Abstract
A probabilistic and nonparametric measure of replication (White and Pesner 1979) or probability that two bivariate distributions come from the same population, is presented for use in hypothesis testing. It is argued that relationships can be regarded as invariant within a specified system to the extent that they replicate not only regionally but with respect to third factors specified as inflection points or limits on invariant relationships: relationships are intrasystemically invariant and inter- systemically variant. System boundary conditions should show a high density of "interaction effects" for relationships which vary from system to system, or which fail to replicate cross-systemically. A heuristic system is proposed to decompose the variables and cases of an empirical population into component systems with inva riant properties. The procedures are based on the measure of replication and group significance tests.
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