Question

Let say you are running a two way anova in R.

The variables are Gender ( Male and Femaile), age ( Continuous), and GPA.

The model in R looks is   GPA ~ GENDER * AGE.

The result is : Df Sum Sq Mean Sq F value  Pr(>F)   

GENDER       1 0.0588 0.05880 10.706 0.00133 **

age           1 0.0594 0.05936 10.807 0.00127 **

GENDER:age   1 0.0132 0.01317   2.398 0.12368  

Residuals     146 0.8019 0.00549     

I would like to proceed with the POST HOC to know where the differences are.

For gender, it will tell me whether it is Male or Female having a higher difference.

But since age is continuous, How do I tell whether it is the kid or adult having a higher difference?

In either word, how do you run a post hoc with a continuous variable?

Answer 1

If age is working as a continuous variable in the model then the model is not a two-way ANOVA model, rather it is a ANCOVA(analysis of covariance) model. Because for ANOVA, all the variables must be factor variable. Look at the the model output of coefficients, you must get a coefficient for the the continuous variable age, with some p-value. If the p-value is significant then age is important covariate in the model. Furthermore, if the coefficient is positive in sign then as age increases, the response will also increase, and if it is negative, the relationship will be opposite.