one big equation, where you plug the estimated effect size along with the α and power you select

into an equation, and calculate the sample size (see Chapter 3 for the scoop on effect size and

selecting α and power).

For a sample-size calculation for a correlation coefficient, you need to plug in the following design

parameters of the study into the equation:

The desired α level of the test: The p value that’s considered significant when you’re testing the

correlation coefficient (usually 0.05).

The desired power of the test: The probability of rejecting the null hypothesis if the alternative

hypothesis is true (usually set to 0.8 or 80 percent).

The effect size of importance: The smallest r value that is considered practically important, or

clinically significant. If the true r is less than this value, then you don’t care whether the test

comes out significant, but if r is greater than this value, you want to get a significant result.

It may be challenging to select an effect size, and context matters. One approach would be to

start by referring to Figure 15-1 to select a potential effect size, then do a sample-size calculation

and see the result. If the result requires more samples than you could ever enroll, then try making

the effect size a little larger and redoing the calculation until you get a more reasonable answer.

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