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

The Cohen's D is given by this formula:

`D = (\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 = √(4)= 2`

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

`D = (1)/(2)= 0.5`

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

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 = (\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 = √(4)= 2`

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

`D = (1)/(2)= 0.5`

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