When magnitude estimation procedures are used in psychophysical experiments, the subject is presented several stimuli of varying magnitudes and is requested to supply a number that matches the magnitude of each stimulus. Since Stevens (1957) first suggested these procedures, it has been widely believed that the relationship between the stimulus magnitude values and the response magnitude values is properly described by a power function. Sometimes the adequacy of the power function model is assessed by examining the correlation between the logarithm of the stimulus and the logarithm of the response.The work of several investigators, however, should lead to questioning the advisability of testing the goodness of fit of the power function model by examining the magnitude and significance of this correlation. The criticisms that have been made apply not only to the power function model, but to logarithmic and exponential models as well. In fact, the criticisms apply to the use of the correlation coefficient to measure the goodness of the fit of any model to magnitude estimation data or to any cross-modal matching data in general.Ynterna and Torgerson (1961), for example, make the general point that the linear model often provides a good approximation, even when there are significant curvilinear or configural relationships in the data. Anderson and Shanteau (1977) and Birnbaum (1973) have pointed out that any monotone function will have a large linear component. Good (1972) has shown that, even for very nonlinear monotone functions, the linear correlation coefficient can be quite close to 1.00.It is an elementary algebraic demonstration that for n equally spaced values of x, if y is any monotone increasing function of x, then the lower bound for the linear correlation, r, between x and y is r = [3/(n + I)jY2. Thus, if the number of data points is small, the correlation between x and y is bound to be fairly high, even for an inappropriate model. The first author is now at the University of California, San Diego. A version of this paperwas presented at theConvention of the Western Psychological Association, San Diego, April 1979, and was supported in part by Grant R03MH31598 from the National Institute of Mental Health. Theauthors are indebted 10 Dr. Norman H. Anderson, University of California, San Diego, for outlining this problem and thegeneral method of solution.Copyright 198] Psychonornic Society, Inc.Thus, the size and significance of the correlation coefficient may be largely tangential to the question of whether a given model is appropriate. A significant correlation simply allows us to reject the null hypothesis that the population correlation is zero. Since the lower bound for this correlation will generally be greater than zero, the null hypothesis that the population correlation is zero will be inappropriate. And since all monotonic increasing models will tend to have high correlations, a high and significant correlation does not tell us whether our model, or some other model, is appropriate for the data.A...