I understand that ANCOVA has a continuous outcome variable, and a categorical predictor, and (at least) one continuous covariate. Can this be run as a mediation model instead, and if so what are the differences between this and regular ANCOVA?
Solved – What’s the difference between including a variable as a mediator in a mediation analysis, and including a variable as a covariate in ANCOVA
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There really isn't a difference. In matrix algebra form, regression, ANOVA and ANCOVA are all written as
$Y = X\beta + \epsilon$
They arose in different fields and the output is typically formatted differently, but the meaning is the same. However, in the usual usage of the words, regression incorporates the other two, because ANOVA is usually used only when all the independent variables are categorical; ANCOVA when one is continuous (usually) and the others categorical, and regression for any IVs at all.
To test mediation effect (full or partial), you can you Sobel's test [As it suffers from normality issues for small samples, Bootstrapping is more preferred approach.]
Both can be done in SPSS by using process macro by Andrew F. Hayes. See for more details
After installing process macro in SPSS; follow these steps:
- Analyze > Regression > Process by Andrew F. Hayes
- Select DV, IDV and mediating variable; select model number 4; select number of bootstrap samples; and in Options, click on Sobel's test and other required statistics; click
Screenshots of steps:
Analyze > Regression > Process by Andrew F. Hayes
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Best Answer
The difference is that in mediation the predictor X is theorized to cause Y, and this causal effect is theorized to depend (in whole, or substantially) via X causing the mediator M which in turn causes the outcome Y.
That causal chain need not be theorized in ANCOVA. In ANCOVA the predictor X need not be thought to plausibly exert any causal influence on the covariate C, or on the outcome via the covariate. In ANCOVA a rationale for including C is that it explains variation in the outcome variable and thus including it in the model improves the strength with which X predicts the outcome Y.