CHAPTER 15 Introducing Correlation and Regression 207

You can use software like G*Power (see Chapter 4) to perform the sample-size

calculation. If you use G*Power:

1.

Under Test Family, choose t-tests.

2.

Under Statistical Test, choose Correlation: Point Biserial model.

3.

Under Type of Power Analysis, choose A Priori: Compute required sample

size – given α, power, and effect size.

4.

Under Tail(s), because either r could be greater, choose two.

5.

Under Effect Size, which is the expected difference between r1 and r2, enter the

effect size you expect.

6.

Under α err prob, enter 0.05.

7.

Under Power (1-β err prob), enter 0.08.

8.

Click Calculate.

The answer will appear under Total sample size. As an example, if you enter these

parameters and an effect size of 0.02, the total sample size will be 191.

Regression: Discovering the Equation

that Connects the Variables

As described earlier, correlation assesses the relationship between two continuous

numeric variables (as compared to categorical variables, as described in

Chapter  8). This relationship can also be evaluated with regression analysis to

provide more information about how these two variables are related. But perhaps

more importantly, regression is not limited to continuous variables, nor is it

limited to only two variables. Regression is about developing a formula that

explains how all the variables in the regression are related. In the following sec-

tions, we explain the purpose of regression analysis, identify some terms and

notation typically used, and describe common types of regression.

Understanding the purpose

of regression analysis

You may wonder how fitting a formula to a set of data can be useful. There are

actually many uses. With regression, you can