In AB test groups, upon random smapling, how to statically check if the covriates' distribution in both the test and control group are same Say, I want to do an AB test (on a website, change being a new button color). I will assign the incoming users into test and control groups randomly. But, I am interested in some particular features (covariates) of the users like 'powers(heavy) users or not', 'new users or existing users', age groups of users.
How to statistically check if the proportion/distribution of these 3 covariates is uniform/same across both the control and test. One reason for checking is to confirm there is no skew in these covariates that can impact the test result and other can be to make sure the randomizer is working properly.
edit : I understand randomization with large sample size, should take care of this, but there is a way to check the distribution of different covariates in test vs. control is statistically same.
 A: You could perform simple statistical tests to compare your variables for "covariate balance."  For example you may want to perform simple $t$-tests to verify that the means/proportions of the two groups do not differ statistically from one another.  Test that fail to show differences combined with your randomization scheme should provide sufficient evidence that none of your observed variables are confounding your results.
Or you could check the distributions themselves using something like the Kolmogorov-Smirnov test.
But one thing you should think about is what happens if you find some imbalance in the distributions?  What would you do then?  If you tried to adjust and balance the covariates manually (i.e. disregarding randomization to adjust), you risk mucking up balance on potential unobserved confounders -- this is why randomization with sufficient sample size is the way to proceed.  Replication of the test with new samples, when affordable/feasible is always helpful too and provides added confidence.
You will likely find some of the following references on re-randomization helpful too if you find imbalances (or even if you don't they are helpful to understand the concepts of confounding and potential pitfalls in randomization):
https://projecteuclid.org/euclid.aos/1342625468
https://healthpolicy.usc.edu/evidence-base/rerandomization-what-is-it-and-why-should-you-use-it-for-random-assignment/
http://www2.stat.duke.edu/~kfl5/Lock2011.pdf
Unfortunately, however, if you are randomly assigning treatments in real-time and then exposing subject immediately thereafter to treatment using computers and a website, it's unlikely you'd be able to re-randomize.
