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 "ρρ" when it is measured in the population and "rr" when it is measured in a sample. Because we will be dealing almost exclusively with samples, we will use rr to to represent Pearson's correlation unless otherwise noted.

Pearson's rr can range from -1-1 to 11. An rr of -1-1 indicates a perfect negative linear relationship between variables, an rr of 00 indicates no linear relationship between variables, and an rr of 11 indicates a perfect positive relationship between variables. Figure 1 shows a scatter plot for which r=1 r1.

Figure 1: A perfect linear relationship, r=1 r1.

Figure 2 shows a perfect negative linear relationship. Notice that as XX increases, YY decreases.

Figure 2: A perfect negative linear relationship, r=-1 r-1.

Figure 3 shows a scatter plot for which r=0 r0. Notice that there is no relationship between XX and YY.

Figure 3: There is no linear relationship between the variables, r=0 r0.

With real data, you would not expect to get values of rr of exactly -1-1, 00, or 11. The data for spousal ages shown in Figure 4 and described in the introductory section has an rr of 0.970.97.

Figure 4: Scatter plot of spousal ages, r=0.97 r0.97.

The relationship between grip strength and arm strength depicted in Figure 5 (also described in the introductory section) is 0.630.63.

Figure 5: Scatter plot of Grip Strength and Arm Strength, r=0.63 r0.63.

Content actions

Add module to:

My Favorites Login Required (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own Login Required (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Footer

This work is licensed by Erin Maloney under a Creative Commons Attribution License (CC-BY 1.0), and is an Open Educational Resource.

Last edited by Liqun Wang on Jul 7, 2003 12:00 am -0500.