I am doing a 2 sample t test between 2 matched groups... is cobvariating age and gender necessary?
also if i do a paired t test for a before and after of one group is matching necessary?
I don't see any advantage in matching samples for tests. Today we do have methods and tools to include potentially influential covariates in appropriate models so that we can analyze the effects of the interesting factors that are "statistically adjusted" for the effects of other factors.
You don't have to include age and gender as covariates, but the result might be more interesting if you do.
If you _can_ pair before and after data, you probably want to.
If it is possible that age and gender could affect the results, then including them as covariates is always ideal. "Matching statistically" is actually pretty meaningless. I assume you mean that you did a separate t-test and showed that the two groups did not significantly differ in age, and a chi-squared test showing that the two groups did not significantly differ in gender; however, significance tests are only for making inferences about a population, which is irrelevant here (the important question is not whether the two groups come from populations with different ages, but whether the two groups themselves differ in age, which is not a statistical question; it's just a question that relies on theoretical assumptions about how big a difference in age would be necessary to be a concern). So there are two options. One is to conceptually rule out effects of age (e.g., by showing that the age difference between groups is either not in the direction that would cause the expected difference in your DV, or is too small to cause a difference), the other is to include age as a covariate; same goes for gender. The easiest way to do this is with multiple regression (for the 2-sample test) or linear mixed effects (for the paired test).
As for your second question, if you mean that you are only interested in the difference scores for each group, then matching is not strictly necessary: group 1 could increase from 3 to 5 and group 2 could increase from 10 to 12, but the change is still the same. However, in practice this doesn't always work out; there could be ceiling or floor effects, so if one group has less change than the other group and the two groups were already different at baseline then this can complicate the interpretation of the effects.
I don't see any advantage in matching samples for tests. Today we do have methods and tools to include potentially influential covariates in appropriate models so that we can analyze the effects of the interesting factors that are "statistically adjusted" for the effects of other factors.
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