Memory for psychophysical scaling judgments

In three experiments, we examined memory for responses and stimuli experienced in a single direct psychophysical scaling session in which subjects made absolute magnitude estimations of the loudnesses of pure tones. Recall of scaling responses was found to be accurate for the softest and loudest stimuli, but systematically greater than actual judgments for the intermediate stimulus amplitudes, yielding distorted psychophysical functions for the recall data which nonetheless had the same power function exponent as that for the judged stimuli. Also, memory for the range of stimulus amplitudes was fairly accurate, but subjects could not distinguish between judged and nonjudged amplitudes within that range. The results are consistent with the role of extreme stimuli as anchors for judgment, and indicate that memories for these stimuli and responses made to them can be expected to influence future scaling judgments. These results also are consistent with the uncertainty hypothesis of mnemophysics. The present research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada to L.M.W. Thanks to the reviewers for insightful critiques.     

Sequential dependencies and regression in psychophysical judgments

A tendency for judgments of stimulus magnitude to be biased in the direction of the value of the immediately preceding stimulus is found in magnitude estimations of loudness. This produces a bias in the empirical psychophysical function that results in underestimation of the exponent of the unbiased function presumed to relate number and stimulus intensity, N = aSⁿ. The biased judgment can be represented as a power product of focal and preceding stimulus intensity, N_ij= aS ^m S_j ^b. A bias-free estimate of the correct exponent, n, can be obtained from the relation n = m + b.     

Higher order sequential effects in psychophysical judgments

We found that the depth of sequential effects depends on the judgment task. An experiment with squares indicated that stimulus-response pairs up to two trials back were included in the judgment process when subjects were required to make category judgments of size, whereas only the immediately preceding event was incorporated when subjects were making magnitude estimations. In the case of category judgment, interactions between the current stimulus and prior stimuli as well as configural effects indicated that events one and two trials back meet an equivalent function in the judgment process and that these events may jointly operate in one trial. These findings can be explained by a class of models that assume that the position of preceding stimuli relative to the current stimulus is decisive in the judgment process. The multiple-standards model is a representative of this class according to which there are two types of standards: (1) the endpoints of the range as long-term standards and (2) traces of preceding stimuli as short-term standards.     

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.     

Higher order sequential effects in psychophysical judgments

We found that the depth of sequential effects depends on the judgment task. An experiment with squares indicated that stimulus-response pairs up to two trials back were included in the judgment process when subjects were required to make category judgments of size, whereas only the immediately preceding event was incorporated when subjects were making magnitude estimations. In the case of category judgment, interactions between the current stimulus and prior stimuli as well as configural effects indicated that events one and two trials back meet an equivalent function in the judgment process and that these events may jointly operate in one trial. These findings can be explained by a class of models that assume that the position of preceding stimuli relative to the current stimulus is decisive in the judgment process. The multiple-standards model is a representative of this class according to which there are two types of standards: (1) the endpoints of the range as long-term standards and (2) traces of preceding stimuli as short-term standards.     

Rats' lever-press durations as psychophysical judgments of time

Hungry rats received food following lever-press durations exceeding a minimum value, which ranged from 0 to 6.4 sec. When no intertrial intervals separated successive presses, modal press durations remained at very short values as the minimum value required for food was increased. This was particularly true immediately after a food presentation. When an 8-sec intertrial interval followed each lever release, modal press durations were always at or beyond the minimum value required for food, and outcome of the preceding press had no effect on press duration. Possible reasons for the effects of intertrial intervals included punishment of short presses, increased delay of reinforcement of short presses, and reduced density of reinforcement. In addition, functions relating discrete-trials lever-press duration to minimum duration required for food were found to be qualitatively and quantitatively similar to the power functions recently proposed by Catania (1970) for interresponse time and response latency. This similarity was taken as support for a general psychophysical law of temporal judgments.     

Contrast effects on the auditory evoked response and its relation to psychophysical judgments

An auditory average evoked response (AER) procedure was used to search for a physiological counterpart of the contrast effect-the tendency for a S’s judgment of the intensity of a stimulus to be modified by the intensity of prior stimulation. When a tone was preceded by a softer tone, its AER amplitude increased; conversely, when a tone followed a louder tone, amplitude decreased. Irregular intervals between tones decreased the AER contrast effect, as did increasing the interval between tones. Further, significant correlations were found between individual scores on the AER contrast procedure and performance on a battery of psychophysical tasks.     

The effect of testing procedure on remember-know judgments

Remember-know (R-K) judgments are commonly used to assess conscious recollection of the study episode during recognition. We varied whether participants judged items as R, K, or new (one-step) or first made an old-new judgment and then made the R-K judgment (two-step). The one-step group had a higher R hit rate and K false alarm rate than did the two-step group. In addition, the K responses of the one-step group did not reliably discriminate between old and new items. When a “guess” response category was available, both groups were able to discriminate old and new items using the K response; however, K responses remained more accurate in the two-step condition. R responses appeared to be relatively immune to the effects of testing procedure when the guess category was provided. This suggests that, under some conditions, the R label can reliably indicate a distinct form of recognition memory, suggesting that allowing participants to use a guess response may help them to confine their R-K judgments to confidently recognized items. When participants are not given the option of making a guess response, they may use the R-K distinction to indicate the trace strength of the memory.     

Empirical evaluation of a model of global psychophysical judgments: III. A form for the psychophysical function and intensity filtering

In part I, a concept of ratio estimation is defined and it is shown that if such estimates depend only upon the physical ratio of the signal to the reference signal, the psychophysical function must be a power function. Assuming the same exponents for each component, an invariance condition, equivalent to a sum of power functions, is studied empirically for binaural loudness. It is fully or partially sustained for 19 of 22 respondents. Since failures may be attributable to different exponents in the two ears, the ratio of the two exponents is estimated but that fails to explain the failures. Other possible explanations are suggested. In part II, an intensity filtering model is presented, accounting for the phenomenon where monaural loudness matches show a bias depending on the matching ear. We show (a) that the existence of such a bias does not alter the prior experimental results; and (b) assuming the power function, that five respondents attenuate the opposite ear and two enhance it.     

The effect of local kinematic changes on anticipation judgments

Skilled tennis players rely on a more global than local perceptual strategy when anticipating an opponent’s shot direction in tennis (Williams, Huys, Cañal-Bruland, & Hagemann, 2009). Global perceptual strategy refers to the pick-up of dynamic information across different body areas rather than from a single source such as the arm or racket. We extend previous work by examining the spatiotemporal characteristics of visual information pick-up when anticipating shot direction in tennis. We perturbed information from various body locations by interchanging the dynamics of selected areas with those from strokes played to the opposite side of the court. In addition, we presented each manipulation under four different temporal occlusion conditions (from 240 ms prior to racket-ball contact) to examine the time course of information extraction. Skilled tennis players outperformed less skilled counterparts in predicting shot direction, even at early phases of the opponent’s motion. Moreover, skilled players showed significant decrements in performance when the arms and racket were perturbed, highlighting the relevance of distal information when anticipating opponents’ intentions.     

How the propagation of error through stochastic counters affects time discrimination and other psychophysical judgments

The performance of fallible counters is investigated in the context of pacemaker-counter models of interval timing. Failure to reliably transmit signals from one stage of a counter to the next generates periodicity in mean and variance of counts registered, with means power functions of input and standard deviations approximately proportional to the means (Weber's law). The transition diagrams and matrices of the counter are self-similar: Their eigenvalues have a fractal form and closely approximate Julia sets. The distributions of counts registered and of hitting times approximate Weibull densities, which provide the foundation for a signal-detection model of discrimination. Different schemes for weighting the values of each stage may be established by conditioning. As higher order stages of a cascade come on-line the veridicality of lower order stages degrades, leading to scale-invariance in error. The capacity of a counter is more likely to be limited by fallible transmission between stages than by a paucity of stages. Probabilities of successful transmission between stages of a binary counter around 0.98 yield predictions consistent with performance in temporal discrimination and production and with channel capacities for identification of unidimensional stimuli.     

Regression effect in psychophysical judgment

Psychophysical judgment, like all other kinds of judgment, involves a matching or equating of two different domains. When the judgment involves the matching of values on two perceptual continua, the observer tends, on the average, to constrict the range of his adjustments on whichever variable is placed under his control. When the observer adjusts each variable in turn, two different regression lines are produced. This regression effect presumably occurs whenever the results of the matching judgments yield less than a perfect correlation. Illustrative examples are given for the continua, loudness, vibration, brightness, and duration.     

Regression effect in psychophysical judgment

Psychophysical judgment, like all other kinds of judgment, involves a matching or equating of two different domains. When the judgment involves the mate hing of values on two perceptual continua, the observer tends, on the average, to constrict the range of his adjustments on whichever variable is placed under his control. When the observer adjusts each variable in turn, two different regression lines are produced. This regression effect presumably occurs whenever the results of the matching judgments yield less than a perfect correlation. Illustrative examples are given for the continua, loudness, vibration, brightness, and duration.     

Metacognition in psychophysical judgment: An unfolding view of comparative judgments of mental workload

An experiment is reported in which it was found that when subjects were required to indicate which of two visual extents was more difficult to categorize as “long” or “short,” they executed these categorizations and then measured the distance of the representation of each stimulus from the long-short category boundary; the stimulus nearer the boundary was judged to be the more difficult. When they were requested to indicate which was easier to categorize, they selected the alternative that was farther. Coombs’s theory of data (1952, 1964) and his unfolding theory of preferential choice (1950, 1964) provided the conceptualization of metacognition in this psychophysical task context. Strong support for the probabilisitic version of unfolding theory was obtained from the observed selective effects of laterality on the levels of stochastic transitivity attained for various classes of triples and the reliably longer times for comparisons with bilateral pairs than with unilateral pairs. The semantic congruity effects obtained, together with the changes in the form of the relationship between probability and response time as a function of practice, can be best accounted for by an evidence accrual theory in which the distances from the active reference point are measured and compared with a criterion on each evidence accrual. No support is provided for the view that propositionally based semantic “ease”- “difficulty” codes serve as the basis for these metacognitive comparative judgments of ease and difficulty.