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?

The Cohen's D is given by this formula:

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

represent the pooled variance

So then the pooled deviation would be:

And the difference of the two samples is , and replacing we got:

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:

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

represent the pooled variance

So then the pooled deviation would be:

And the difference of the two samples is , and replacing we got:

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

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)