Cross-task validation of functional measurement

Ss judged average heaviness of two unseen lifted weights on a 20-step rating scale. They also rated heaviness of a single visible object of variable size and weight. The data for each task obeyed the parallelism prediction of the linear integration model. This within-task consistency validates jointly the model and the response scale. Functional measurement procedure yielded independent scales of subjective heaviness from each task. These were linearly related, a criterion of external consistency. The plot of subjective heaviness against objective weight was slightly negatively accelerated. These results disagree with those that have been obtained with magnitude estimation. Since the rating data satisfy both internal and external consistency, they constitute the true measure of sensation. Magnitude estimation, in contrast, must be biased and invalid.     

Geometrical representation of two methods of linear least squares multiple correlation

Geometrical properties and relationships of the Doolittle and square root methods of multiple correlation, as represented in the variable subspace of an orthogonal person space, are shown. The method of representation is also useful for depicting zero-order and partial correlations, as well as for the more general problem of the combination of variables.     

Some multiple correlation and predictor selection methods

The Doolittle, Wherry-Doolittle, and Summerfield-Lubin methods of multiple correlation are compared theoretically as well as by an application in which a set of predictors is selected. Wherry's method and the Summerfield-Lubin method are shown to be equivalent; the relationship of these methods to the Doolittle method is indicated. The Summerfield-Lubin method, because of its compactness and ease of computation, and because of the meaningfulness of the interim computational values, is recommended as a convenient least squares method of multiple correlation and predictor selection.