Constant-Ratio Rule for Confusion Matrices in Speech Communication

Abstract

Three experiments are reported which give support to an empirical rule which may be used for predicting the entries in a closed confusion matrix for any subset of items drawn from a master set of items with a known confusion matrix. This rule, the constant-ratio rule, states that the ratio between any two entries in a row of a submatrix is equal to the ratio between the corresponding two entries in the master matrix. For this statement of the rule it is assumed that the only variables which differ systematically in obtaining the two matrices are the different sets of messages and the allowable responses. This is an empirical rule which was formulated after examination of three 6×6 master matrices for CV's (consonant-vowel syllables) and six 3×3 submatrices. Two more experiments using monosyllables and digits were then conducted to test further the rule. Although no direct experimental evidence is reported, the use of the constant-ratio rule for predicting a master matrix given some of its possible submatrices is discussed.