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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
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Z (Sex) |
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Z1 (females) |
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Z2 (males) |
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XY |
XY |
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Outcomes |
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¼ |
¼ |
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Sig |
Sig |
¹Z has no effect on xy |
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Not Sig |
Not Sig |
¹Spurious association |
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Not Sig |
Sig |
¹Interaction |
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Sig + |
Sig - |
¹Interaction |
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