Dear all,
I have a concern about the assumption of the t-test in a dummy regression:
It is a multiple linear regression with 3 categorical variables (dummy-coded) und 1 metric variable as independent variables. The dependent variable is metric.
The dummy regression coefficients are the differences between reference group and treatment groups.
Do I have to check the assumptions of the used t-test for the significance of the regression coefficients? .
Thanks in advance.
The assumptions should make sense. If you have doubts, you may check if the data at hand grossly contradicts the assumptions. The best approach is to have a look at some residual diagnostic plots (residuals vs. fitted, residuals vs. group, normal-qq-plot of the residuals).
The problem is that the choice of the transformation or analysis should *not* be made based on the same data that is used for testing, because this invalidates the p-values (key phrase: "garden of forking paths" and "researcher degrees of freedom"). So you may use your current data to decide for a startegy to transform/model/test, but then you would actually need *new* data to actually fit the model and do the tests. If you have enough data you can split it.
PS: Note that assumptions are not to be proven. They either make sense or they don't.
Do I have to make a test for the homegeneity of variance between the reference group and treatment groups as an requirement for a t-test of regression coefficients?
A formal test is not helpful. Look at the residual diagnostic plots, if you doubt that the assumption makes sense.
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