A school counselor tests the level of depression in fourth graders in a particular class of 20 students. The counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. On the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports, she is able to find out about past testing. Fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fiftsh graders has a mean depression score of 4.4.
Suppose the standard deviation she figures (the square root of the unbiased estimate of the population variance) is .85. What is the effect size?
To calculate the effect size, we need to compare the mean depression score of the fourth graders in this particular class to the mean depression score of fourth graders in general at the school, taking into account the standard deviation.
The formula for effect size (Cohen's d) is:
d = (mean1 - mean2) / standard deviation
In this case, the mean depression score for fourth graders in general at the school is 5, and the mean depression score for the 20 fourth graders in this particular class is 4.4.
Plugging in the values, we get:
d = (4.4 - 5) / 0.85
Calculating this, we find:
d ≈ -0.59
Therefore, the effect size (Cohen's d) for this comparison is approximately -0.59.