Biostatistics For Dummies, 2nd Edition (Monika Wahi, John Pezzullo)

206 PART 5 Looking for Relationships with Correlation and Regression

Calculate the test statistic:

0 269 0 131

2 05

Look up 2.05 in a normal distribution table or web page such as https://

statpages.info/pdfs.html (or edit and run the R code provided earlier

in “Testing whether r is statistically significantly different from zero”),

and observe that the p value is 0.039 for a two-sided test.

A two-sided test is used when you’re interested in knowing whether either r is

larger than the other. The p value of 0.039 is less than 0.05, meaning that the

two correlation coefficients are statistically significantly different from each

other at α = 0.05.

Determining the required sample

size for a correlation test

If you are planning to conduct a study where the outcome is a correlation between

two variables designated X and Y, you need to be sure to enroll a large enough

sample so that if the correlation is indeed statistically significant, you have enough

sample for r to show it. As described in Chapter 11 with the t test and the ANOVA,

the sample size can be estimated through 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 hypoth-}

esis 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 sam-

ples 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.