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?

(5-4.4)/.85 = .71

The counselor calculates the unbiased estimate of the population’s variance to be 15. What is the variance of the distribution of means?

A) 15/20 = 0.75
B) 15/19 = 0.79
C) 152/20 = 11.25
D) 152/19 = 11.84

To calculate the effect size, we first need to determine the difference between the mean depression score of the fourth graders in the particular class (4.4) and the mean depression score of fourth graders in general at the school (5).

The formula for effect size is:
Effect Size = (Mean1 - Mean2) / Standard Deviation

Substituting the given values:
Effect Size = (4.4 - 5) / 0.85

Calculating the difference between the means:
Effect Size = -0.6 / 0.85

Dividing the difference by the standard deviation:
Effect Size ≈ -0.71

Therefore, the effect size is approximately -0.71.