In a research study with an effect size of .20, the populations of individuals have an overlap of about:
85%
25%
To determine the overlap between populations in a research study with an effect size of 0.20, you will need to consider a statistical method known as Cohen's d. Cohen's d quantifies the standardized difference between two means and provides a measure of effect size.
The formula for calculating Cohen's d is:
d = (M1 - M2) / SDpooled
Where:
- M1 and M2 are the means of the two populations (or groups being compared).
- SDpooled represents the pooled standard deviation of the two populations.
To calculate the overlap between the populations, we need to convert Cohen's d into a measure of overlapping coefficient (OVL). OVL can range from 0 to 1, where 0 indicates no overlap and 1 indicates complete overlap.
The formula to calculate OVL is:
OVL = 1 - (|d| / 2)
Applying this formula to a research study with an effect size of 0.20:
OVL = 1 - (|0.20| / 2) = 1 - 0.10 = 0.90
Therefore, the populations of individuals in this study have an overlap of about 0.90 or 90%.