. 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 fifth 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?
5/.85 = 5.88
.85/5 = .17
(5-4.4)/.85 = .71
.85/(5-4.4) = 1.42
To calculate the effect size, we need to compare the mean depression score of the fourth graders in the counselor's class with the average score of fourth graders in general at her school.
The effect size measures the standardized difference between the two means and helps us determine the practical significance of the difference. In this case, the effect size is calculated using the formula:
Effect size = (Mean of the sample - Mean of the population) / Standard deviation
Given the information above, the mean depression score of the fourth graders in the counselor's class is 4.4, the mean depression score of fourth graders at her school is 5, and the standard deviation is 0.85.
Plugging these values into the formula, we have:
Effect size = (4.4 - 5) / 0.85
Simplifying this calculation, we get:
Effect size = -0.6 / 0.85
Dividing -0.6 by 0.85, we find:
Effect size ≈ -0.71
Therefore, the effect size is approximately -0.71.