Tests for relation type – equivalence or tolerance – in a finite set of elements

The statistical procedure for determination of the type of relation – equivalence or tolerance – in a finite set of elements, estimated on the basis of pairwise comparisons with random errors, is presented. The procedure consists of two tests based on Chebyshev's inequality for variance of a random variable; the test statistic is a mixture of some random variables. An example of application of the procedure – determination of relation type in the set of functions expressing profitability of treasury securities sold at auctions in Poland – is presented, too.