1

I'm reading Field (2013), in which there is an ANCOVA example with a categorical predictor Viagra, a continuous covariate, and a continuous outcome variable libido.

I understand that in ANCOVA we are hoping for situation B in the diagram, in which the covariate reduces the unexplained variance but doesn't reduce the variance explained by the categorical predictor.

Diagram from Field (2013)

In the book example, the values are as follows.

Original model: SSviagra = 16.844, SSerror = 94.123, SStotal = 110.967

Model with covariate added: SSviagra = 25.185, SScovariate = 15.076, SSerror = 79.047, SStotal = 110.967

I can understand why SSerror went down. However, I don't understand why the SSviagra (the SS for the categorical predictor) went up.

Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.

user1205901 - Reinstate Monica
  • 11,303
  • 26
  • 77
  • 152
  • I think it's a misprint. There is no way for SSViagra to go up. – James Jun 05 '15 at 14:52
  • It's possible if the covariate is negatively correlated with the predictor (i.e., suppression). Suppression would also be consistent with the observation that the individual SSs don't add up to the total SS here ($25.185+15.076+79.047>110.967$). But this would be a little weird since suppression cannot really be adequately illustrated using Venn diagrams like Figure C here (see bottom of this answer: http://stats.stackexchange.com/a/73876/5829 ), so if it is suppression and not a misprint, then the figure is a little misleading. – Jake Westfall Jun 05 '15 at 19:01
  • The sign of correlation shouldn't matter. E.g. if you multiply the predictor by -1, all of the SS should be the same. – James Jun 06 '15 at 22:13
  • Yes, I was not precise in my comment, although I hoped the reference to suppression would help to clarify the situation I'm referring to. The more correct statement is that this is possible when the covariate correlates in opposing directions with the predictor and the outcome (i.e., positively with one, negatively with the other). In my comment the unstated assumption was that the correlations between outcome and predictor and between outcome and covariate are both positive. – Jake Westfall Jun 06 '15 at 23:03
  • Does it say what type of SS is used? – James Jun 08 '15 at 00:03

0 Answers0