A practice that is often seen in reports of randomised trials is carrying out significance tests on baseline characteristics, in the belief that this will provide useful Information. The main reason for significance tests is to test whether the null hypothesis is true, and it is this that motivates testing of baseline characteristics. Investigators want to see whether there is a “significant” difference between the groups at baseline, because they have been brought up to believe that a “statistically significant” difference is a real difference. [I’ll leave aside the logical fallacy in deciding on the truth or otherwise of the null hypothesis based on a p-value – see other posts]. Obviously, with baseline characteristics in a randomised trial, this is pointless, because you already know that the null hypothesis is true i.e. on average there are no differences between the randomised groups, and any differences that are seen are due to chance.
Significance testing of baseline characteristics has been extensively criticised; for example the CONSORT guidelines say:
“Unfortunately significance tests of baseline differences are still common…. Such significance tests assess the probability that observed baseline differences could have occurred by chance; however, we already know that any differences are caused by chance. Tests of baseline differences are not necessarily wrong, just illogical. Such hypothesis testing is superfluous and can mislead investigators and their readers.”
But significance testing of baseline characteristics has proved very hard to eradicate. Here is an extract from the instructions for authors from the New England Journal of Medicine (I’ve checked and it is still there in June 2013: http://www.nejm.org/page/author-center/manuscript-submission):
“For tables comparing treatment or exposure groups in a randomized trial (usually the first table in the trial report), significant differences between or among groups should be indicated by * for P < 0.05, ** for P < 0.01, and *** for P < 0.001 with an explanation in the footnote if required.” [my bold and underlining]
That is a pretty surprising thing to find in a top journal’s instructions, especially as the next point in the list says that “authors may provide a flow diagram in CONSORT format and all of the information required by the CONSORT checklist”.
The wording of the CONSORT guidance is less than ideal and I hope it will be changed in future revisions. It says “Significance tests assess the probability that observed baseline differences could have occurred by chance…”. This seems a bit misleading, as this isn’t what a p-value means in most cases, though it is more correct for comparisons of baseline characteristics in a randomised trial. The p-value is the probability of getting the data observed (or a more extreme result) calculated (and the significance test performed) if the null hypothesis is true i.e. it is based on the assumption that there is no difference. Obviously it can’t also measure the measure the probability that this assumption is correct.