MAGNITUDE ESTIMATION OF HEAVINESS AND LOUDNESS BY INDIVIDUAL SUBJECTS: A TEST OF A PROBABILISTIC RESPONSE THEORY¹

Abstract

One hundred magnitude estimates of heaviness were obtained for each of 18 weights from each of six S s and of loudness for each of 20 intensities from another six Ss. T h e stimuli were spaced at approximately equal logarithmic intervals. T h e mean magnitude functions of individual Ss appear, in general, to deviate systematically from power functions. The distributions of responses, normalized by the mean response, appear to be skewed, highly peaked, and to have high tails. For at least half of the Ss, this response variability is no more than is needed to account for the errors in a simple two-stimulus two-response recognition experiment run under the same conditions. The data are examined in terms of a probabilistic response theory. Although the theory is clearly wrong in some of its details, certain of its qualitative features appear to be sustained.

Variability of magnitude estimates: A timing theory analysis

“…I. As is by now familiar from a number of studies (Braida & Durlach, 1972;Luce & Mo, 1965;Pradhan & Hoffman, 1963), functions obtained with this many observations per point are roughly power functions, but with deviations of as much as 5 dB from the best fitting power functions. (This is equally true when only a few observations are obtained, but the variability of one or two responses per signal is so great that one cannot reject the hypothesis of a power function; see Ekman et al, 1967, andGuirao, 1964.)…”

“…This variability is both between observers, with exponents of the power function fitted to loudness data ranging from at least .15 to .60 (using an intensity measure), and within observers, with the coefficient of variation (aim) being of the order of .2-.3 (Luce & Mo, 1965;Schneider & Lane, 1963;Stevens & Guirao, 1964). The question we wish to consider here is whether this variability contains any interesting information.…”

A consistent failure of the power law for lifted weight

“…It also appears desIJite variatien between experiments and between Ss within experiments in the range of numerical estimates used (cf. Luce & Mo, 1965 The standard stimulus, presented once only at the beginning of the experiment, was the 5()().g weight. The S then judged all 17 weights for JO trials.…”

The geometric mean: Confidence limits and significance tests

“…The Lognormal Assumption The data of Luce and Mo (1965) suggest that the distribution of magnitude estimates may not he lognormal. This may well be correct.…”

“…For example, Edwards (1968, p. 78) illustrates how the sampling distribution of the mean of even a completely rectangular distribution approaches normality closely in samples as small as n = 4. For unimodal leptokurtic distributions like those in Figure 6 of Luce and Mo (1965), the approach to normality should be even more rapid. To check on this assumption, we constructed hypothetical distributions similar to those in Figure 6 of Luce and Mo, and the actual standard errors of the geometric means in samples of size n = 3 were determined using Monte Carlo methods.…”