Values of the Pearson Correlation

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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.

Pearson-R1.jpg

r=-1

A perfect negative linear relationship, r = -1.

Pearson-R2.jpg

r=0

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

Pearson-R3.jpg

-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.

Age scatterplot.jpg


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

Strength.jpg


Quiz

1 The scatter plot below represents

Sc1.gif

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

Sc2.gif

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.