I have a fairly large data set with 500000 observations for 100 variables. Observations are randomly assigned to treatment and control group. How do I infer that treatment has indeed been randomized in the data set. I ran t-tests on a couple of explanatory variables. Some have given significant p-values, some insignificant. What would be the most suitable check for randomization here?
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1$\begingroup$ You can't. Someone may have deterministically matched the two groups on the covariates, so the variables may be equally distributed between both groups, with no randomization whatsoever. I suspect that your actual problem is not whether your data have been randomized, but something else. Can you edit your question to give us your actual problem? $\endgroup$– Stephan KolassaCommented Mar 13, 2018 at 7:02
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$\begingroup$ The "test for randomization" is that you believe that whoever randomized did it correctly. $\endgroup$– Peter FlomCommented Mar 13, 2018 at 13:51
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Ideally, the person who undertakes the randomisation should have created some replicable coding to allow the randomisation to be audited and reproduced. If randomisation is done in R this can be done by using set.seed and having the code generating the randomisation.
In the case where the randomisation is not replicable, it is effectively then just a bunch of numbers that have come from somewhere. You can conduct post-hoc "balance tests" to see if there different groups appear to have been randomised, but that is all you can do. The other thing you should do is get very cranky at the person who did the randomisation.
