Generalization and simplification of the Moore-Goodman test for significant of alignment homologies

A test given by Moore and Goodman (1977) that checks the significance of a homology between protein sequences is generalized to any type of distance measure and to any classification of codon pairs or amino acids according to this measure. A normal distribution is shown to approximate satisfactorily the probability distribution underlying this test for the examples chosen, and supposedly for any distance measure. The test accordingly reduces to a simple standard procedure.