Methods of Estimating Mental Factors

MR. M. S. BARTLETT has proposed1 formulæ for the estimation of mental factors as alternatives to formulæ I have given2. My formulæ were arrived at by the ordinary regression method. Bartlett's estimates and the regression estimates attain different ends, and it is agreed that each method is correct in the right place. The regression estimates minimize the squares of the discrepancies between the estimates and the true values, summed over the population of persons. Bartlett's estimates minimize the squares of a man's specific factors, summed over the tests. If the scores expressed in matrix notation as linear functions of the true factors are the two sets of estimates, for the common factors only, are . The regression method has the quality that if factors estimated by it are inserted in the specification equation which defines a vocation in terms of factors, the result is the same as a direct regression estimate of vocational ability from the tests.