Values of the Pearson Correlation
Prerequisites
Introduction
to Bivariate Data
Learning Objectives
 Describe what Pearson's correlation measures
 Give the symbols for Pearson's correlation in the sample and in the
population
 State the possible range for Pearson's correlation
 Identify a perfect linear relationship
The Pearson productmoment correlation coefficient
is a measure of the strength of the linear
relationship between two variables. It is referred to as Pearson's
correlation or simply as the correlation coefficient. If the relationship
between the variables is not linear, then the correlation coefficient
does not adequately represent the strength of the relationship
between the variables.
The symbol for Pearson's correlation is "ρ"
when it is measured in the population and "r" when it is measured
in a sample. Because we will be dealing almost exclusively with
samples, we will use r to to represent Pearson's correlation unless
otherwise noted.
Pearson's r can range from 1 to 1. An r of 1
indicates a perfect negative linear relationship between variables,
an r of 0 indicates no linear relationship between variables,
and an r of 1 indicates a perfect positive relationship between
variables. Figure 1 shows a scatter plot for which r = 1.
Figure 2 shows a perfect negative linear relationship.
Notice that as X increases, Y decreases.
Figure 3 shows a scatter plot for which r = 0. Notice that there
is no relationship between X and Y.
With real data, you would not expect to get values of r of exactly
1, 0, or 1.
