8.3 - Steps in ANCOVA

To use a coviariate in ANCOVA, we have to go through several steps. First, we need to establish that for at least one of the treatment groups there is a significant regression relationship with the covariate. Otherwise, including the covariate in the model won’t improve the estimation of treatment means.

Secondly, we have to be sure that the regression relationship of the response with the covariate has the same slope for each treatment group. This is an extremely important point. In our example, we need to be sure that the lines for Males and Females are parallel (have equal slope).

Depending on the outcome of the test for equal slopes, we have two alternative ways to finish up the ANCOVA:

  1. Fit a common slope model and adjust the treatment SS for the presence of the covariate
  2. Evaluate the differences in means at at least three levels of the covariate

These steps are diagrammed below:

No
No
Yes
Yes
Step 1: Are the regression slopes all equal to 0?
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No
No
Yes
Yes
Step 2: Are the regression slopes all equal?
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Stop!
The analysis is just an ANOVA
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Step 3 (different slopes): If slopes differ significantly, then individual regressions for each level of he treament are reported. LSmeans are compared to at least 3 points along the covariate.
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Step 3 (equal slopes): If slopes differ not significantly, generate a common slope and use LSmeans to compare responses at a common (mean) value of the covariate.
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Note! The figure above is presented as a guideline, and does require some subjective judgement. Small sample sizes, for example, may result in none of the individual regressions in step 1 being statistically significant, yet the inclusion of the covariate in the model may still be advantageous. Exploratory data analysis and working with the regression diagnostics is an important aspect of ANCOVA.