CHAPTER 15 Introducing Correlation and Regression 203

Analyzing correlation coefficients

In the following sections, we show the common kinds of statistical analyses that

you can perform on correlation coefficients.

Testing whether r is statistically significantly

different from zero

Before beginning your calculations for correlation coefficients, remember that the

data used in a correlation — the “ingredients” to a correlation — are the values

of two variables referring to the same experimental unit. An example would be

measurements of height (X) and weight (Y) in a sample of individuals. Because

your raw data (the X and Y values) always have random fluctuations due to either

sampling error or measurement imprecision, a calculated correlation coefficient is

also subject to random fluctuations.

Even when X and Y are completely independent, your calculated r value is almost

never exactly zero. One way to test for a statistically significant association

between X and Y is to test whether r is statistically significantly different from zero

by calculating a p value from the r value (see Chapter 3 for a refresher on p values).

The correlation coefficient has a strange sampling distribution, so it is not useful

for statistical testing. Instead, the quantity t can be calculated from the observed

FIGURE 15-1:

100 data points,

with varying

degrees of

correlation.

© John Wiley & Sons, Inc.

FIGURE 15-2:

Pearson r is

based on a

straight-line

relationship.

© John Wiley & Sons, Inc.