Values of the Pearson Correlation

Pearson's correlation

• The Pearson product-moment 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 represent Pearson's correlation unless otherwise noted.

Pearson's r

Pearson's r can range from -1 to 1.

• r = 1 indicates a perfect positive linear relationship between variables
• r = -1 indicates a perfect negative linear relationship between variables
• r = 0 indicates no linear relationship between variables

r=1

A perfect positive linear relationship, r = 1.

r=-1

A perfect negative linear relationship, r = -1.

r=0

A scatter plot for which r = 0. Notice that there is no relationship between X and Y.

-1<r<1

With real data, you would not expect to get values of r of exactly -1, 0, or 1.

• The data for spousal ages shown in the figure below and described in the introductory section has an r of 0.97.

• The relationship between grip strength and arm strength depicted in the figure below (also described in the introductory section) is 0.63.

Quiz

1 The scatter plot below represents

	a positive association
	a negative association
	no association

Answer >>

a positive association

As X increases, Y tends to increase, so it is a positive association.

2 The scatter plot below represents

	a positive association
	a negative association
	no association

Answer >>

a negative association

As X increases, Y tends to decrease, so it is a negative association.