Question

A researcher selects two samples of equal size and computes a mean difference of 1.0 between the two sample means. If the pooled sample variance is 4.0, then what is the effect size using the estimated Cohen’s d formula?

Answer 1

Answer:

The Cohen's D is given by this formula:

$D = \frac{\bar X_A -\bar X_B}{s_p}$

Where $s_p$ represent the deviation pooled and we know from the problem that:

$s^2_p = 4$ represent the pooled variance

So then the pooled deviation would be:

$s_p = \sqrt{4}= 2$

And the difference of the two samples is $\bar X_a -\bar X_b = 1$, and replacing we got:

$D = \frac{1}{2}= 0.5$

And since the value for D obtained is 0.5 we can consider this as a medium effect.  

Step-by-step explanation:

Previous concepts

Cohen’s D is a an statistical measure in order to analyze effect size for a given condition compared to other. For example can be used if we can check if one method A has a better effect than another method B in a specific situation.

Solution to the problem

The Cohen's D is given by this formula:

$D = \frac{\bar X_A -\bar X_B}{s_p}$

Where $s_p$ represent the deviation pooled and we know from the problem that:

$s^2_p = 4$ represent the pooled variance

So then the pooled deviation would be:

$s_p = \sqrt{4}= 2$

And the difference of the two samples is $\bar X_a -\bar X_b = 1$, and replacing we got:

$D = \frac{1}{2}= 0.5$

And since the value for D obtained is 0.5 we can consider this as a medium effect.