Published online by Cambridge University Press: 01 January 2025
It seems intuitively compelling to many investigators that measurements, on the same subjects by different methods, purportedly of the same given trait are somehow better evidenced to be mutually valid measurements of that trait to the degree that they are intercorrelated. It is similarly compelling that measurements on the same subjects of purportedly different and uncorrelated traits are somehow better evidenced to be valid measurements to the degree that they are not intercorrelated. Further, a demonstration of hetero-method mono-trait intercorrelation (convergence) jointly with one of hetero-method, or preferably mono-method, hetero-trait independence (discrimination) is more compelling than either single demonstration alone [see Campbell & Fiske, 1959]. I hope to show in what follows that this intuition is misleading unless certain rather demanding prerequisites are satisfied. Then I hope to show that contrary demonstrations are generally too indecisive to consitute validity disconfirmations. Finally, I shall consider some issues in the practical use of the indecisive multitrait-multimethod data.
An earlier version of this paper was presented at the Midwestern Society of Multivariate Experimental Psychology meetings of May 1969 in Chicago. Some explication of the concept of measuring instrument has also been presented elsewhere [Krause, 1969].
A factor vector defined by these m sets of measurements is properly interpretable as a best estimate of i only insofar as the pij projections on it are maximized. The centroid or principal component of the m vectors m appropriate if all their pij are taken to be equal, perhaps on some sort of indifference principle.