It has been a while since my logic classes in philosophy. I was wondering if equality and an absence of difference amount to the same thing, logically.
An example would be the baseline table in reports of randomised controlled trials. These tables are presented to demonstrate that the experimental groups had no statistical differences prior to the experiment beginning, and thus that any observed differences during testing are not an artifact of pre-existing differences. Traditional null-hypothesis significance tests are used in this context to demonstrate the absence of differences (e.g. p=.35 therefore no significant difference between groups on variable x). However it seems to me that this is taken to mean 'these groups are equivalent'. I was wondering therefore if the statements 'there are no observed differences on any of the variables measured' and 'the two groups were the same with regards to the variables measured' amount (semantically or logically) the same thing. I was hoping to leave statistics out of the discussion and to confine it to logic and/or semantics.