In Effect Size we introduce the notion of effect size, and briefly mention Cohen’s d. We will now explain this concept further.
Definition 1: Cohen’s d, a statistic which is independent of the sample size and is defined as
where m1 and m2 represent two means and σpooled is some combined value for the standard deviation.
The effect size given by d is conventionally viewed as small, medium or large as follows:
- d = 0.20 – small effect
- d = 0.50 – medium effect
- d = 0.80 – large effect
For single sample hypothesis testing of the mean, we use the following value for d
Example 1: National norms for a school mathematics proficiency exam are distributed N(80,20). A random sample of 60 students from New York City is taken showing a mean proficiency score of 75 (as in Example 1 of Single Sample Hypothesis Testing). Find the effect size for the sample mean.
Per Definition 1,
which indicates a small effect. Note that the effect size is independent of the sample size. We should interpret d to mean that the sample mean is a quarter of a population standard deviation below the population mean.