaller the variance within the two populations, the greater the effect size.
The division of mean difference by the standard deviation standardizes the difference between means and puts the difference on a scale that is adjusted for the standard deviation of the particular measure used. This has the same kind of effect as converting a raw score to a z score. Therefore, you can use d to compare results of very different studies, even those using different sample sizes.
Definition 2: The extent to which the two populations do not overlap is called the effect size because it is the extent to which the experiment has an effect of separating the two populations.
Effect size convention (Cohen, 1988): Cohen came up with some effect size conventions based on the effects found in psychology research in general.
Verbal description effect
size (d) % of overlap
Small
.20
85
Medium
.50
67
Large
.80
53
Small
.20
85
Medium
.50
67
Large
.80
53
Effect size and nonoverlapping areas (%) between two pop. distributions
d 
% of nonoverlap 
0 
O 
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (Table 2.2.1 p.22). Hillsdale, NJ: Lawrence Erlbaum.
3. Significance level vs. Effect Size

p 
effect size 
definition 


effect of sample size 


use for comparison purpose 

4. Role of significance and sample size in interpreting experimental results
Outcome statistically significant 
Sample size 
Conclusion 
Yes Yes No No 
Small Large Small Large 
