Information integration theory (IIT) has been developed in collaboration with many students and colleagues. I wish to express my heartfelt appreciation to these men and women (see Anderson, 1996a, p. v) for their dedicated labors, and to compliment them for their enduring contributions to psychological science.
Also unique to functional measurement is its extensive empirical foundation. When I introduced this functional approach (Anderson, 1962a, b), I realized that making measurement theory an integral part of substantive investigation represented a 180° conceptual shift from traditional approaches, which had viewed measurement as a preliminary to substantive inquiry. I also realized that the worth of this functional approach depended on establishing empirical validity of algebraic laws. With the blessing of Nature, such laws have been established. The true foundation of psychological measurement theory lies in such empirical investigations.
The necessity of empirical foundation is underscored by the averaging model, unexpectedly found to be the main integration rule in the empirical analyses. The traditional conception of measurement in terms of the single dimension of scale value was inherently too narrow. Measurement theory must recognize the coequal status of two scales of measurement—of weight and value.
In the experiment of Figure 21.8 (next page), subjects were shown two Munsell gray chips from Figure 21.1 and instructed to judge their average grayness. This prescribed averaging model, seemingly prosaic and uninteresting, has an important function—as a validity criterion for response linearity. Since subjects are told to average, the factorial plot may be expected to exhibit parallelism—if the response is a linear scale.
Judgments with magnitude estimation are shown in the right panel; these are radically nonparallel, as shown by the two equal-length vertical bars. Judgments with ratings are shown in the left panel; these are roughly parallel.
As far as one experiment may go, this one implies that magnitude estimation is biased and invalid (see further Notes 21.6.3g, h). Rating and magnitude estimation had equal opportunity; the parallelism theorem acted as an impartial judge of both methods. Magnitude estimation could have succeeded, but it failed. The rating method could have failed, but it succeeded.