In Chapter 10 we saw that if a hypothesis test is deemed significant, we then are interested in how significant the result really is. Cohen’s- can be extended to the case when two independent populations means are being tested. In this case, we can estimate Cohen’s- using the following formula.
The Cohen’s- effect size of a hypothesis test for two population means can be approximated using the formula
where is the pooled standard deviation given by Eq. (12.5).
Since we are estimating the effect from two different samples, we use a poooled standard deviation of the two.5151There are varying estimators of effect size known. Here, we give just a basic treatment of effect sizes. That is to say, this is not a thorough treatment of effect size measures. Judging by the value of Cohen’s-, we then can determine the importance of the result. As before, we use the following table to determine an appropriate description
| Cohen’s- | Effect Size |
|---|---|
| 0.2 | Small |
| 0.5 | Medium |
| 0.8 | Large |
Using Excel, calculate Cohen’s- for the College Algebra data in Example 12.3.2. Explain how its significance.
Create a Python script file that imports two data sets. Have the script output Cohen’s-. In addition, have Python determine if the value of is small, medium or large based on where it falls.
An alternative to using is to use the sample standard deviations of one of the samples. This is called Glass’-. Explain the impact of having sample standard deviations that are relatively different from one another. Which is best to choose?