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 considered a medium effect size for a t test for dependent means? (Points :1)
To determine what is considered a medium effect size for a t test for dependent means, you would typically look at the Cohen's d statistic. Cohen's d is a measure of effect size that indicates the standardized difference between two means.
In the context of a t test for dependent means, a medium effect size is typically considered to be around 0.5. This means that the mean difference between the two dependent variables is half of a standard deviation apart.
To calculate Cohen's d, you would use the formula:
d = (mean difference) / (standard deviation of the differences)
In this case, the mean difference is an increase of 5.2, and the standard deviation of the distribution of means of change scores is 2.0.
Therefore, Cohen's d would be:
d = 5.2 / 2.0 = 2.6
Given that the cutoff "t" needed is -1.8333, we can compare this value to the values on a standard normal distribution table to see if it falls within the range that corresponds to a medium effect size.
Since a t value is equivalent to the corresponding Cohen's d value in absolute terms, we can compare the cutoff t value (-1.8333) to the standard normal distribution table to determine the effect size. Looking up the value in the table, we find that a t value of -1.8333 corresponds to a Cohen's d value of approximately 0.38.
Since the calculated Cohen's d value of 2.6 is much larger than the Cohen's d value associated with a medium effect size (0.38), we can conclude that the effect size in this study is large, rather than medium.