Stimulus discriminability in the magnitude estimation and category rating of loudness

Thirty-three Ss made category ratings and magnitude estimations of 10 auditory stimuli differing in loudness. The results from each task were examined in terms of the response uncertainty conditional upon each stimulus. The results did not support the suggestion that category judgments are influenced by the relative discriminability of stimuli in a way which is not characteristic of magnitude estimates, but were found to be consistent with the subjective Standard hypothesis. It is argued that the observed quasi-logarithmic relationship between category scale and ratio scale values reflects the constraints placed upon responses in category rating tasks.     

SCALES OF UNPLEASANTNESS OF ELECTRICAL STIMULATION

The subjective unpleasantness elicited by an A.C. current of 50 c/sec. applied to two fingers was scaled by 14 subjects using the methods of magnitude and of category estimation. Nine current intensities, ranging between 2 and 10 times the individual sensation thresholds, were used as stimuli. A power function yielded a good fit to the magnitude-estimation data; the exponent was 1.81. The difference between this value and a considerably higher exponent reported by previous investigators was interpreted in terms of the wider stimulus range used in the present study. The relation between the category scale and the magnitude scale had the same general form as that found in several previous investigations.     

Is an equal interval scale an equal discriminability scale?

Stevens and Galanter’s (1957) iterative procedure for minimizing bias in category scaling was used for the scaling of loudness of white noise. The spacing obtained deviated systematically from a spacing constructed in accordance with an equal discriminability scale from a previous experiment (Eisler & Montgomery, 1972). For the stimulus spacing yielding a “pure” category scale, a magnitude scale was constructed too. Since the category scale could be predicted accurately by Fechnerian integration of this magnitude scale, it was concluded that the “pure” category scale is a pure discrimination scale. The discrepancy between the equal discriminability scale and the “pure” category scale was interpreted as a bias in the former scale due to greater recognizability of stimuli located at the extremes of the stimulus range.     

Sensory scales of taste intensity

The subjective intensity of taste was scaled by the method of magnitude estimation in which Os assigned numbers to designate the apparent strength ofstimulus concentrations. Substances used were sucrose, dextrose, maltose, fructose, saccharin, Sucaryl, sodium chloride, and quinine sulfate. For aqueous solutions of each substance, taste intensity was found to increase as a power function of concentration by weight. Some approximate exponents were: sucrose, 1.3; sodium chloride, 1.4; quinine sulfate. 1.0. The magnitude scale for sucrose was compared with the category scale obtained by a commonly used rating procedure. The category scale turned out to be highly nonlinear.     

EMPIRICAL TEST OF A MODEL RELATING MAGNITUDE AND CATEGORY SCALES

E isler , H. Empirical test of a model relating magnitude and category scales. Scand. J. Psychol ., 1962, 3 , 88–96.—The function K =α log( φ+ q/k) +β seems to describe the relation between category scale values K and subjective magnitudes φ. The additive constant q/k is obtained from the S ds of the magnitude estimates.
The model was empirically confirmed for the loudness and softness of white noise scaled by the methods of magnitude estimation and category rating.     

Magnitude scales,category scales,and the general psychophysical differential equation

The general psychophysical differential equation (GPDE) which relates scale values and Weber functions for two subjective variables was tested statistically with data from a number of category rating and magnitude estimation experiments. In all tests. it was investigated whether the GPDE is compatible with the assumption that the Weber function of the category scale is constant. This assumption implies that the category scale may be regarded as a discrimination scale. The tests were carried out by estimating the Weber function of the category scale by means of the GPDE and testing these estimates for constancy, For group data, there were fairly small systematic deviations from constancy across different experiments in the Weber functions that were estimated by the GPDE, and the hypothesis of a constant estimated Weber function could not be rejected statistically (p>.05) in most experiments. For individual data the estimated Weber functions deviated from constancy in idiosyncratic ways, and these deviations were statistically significant (p<.05)for most subjects.     

On theoretical and realizable ideal conditions in psychophysics: Magnitude and category scales and their relation

By spacing 10 stimuli (white noise) between 40 and 110 dB according to two criteria [equal response ambiguity (ERA) and equal discriminability (ED)], an attempt was made to construct an “ideal” case for magnitude estimation and category rating. The “ideal” case is defined by linear and constant Weber functions (SDs as a function of scale values) for the two scales, respectively. Altogether, three group and two individual magnitude and category rating experiments were run with these two spacings. It was found that the ERA spacing approximated the ideal case well for both Weber functions and the ED spacing only for the Weber function of the category scale. The general psychophysical differential equation that relates scale values and Weber functions for the two scales allowed good prediction of the category scales from the magnitude scales and the Weber functions. The data suggested a distinction between phenotypic (empirical) and genotypic Weber functions, analogous to “real” and “ideal” cases in physics.     

On the "absoluteness" of category and magnitude scales of pain

The concept of "absolute scaling" (Zwislocki & Goodman, 1980) implies that direct judgments of sensory magnitude not only reflect the relative positions of the stimuli being judged, but also permit us to assess level differences in sensation. In order to explore this notion for different scaling methods, in the present investigation we compared magnitude estimation with category partitioning, a verbally anchored categorization procedure, in scaling painful pressure stimuli covering different intensity ranges. The results indicate that when the same stimulus range was presented after 1 week, both methods appeared to be highly reliable, with category partitioning faring somewhat better than magnitude estimation. When the stimulus range was unobtrusively changed between sessions, both methods reflected the within-subjects shift in absolute level. When two different sets of subjects judged the slightly different stimulus ranges, both methods resulted in scale values consistent with absolute scaling, though only category partitioning was sensitive enough to differentiate the two stimulus ranges. The results are discussed in the context of different possibilities of anchoring direct scaling methods in order to obtain "absolute" level information.     

On the “absoluteness” of category and magnitude scales of pain

The concept of “absolute scaling” (Zwislocki & Goodman, 1980) implies that direct judgments of sensory magnitude not only reflect the relative positions of the stimuli being judged, but also permit us to assess level differences in sensation. In order to explore this notion for different scaling methods, in the present investigation we compared magnitude estimation with category partitioning, a verbally anchored categorization procedure, in scaling painful pressure stimuli covering different intensity ranges. The results indicate that when the same stimulus range was presented after 1 week, both methods appeared to be highly reliable, with category partitioning faring somewhat better than magnitude estimation. When the stimulus range was unobtrusively changed between sessions, both methods reflected the within-subjects shift in absolute level. When two different sets of subjects judged the slightly different stimulus ranges, both methods resulted in scale values consistent with absolute scaling, though only category partitioning was sensitive enough to differentiate the two stimulus ranges. The results are discussed in the context of different possibilities of anchoring direct scaling methods in order to obtain “absolute” level information.     

Contextual and sequential effects on judgments of sweetness intensity

Presenting stimuli from skewed concentration distributions affects mean responses on category scales. However, if the number of categories on the response scale is increased, the degree of separation between the mean responses obtained for a positively as opposed to a negatively skewed concentration distribution diminishes. The present study investigates the effect of skewed concentration distributions upon ratings on a line scale and compares it to the context effect found for a 7-point category scale. In addition, sequential dependencies between consecutive stimuli and responses are investigated in order to assess their relevance in tasteintensity scaling studies. The context effects are similar for the 7-point category scale and for the line scale. The analyses of sequential effects show that both preceding responses and preceding stimuli affect current responses. However, since these two factors work in opposite directions, only a small contrast effect from the previous stimulus is significant in an overall analysis. The present study shows that even though the overall sequential effects between consecutive stimuli and responses are small, the effect of experimental context may be considerable. Since subjective context is established at the beginning of a session and sequential dependencies operate throughout the whole session, it is argued that contextual and sequential effects are only indirectly related.     

Contextual and sequential effects on judgments of sweetness intensity.

Presenting stimuli from skewed concentration distributions affects mean responses on category scales. However, if the number of categories on the response scale is increased, the degree of separation between the mean responses obtained for a positively as opposed to a negatively skewed concentration distribution diminishes. The present study investigates the effect of skewed concentration distributions upon ratings on a line scale and compares it to the context effect found for a 7-point category scale. In addition, sequential dependencies between consecutive stimuli and responses are investigated in order to assess their relevance in taste-intensity scaling studies. The context effects are similar for the 7-point category scale and for the line scale. The analyses of sequential effects show that both preceding responses and preceding stimuli affect current responses. However, since these two factors work in opposite directions, only a small contrast effect from the previous stimulus is significant in an overall analysis. The present study shows that even though the overall sequential effects between consecutive stimuli and responses are small, the effect of experimental context may be considerable. Since subjective context is established at the beginning of a session and sequential dependencies operate throughout the whole session, it is argued that contextual and sequential effects are only indirectly related.     

Two subjective scales of number

The way in which the apparent magnitude of numbers grows with their absolute magnitude was measured with a modified version of the direct technique Marks and Slawson (1966) used to determine the psychophysical exponent for loudness. This modified technique required subjects to estimate how evenly and randomly a sequence of integers appeared to sample the numerical continuum. The results indicate that the apparent magnitude of numbers increases with a decelerated power function of their arithmetic magnitude when a series samples from an open-ended range. However, when an upper boundary of the range is specified, the subjective scale seems to be linear. Random productions of numbers parallel the results found with judgments of presented sequences. The two scales of number provide the basis for an interpretation of the difference between magnitude and category scales: that subjects use numbers differently when the response scale is open-ended Imagnitude estimation than when it has a fixed upper limit tcategory scale. Given the assumption that subjects use numbers in this way in the two tasks, the qualitative relation between magnitude and category scales is predicted.     

PSYCHOPHYSICAL SCALES OF THE ODOR INTENSITY OF AMYL ACETATE

The paper presents psychophysical scales of amyl acetate in benzyl benzoate sniffed from cotton. Four scales obtained by direct scaling procedures, ratio estimation and magnitude estimation, yield functions of the form R = kSⁿ , with n ranging from 0.39 to 0.57. These data support earlier findings that the intensity of smell is a negatively accelerated function of stimulus intensity. In addition, comparison of magnitude and category scales indicate that the subjective intensity of smell is a prothetic continuum. Finally, further analysis of subjective ratios as a function of stimulus ratios again shows that ( a ) the magnitude scale is a ratio scale and ( b ) the function obtained conforms to the power law.     

Saturation of red: A prothetic continuum

A battery of procedures was used to scale the saturation of colors produced by mixtures of red and gray papers. By direct magnitude estimation, the apparent saturation was found to grow as the1.7 power of the percentage of red in the mixture. The power law was confirmed by the cross-modality matching of loudness to saturation. The inverse continuum, paleness, was also scaled. Saturation appears to be a prothetic continuum because the category scale is curved and the subjective size of the jnd increases as saturation increases.     

Direct quantitative judgments of sums and a two-stage model for psychophysical judgments

Judged magnitudes of differences between stimuli have previously been shown to support a two-stage interpretation of magnitude estimation, in which input transformations and output transformations are each describable as power functions. In an effort to provide support for the model independent of the difference estimation procedure. the present investigation employed two additional judgment tasks. We obtained magnitude judgments and category judgments of the combined magnitudes (sums) of paired weights from two groups of Ss. Values of the inferred input exponent k calculated from the two sets of data were very similar and were also remarkably similar to the exponent previously calculated from magnitude estimations of differences between weights. The output exponent calculated from magnitude judgments of sums described a concave upward function; however. the similar function describing category judgments was essentially linear. These results show that the inferred input exponent is not the result of the difference estimation task, and in addition provides support for the contention that the interval scale may be a less biased sensory measure than the magnitude scale. The introduction of an additive constant to the model improved its fit to the data but the rule by which it was introduced made very little difference.     

Cross-modal additive conjoint structures and psychophysical scale convergence

I investigated a variety of issues related to the measurement of the magnitude of psychological experience, especially the magnitude of sensations. Different groups of subjects made pair comparisons, magnitude estimations, and category judgments of the "total sensory magnitude" of light and sound stimuli presented conjointly. Another group judged the dissimilarity of pairs of conjoint stimuli. Various axioms, especially double cancellation, were tested on the resulting rank orders of conjoint stimuli. Judgements of the total magnitude of conjoint combinations of sound and light stimuli formed an additive conjoint structure. Dissimilarity judgments gave rise to a closely related lattice structure. Moreover, various scales of the individual attributes (loudness and brightness) calculated from the two types of judgments of the conjoint stimuli displayed substantial convergence, each scale for a given modality being linear with all other scales for that modality.     

Constrained scaling: the effect of learned psychophysical scales on idiosyncratic response bias

We report seven experiments in which subjects were trained to respond with numbers to the loudness of 1000-Hz pure tones according to power functions with exponents of 0.60, 0.30, and 0.90. Subjects were then presented with stimuli from other continua (65-Hz pure tones or 565-nm lights varying in amplitude) and were asked to judge the subjective magnitude of these stimuli on the same numerical scale. Stimuli from the training continuum were presented, with feedback, on every other trial in order to maintain the trained scale. Except for the 0.90 scale, subjects readily learned the predetermined scales and were able to use them to judge the non-training stimuli with group results consistent with those usually reported. Also, in contrast to the usual magnitude estimation results, these results produced extremely low levels of intersubject variability. We argue that such learned scales can be used as "rulers" for measuring perceived magnitudes, according to a common unit.     

Comparative judgments with numerical reference points

A model of subjective magnitude comparisons is explored, which assumes that subjects compare symbolic stimulus magnitudes with respect to a reference point. The reference point may be established implicitly by the question (e.g., “Which is larger?” vs “Which is smaller?”) or be presented explicitly (e.g., “Choose the stimulus closer to X.”). The model was tested in five experiments in which subjects judged which of two comparison digits was closer to (or further from) a reference digit. Regression analyses in three experiments revealed that reaction time depended on the ratio of the distances from the comparison items to the reference point. The other two experiments provided evidence that subjects can strategically vary the processes by which they compare stimuli to a reference point. The results indicated that subjects can perform various types of “analog arithmetic” using either the linear number scale or a nonlinear scale of subjective digit magnitude.     

Subjective ratios and differences in perceived heaviness

In previous studies, judgments of ratios and differences in subjective magnitude have yielded similar orders, consistent with a hypothesis that a single perceived relation underlies both judgment tasks. In the present research, 15 subjects estimated heaviness differences between 28 pairs of eight weights and each of 8 groups of 10 subjects evaluated heaviness ratios of eight variable stimuli with respect to a different standard stimulus. Presenting stimuli that were equally spaced on a cube-root scale of weight enhanced expected ordinal discrepancies between ratio and difference estimates, and employing independent groups for each standard stimulus in ratio estimation eliminated a possible bias due to varying standards within the presentation sequence. Differences in orders of ratio and difference estimates together with differences in scales obtained from non-metric analyses in terms of a difference model indicated that the judgments were based on two perceived relations that are ordinally consistent with arithmetic operations of ratios and differences. A ratio scale of heaviness was derived from the combined orders of subjective ratios and differences.