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Applied Statistics Handbook
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Controlling for Third Variable


Controlling for a third variable provides two or more bi-variate crosstabulations that assist in determining if the initial association between two variables interacts with another (third) variable and whether the initial association is spurious. Interaction occurs when the statistical significance and/or direction of a bivariate relationship varies depending on a particular category of a controlling variable. A spurious association is exhibited between two variables when the association can be better explained by or depends greatly upon a third variable. Suggests there is not a relationship between the two variables.  Instead, the two variables are caused or strongly related to a third (control) variable.


Example where there is a significant positive association between education and income:


  X        =  Education level (< 12 years, 12 years, >12 years)

  Y        =  Individual Income category (low, moderate, high)

  Z        =  Sex (1=female, 2=male)

 XY       =  Relationship between dependent (Y) and independent (X) variables

Sig       =  Statistically significant

 "-"       =  negative relationship

"+"       =  positive relationship



Z (Sex)








Z1 (females)



Z2 (males)
















Z has no effect on xy

Not Sig

Not Sig

Spurious association

Not Sig



Sig +

Sig -





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