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Can I do a randomization test using a simple t-test? In particular, I have data and already checked the difference in group means of dependant variables by using t-test, but I also would like to check if control variables (e.g., age, gender, etc) in both groups are randomized to make sure the difference in values of control variables between two groups does not affect the main results? The central question is can I do that with t-tests or there are other appropriate methods that I should implement here?

helplzz
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    It depends on the variable, and to some extent on the sample size. For categorical variables like sex, you can't use a t-test, so a Chi Square or Fisher test would be appropriate. If the samples are small and obviously not normally distributed, or if the variables can be ordered but aren't proportional (like shoe size or Likert scales) then a Mann-Whitney test would be better than a t-test. For approximately normally distributed samples of any size a t-test would be right. It is likely that you can use a t-test for age but a chi-square for gender. – Allan Cameron Jul 05 '20 at 13:33
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    Agree with Allan that it depends on the types of variables you have. But to answer your last question, "are there other appropriate methods that I should implement here?" you could also consider conducting ANOVA `aov` to see if the "main effect" for whatever you are studying persists in the presence of these other variables like gender or `age` etc. – Chuck P Jul 05 '20 at 13:55

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