What is a Partial Correlation?

Welcome to this brief explanation on a Partial Correlation!

Partial correlation is an expression of analyses of co-variance (ANCOVA) applied to questions of prediction and relationship

Partial correlation is an expression of analyses of co-variance (ANCOVA) applied to questions of prediction and relationship

Prediction

&Relationship

. . . rather than questions of differences addressed by ANCOVA.

. . . rather than questions of differences addressed by ANCOVA.

Partial correlation estimates the relationship between two variables while removing the influence of a third variable from the relationship.

Partial correlation estimates the relationship between two variables while removing the influence of a third variable from the relationship.

Relationship between a guy and a girl

Partial correlation estimates the relationship between two variables while removing the influence of a third variable from the relationship.

Taking out the effect of video games on that relationship

For example, a researcher might want to know the relationship between height and weight.

For example, a researcher might want to know the relationship between height and weight.

&

However, she is aware that people’s bone and muscle structures vary according to gender.

However, she is aware that people’s bone and muscle structures vary according to gender.

She can calculate a partial correlation between height and weight while removing (holding constant, eliminating) the effect of gender on the correlation.

She can calculate a partial correlation between height and weight while removing (holding constant, eliminating) the effect of gender on the correlation.

&

She can calculate a partial correlation between height and weight while removing (holding constant, eliminating) the effect of gender on the correlation.

&

She can calculate a partial correlation between height and weight while removing (holding constant, eliminating) the effect of gender on the correlation.

&The Effect of Gender

Here’s the data set:

Here’s the data set:

Individual Height (inches)

Weight (pounds)

Gender (1 – male, 2 – female)

A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2

Here’s the data set:

Individual Height (inches)

Weight (pounds)

Gender (1 – male, 2 – female)

A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2

First let’s see what the correlation between height and weight is and then we will see what the correlation would be if we controlled for gender

Correlation between Height and Weight

Correlation between Height and Weight

Individual Height (inches)

Weight (pounds)

Gender (1 – male, 2 – female)

A 73 240 1 B 70 210 1 C 69 180 1 D 68 160 1 E 70 150 2 F 68 140 2 G 67 135 2 H 62 120 2

Correlation between Height and Weight

Correlation between Height and Weight

& = .825

However, when controlling for gender the correlation between height and weight is:

However, when controlling for gender the correlation between height and weight is:

& controlling for

However, when controlling for gender the correlation between height and weight is:

& controlling for

= .770

While still large, the relationship between height and weight is accounted for in part by gender.

While still large, the relationship between height and weight is accounted for in part by gender.

A partial correlation makes it

possible to eliminate the effect

of a third variable!