I'm having trouble understanding what exactly Type III test statistic does. Here is what I got from my book:
"Type III" tests test for the significance of each explanatory variable, under the assumption that all other variables entered in the model equation are present.
My questions are :
What exactly does "other variable entered in the model equation are present" mean? Let's say I have a Type III test statistics for variable $x_i$, does Type III test tells us whether the coefficient in front of $x_i$ equal to zero or not?
If so, then what's the difference between Type III test statistics and a Wald test? (I believe they are essentially two different things since SAS gives me two different numerical outputs) Currently I have both output for my independent variables (which are all dummy variables). I don't know which p-value to look at to decided which $x$ to drop.