Modelling combined linear and quadratic age effects

Question

I am running a GLM (Type III) with several predictors, including ${\rm age}$ and ${\rm age}^2$ as predictors. I am interested in knowing the combined effect size and p-value of ${\rm age}+{\rm age}^2$, since neither is significant when both are included. Is there a way to do this in SPSS?

Answer 1

To get a simultaneous test of several variables, you simply fit a 'reduced' model without those variables and perform a nested model test. (This is also called an $F$-change test, $R^2$-change test, multiple partial $F$-test, etc.) I discuss the process rather thoroughly here: Testing for moderation with continuous vs. categorical moderators.

In your case, you would fit a full model that included ${\rm age}$ and ${\rm age}^2$, and a reduced model that didn't have those two variables, but was otherwise identical. Then you would perform a nested model test to see if dropping those two variables significantly worsened the model's fit. It has been a long time since I've used SPSS, but as I recall, it was possible to enter variables in 'blocks'. Thus you could have an initial block without those two variables and a subsequent block that entered them. I believe an $F$-change test for the blocks is reported in the output somewhere.

Having tested the variables, you can compute the effect size associated with the set of variables. A simple effect size to use would be partial $\eta^2$. From the ANOVA table for the full model, sum the partial sum of squares for the variables in question and divide that by the sum plus $SSE$. I would recommend using sequential (type I) sums of squares and adding your variables of interest last. Then: $$ \eta^2_{\rm partial} = \frac{SS_{\rm age} + SS_{{\rm age}^2}}{SS_{\rm age} + SS_{{\rm age}^2} + SSE} $$