I am having trouble understanding this simple example form the book Applied Survival Analysis in R.
The example is as follows,
Consider three cox models
Model A only contains ageGroup
Model B only contains employment
Model C contains employment and ageGroup.
The book writes that
for anova(A,C) we get p=0.1. "and we would conclude that the effect of “ageGroup4” is not statistically significant when “employment” is included in the model."
How I understood it, to me it seemed like this was testing weather ageGroup4 was significant in the presence of employment, since BOTH A and C contain ageGroup4 but only model C contains employment.
Similar for anova(B,C), p=0.002 the book writes "We thus conclude that “employment” belongs in the model if “ageGroup4” is also included, since the p-value for the former is extremely small."
Again to me it seems that since p is small, we can reject the null, the null being that AgeGroup4 is not significant, ie ageGroup 4 is significant.
It seems I have the opposite understanding. Can anyone help me see where I go wrong, and how the correct way to understand this really is?