A researcher conducts a t test for dependent means in which it is predicted that there will be a decrease in unemployment from before to after a particular job-skills training program. The cutoff "t" needed is -1.8333. The standard deviation of the distribution of means of change scores is 2.0 and the mean change score for the sample studied is an increase of 5.2.
What is the effect size
How large was the sample? This determines df.
To determine the effect size for a t-test for dependent means, you can use various measures, such as Cohen's d or the correlation coefficient (r). Since the mean change score is an increase, we need to calculate Cohen's d.
Cohen's d is calculated using the formula:
d = (M1 - M2) / SD
Where:
M1: Mean of the before scores
M2: Mean of the after scores
SD: Standard deviation of the distribution of means of change scores
In this case, since it is predicted that there will be a decrease in unemployment, we need to convert the increase to a decrease by multiplying it by -1. Therefore, the mean change score would be -5.2 (negative value).
Plugging in the given values, the formula becomes:
d = (-5.2) / 2.0
d = -2.6 / 2.0
d = -1.3
The effect size (Cohen's d) for this t-test is -1.3. It indicates a large effect size, which means the difference between the before and after scores is substantial.