I was about to start coding up an ANOVA test to study the differences in house prices between neighborhoods. I read that ANOVA is a great way to find out if there is significance difference in nominal groups of data against a continuous variable.
But then I read about the three assumptions that have to be fulfilled in order to make sure that your ANOVA results can be trusted:
- The experimental errors of your data are normally distributed
- Equal variances between treatments - Homogeneity of variances, Homoscedasticity
- Independence of samples - Each sample is randomly selected and independent
So, part 1 leads me to believe that you must first make some predictions based on your data, and then check the errors.
Does that mean ANOVA tests are always done post-hoc? Or is it talking about the difference between a sample and the mean?
I ask, because I am looking for a way to forecast whether or not a given nominal variable has any significance to a linear regression model. If ANOVA must be done AFTER modeling, then I might as well run the model with and without a given variable, and see which performs better.
Next, I read that you have to perform statistics tests on each of your three assumptions. So basically, to a novice like me, it looks like you are running tests on tests on tests.
In application, how often are these assumptions tested? How often do such tests fail?
I'm just a little blown away how complicated this stuff seems at first look. My stats background is pretty much zilch so forgive my lack refinement.
In the second assumption, what is meant by the word "treatment"
Again, I could just use the formulas on Wikipedia to code something up, but I don't want to be a lazy analyst by glossing over possibly important details! This is what I get for not taking any stats as a math major!