• How big is an effect?

• How exactly to determine this phrase depends on the context and statistical test being performed.

• When comparing a single population mean to a known value or when comparing two population means, the effect size the standardized difference between the two means.

• Given a standard Normal:

• Cohen’s d is a common measure of effect size.

• It is the difference between two means divided by the pooled standard deviation.

• For two independent samples, it is given by:

\[ d = \frac{\bar{x}_1 - \bar{x}_2}{s_p} \]

where:

\[ s_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}} \]

• There are many other measures of effect size.

• We may cover this in more detail in future lectures.

• For now, we just needed a bried introduciton to the concept for the rest of the lecture to make sense.