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?

To calculate the effect size, we need to compare the mean depression score of the fourth graders in the particular class with the mean depression score of fourth graders in general at her school. Here's how you can calculate the effect size:

1. Determine the difference in means: Subtract the mean depression score of fourth graders in general at her school (population mean) from the mean depression score of the fourth graders in the particular class (sample mean).
Difference in means = Sample mean - Population mean
= 4.4 - 5
= -0.6

2. Calculate the effect size: Divide the difference in means by the standard deviation.
Effect size = Difference in means / Standard deviation
= -0.6 / 0.85
≈ -0.706 (rounded to three decimal places)

The effect size in this case is approximately -0.706.