The second context was in an analysis, planned by a colleague, as an indicator of valid randomisation in a meta-analysis of clinical trials. The research hypothesis was that randomisation is sometimes subverted by recruiters. They might do this, for example, by not recruiting a potential participant to a trial if the next treatment, which the recruiter knows or guesses, would be unsuitable in the recruiter’s opinion. Recruiters may do this because they want to favour the intervention by putting less sick or fitter people in intervention group, they may want to protect frailer people from the intervention, or they may want to make sure that sicker people get it. Motivations may be venal or benign, but either would invalidate the trial. An indication almost always reported as a baseline measure in clinical trials is age. A reviewer could test ages between randomised groups, and would expect to get a Uniform distribution for the P-values if the randomisations were all unbiased. Here the reviewer, rather than the trial researchers, would be doing the tests on the baseline ages. The tests would be independent, because each one is for a different trial.
