Deriving the loudness exponent from categorical judgments

The power function exponent for loudness is traditionally determined by means of a process of magnitude estimation. It is demonstrated in this paper that the exponent can also be obtained by using the procedure of absolute identification of sound intensity. It has been shown that subjects' responses to tones of a given intensity are distributed in a normal distribution whose variance depends on the range, R, over which the tones are distributed. By means of a standard statistical transformation, the normal density in log space is converted to the corresponding probability density in linear space. The power function exponent can then be obtained directly from the linear probability density. We also suggest that there is a direct relationship between the information calculated from experiments on absolute identification of sound intensity and the neurophysiological, poststimulus histogram measured in a nerve fiber in the auditory nerve.     

Sequential effects in absolute judgments of loudness

The effects of preceding stimuli on the judgments of current stimuli were examined in a study using absolute judgments of loudness with feedback. It was found that the response on a given trial was dependent on the stimuli in the preceding sequence of at least five trials. Both assimilation and contrast effects were observed. The form of the dependency of a response on a prior stimulus was a function of the ordinal position of the stimulus in the preceding sequence of trials. The stimulus on the immediately preceding trial had an assimilative effect on the response and preceding stimuli two to five trials removed all showed a contrast effect on a given response. The extent to which these preceding stimuli contributed to the contrast effect was an increasing function of their recency. The reversal of the dependency of the response, from assimilation to the stimulus one trial back, to contrast with the stimuli two and more trials back, indicates a unique function of the immediately preceding stimulus in this task. Since there was a reduction in the variance of responses to those stimuli similar in value to the immediately preceding stimulus, it is proposed that the stimulus and feedback on the last trial were remembered and used asa standardin judging the presented stimulus. A model is presented in which it is assumed that the memory of the magnitude of the immediately preceding stimulus is contaminated in specified ways by prior stimuli in the series. The empirical findings of assimilation and contrastare expected consequences of the proposed memorial processes.     

Effects of range on category scaling of loudness judgments

In two experiments subjects judged the loudness of a 1000-Hz tone within a range of three loudnesses. The first used a within-subjects design with ranges of 1-2 sones, 1-4 sones, and 1-8 sones. The second used a between-subjects design with ranges of 1-2 sones, 1-8 sones, and 1-16 sones. Except for two values in the 1- to 2-sone range the two experiments produced comparable results. As range was increased the tendency to round away from the end points increased and the judged mid-point occurred at a higher value. Comparisons are made with rounding patterns that occur in studies of linear scales. The present results are interpreted to support Poulton's (1975) position, that the mid-point of subjective estimates depends on the range of stimuli judged, rather than that of Stevens (1975), that the mid-point on a prosthetic scale is assigned to a value that is lower than the mid-point on the subject's subjective scale.     

The perceptual basis of loudness ratio judgments

In Experiment 1, subjects were required to estimateloudness ratios for 45 pairs of tones. Ten 1,200-Hz tones, differing only in intensity, were used to generate the 45 distinct tone pairs. In Experiment 2, subjects were required to directly compare two pairs of tones (chosen from among the set of 45) and indicate which pair of tones had the greaterloudness ratio. In both Experiments 1 and 2, the subjects’ judgments were used to rank order the tone pairs with respect to their judged loudness ratios. Nonmetric analyses of these rank orders indicated that both magnitude estimates of loudness ratios and direct comparisons of loudness ratios were based on loudnessintervals ordifferences where loudness was a power function of sound pressure. These experiments, along with those on loudness difference judgments (Parker & Schneider, 1974; Schneider, Parker, & Stein, 1974), support Torgerson’s (1961) conjecture that there is but one comparative perceptual relationship for ioudnesses, and that differences in numerical estimates for loudness ratios as opposed to loudness intervals simply reflect different reporting strategies generated by the two sets of instructions.     

Semantic congruity effects in judgments of loudness

This research uses comparative judgments of the relative loudness of sounds to make a critical test of one theory of the mental representation of continuous physical attributes. The first two experiments find a semantic congruity effect, which is an interaction such that subjects can pick the louder of two loud sounds faster than the softer, and the softer of two quiet sounds faster than the louder. According to the theory under test, physical quantities are stored as points on a representational continuum, with a variance as well as a mean placement on it. The theory predicts the semantic congruity effect by assuming that the variance of placement of intensities on the representational continuum is a function of the direction of judgment: a soft sound will have less variance than a loud one when judged for softness and more when judged for loudness. Since the speed of making a judgment increases as variance decreases, the theory predicts a semantic congruity effect. However, for loudness, it can be shown that variance does not change in the manner assumed. The finding of a semantic congruity effect therefore disconfirms the theory. Alternative models are discussed. This research was supported by NSF Grant BNS 78-17442.     

Response requirements and the contrast effect in loudness judgments

Ss responded to a series of soft tones via category judgments, reaction time responses, or simple nonquantitative discrimination judgments. An evaluation was then made of the contrast effects obtained in the category judgments of these same soft tones when subsequently presented along with a series of loud tones. A control group was also used which did not receive the initial trials with the soft tones. The results indicated: (1) equivalent contrast effects for all four groups for the soft tones and (2) significantly greater judgments of the loud tones in the group that had used category judgments on the initial trials with soft tones. These results, alonR with a trend analysis, were used to argue for a joint semantic shift and equalization of category usage process underlying the contrast effect when Ss are required to denote the stimuli initially by means of category judgments.     

Sensory and cognitive factors in judgments of loudness

One thousand Hertz tones were presented at equal or unequal intensities to the two ears. In a binaural-summation experiment, the presentation of components was simultaneous, the auditory system integrated the components automatically, and the subjects judged the loudness of the unitary sensation. In two cognitive-summation experiments, the presentation of components was successive, and the subjects had to integrate the two sensations consciously to judge their "total loudness." Results of all three experiments are consistent with models of linear summation of "loudness," but the loudness scales differ in the two tasks: The scales that underlie binaural summation and cognitive summation are nonlinearly related. This outcome suggests two nested processes: First, the auditory system transduces stimulus energy to loudness sensations by means of a nonlinear function; second, tasks that require subjects to judge combinational relations between sensations may impose additional nonlinear transformations on the sensations before the latter are combined.     

Magnitude judgments of loudness change for discrete, dynamic, and hybrid stimuli

Recent investigations of loudness change within stimuli have identified differences as a function of direction of change and power range (e.g., Canévet, Acustica, 62, 2136–2142, 1986; Neuhoff, Nature, 395, 123–124, 1998), with claims of differences between dynamic and static stimuli. Experiment 1 provides the needed direct empirical evaluation of loudness change across static, dynamic, and hybrid stimuli. Consistent with recent findings for dynamic stimuli, quantitative and qualitative differences in pattern of loudness change were found as a function of power change direction. With identical patterns of loudness change, only quantitative differences were found across stimulus type. In Experiment 2, Points of Subjective loudness Equality (PSE) provided additional information about loudness judgments for the static and dynamic stimuli. Because the quantitative differences across stimulus type exceed the magnitude that could be expected based upon temporal integration by the auditory system, other factors need to be, and are, considered.     

Some hypotheses concerning the evolution of polysemous words

The evolution of polysemous words is examined in three studies. Study 1 indicates that older words are more polysemous than recent words, and that frequently used words are more polysemous than infrequently used words. These effects were replicated, controlling for word concreteness (Study 2) and evaluation (Study 3), using two other samples of words. If words evolve additional meanings through metaphor (MacCormac, 1985), then variables (such as concreteness and evaluation) that play a role in metaphor may mediate the evolution of polysemy. The correlation between concreteness and polysemy was negligible (Study 2). As hypothesized, evaluation is a significant predictor of polysemy: Negative words are more polysemous than positive words, and relatively neutral words are more polysemous than evaluatively extreme words. These findings are consistent with the notion that polysemous words evolve, in part, through metaphor.     

Some correlates of stuttering severity judgments

Thirteen adult male stutterers recorded the Amplifier Passage on high-quality audiotape. One sentence from each recording was paired with one sentence from each of the remaining 12 recordings. The resulting 78 sentence pairs were presented to eight speech-language pathologists who were asked to judge which stutterer in each pair was more severe and to rate the confidence of each of these judgements. The confidence ratings were analyzed by means of the individual differences model of multidimensional scaling. The results suggested that reading rate and the number of intrasentence pauses were important parameters in determining the severity of stuttering.     

Effects of expectations on loudness and loudness difference

To determine how expectations affect loudness and loudness difference, in two experiments we induced some subjects to expect loud sounds (condition L), some to expect soft sounds (condition S), and others to have no particular expectations (control). In Experiment 1, all subjects estimated the loudnesses of the same set of three moderately loud 1-kHz tones. Estimates were greatest for subjects in condition S and smallest for subjects in condition L. Control subjects’ estimates were intermediate but closer to those of condition S subjects. In Experiment 2, subjects estimated the difference in loudness for pairs of moderately loud 1-kHz tones. Again, estimates were smallest for condition L subjects; estimates were greatest for control subjects, and condition S subjects’ estimates were closer to control estimates than to condition L estimates. This pattern of results is explainable by a combination of (1) Parducci’s (1995) range-frequency theory and (2) a gain control mechanism in the auditory system under top-down governance (Schneider, Parker, & Murphy, 2011).