# Congruence coefficient

© Paul Cooijmans

## Explanation

The congruence coefficient is an index between -1 and 1 that indicates to what extent two paired sets of values are congruent, are the same. The difference with the correlation coefficient is that the absolute height of the values is taken into account; in correlation analysis, the values' deviations from the mean form the basis, whereas in congruence analysis, their deviations from zero are used (in other words, the values themselves are used). As a result, for a congruence coefficient to be 1, the values of the two sets need to be identical, while for a correlation coefficient, the values only need to go up and down in the same manner, regardless their absolute height. For instance, the following two paired sets have a correlation of 1, but a congruence coefficient of less than 1:

(1, 3, 2) (1007, 1009, 1008)

The congruence coefficient is primarily used in factor analysis, to verify to what extent two factors are the same, the paired sets being the two factors' vectors with factor loadings of the respective variables (tests) in the matrix on the respective factors. One may also imagine other uses, such as the "matching" of personality or other profiles.

The congruence coefficient *r*_{c} is computed by dividing the sum of cross-products of sets X and Y by the square root of the product of the sum of squares of the one set and the sum of squares of the other set. In a formula:

*r*_{c} = ΣXY / √(ΣX^{2}ΣY^{2})