# Logical difference between 'equivalence' and 'an absence of differences'

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.

• Please expand on what you mean by absence of difference. Do you have any clear cut examples of what an absence of difference? If you are using the phrase as a synonym then there usually are distinctions amongst the different terms. In other words there is a class that both terms can be members of but there are distinct qualities that make one unique and also one of the terms may belong to a sub category that the other term does not belong. – Logikal Apr 11 '18 at 22:59
• If there is no difference between A and B, then we say A=B, so let's say "an absence of differences" is the same as "equality". Then one logical difference is that logical equality is a logical operator while logical equivalence is a "semantic concept". – Nick Apr 11 '18 at 23:09
• equivalence means that two "objects" are interchangeable in a specific context: this does not mean equal. E.g. in propositional logic, where the only "values" are the truth-values T and F, two tautologies are equivalent: but they can be very different formulas. – Mauro ALLEGRANZA Apr 12 '18 at 6:49