Technical Note: Interaction and Confounding in Data Analysis

Suppose that we conduct a study to assess if marathon finishing times are associated with diet while controlling for age (this example was inspired by Gretchen Reynolds recent NYT article).  The extraneous variable is age.  Can we ignore age in our analysis and still assess the association between finishing time and diet?

Confounding exists when different interpretations of the relationship between finishing time and diet exist when age is ignored or included in the data analysis.  The assessment requires a comparison between crude estimate of association and an adjusted estimate of association.

Interaction exists when the relationship between finishing time and diet is different for different age groups.  The assessment requires describing the relationship between finishing time and diet for different age groups.

Interaction and confounding can exist in the same data set.  A variable can be a confounding variable and might also have an interaction.  If a strong interaction is found then an adjustment for confounding is inappropriate.

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