Covariance

Explanations > Social Research > Statistical principles > Covariance

Description | Example | Discussion | See also

Description

Deviation of a variable in a sample is its value minus the sample mean (x-bar).

dev(x) = x - x-bar

Covariance is a measure of how much the deviations of a pair of variables match.

cov(x,y) = SUM( (x - x-bar)*(y - y-bar) )

A higher number for covariance indicates strong matching. A negative number indicates weak matching.

Example

In the first table below, x and y go up and down together. In the second table, they are a lot less similar.

x	y	x-xbar	y-y-bar	(x-xbar)* (y-ybar)
2	1	-2.57	-3.86	9.92
5	6	0.43	1.14	0.49
4	3	-0.57	-1.86	1.06
3	1	-1.57	-3.86	6.06
5	8	0.43	3.14	1.35
6	9	1.43	4.14	5.92
7	6	2.43	1.14	2.78
Mean of above (xbar, ybar):			Covariance (sum of above):
4.57	4.86			27.57

x	y	x-xbar	y-y-bar	(x-xbar)* (y-ybar)
2	8	-2.57	3.57	-9.18
5	2	0.43	-2.43	-1.04
4	7	-0.57	2.57	-1.47
3	8	-1.57	3.57	-5.61
5	1	0.43	-3.43	-1.47
6	2	1.43	-2.43	-3.47
7	3	2.43	-1.43	-3.47
Mean of above (xbar, ybar)			Covariance (sum of above):
4.57	4.43			-25.71

Discussion

There is no limit to covariance, which makes it difficult to assess given a single calculation. It has more value when several sets of similar figures have their covariances calculated. In this case, the set with the highest figure has the greatest matching.

SPSS: Analyze, Correlate, Bivariate; Options: Cross-product deviations and covariations.