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Covariance

 

Explanations > Social ResearchStatistical 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.

See also

 

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