Pervasiveness and magnitude of context effects: evidence for the relativity of absolute magnitude estimation

To test the assertion that absolute magnitude estimation serves to minimize context effects, two experiments were conducted in which area stimuli were judged under differing conditions. In Experiment 1, four groups of subjects made magnitude estimations of triangles ranging in area from 1.5 to 3,072 cm2. No standard or modulus was used, and instructions were similar to those used in absolute magnitude estimation experiments. Each group first judged a different subrange of the stimuli (1.5-24; 48-768; 6-96; or 192-3,072 cm2) before making judgments of the remaining stimuli. In Experiment 2, two groups of subjects made magnitude estimations of triangles ranging in area from 1.5 to 12,288 cm2, with each group first judging a different subrange of stimuli (1.5-24 cm2 or 768-12,288 cm2). The design and instructions were virtually identical to those used in absolute magnitude estimation experiments. Our results indicate that the wording of the instructions is not crucial and that judgments are influenced in two ways that are not predicted by proponents of absolute magnitude estimation. First, the power functions fit to the initially presented subranges (e.g., 1.5-24 cm2), which were judged without contextual effects produced by previously presented stimuli, were inconsistent with one another. Second, judgments of the remaining stimuli were influenced by the subrange of stimuli judged initially. The prevalence of context effects in both experiments, in spite of instructional differences, suggests that although one should avoid using a standard and modulus, there is little else to be gained by adopting the absolute magnitude estimation procedure.     

Stimulus context and absolute magnitude estimation: a study of individual differences

The effect of stimulus context on absolute-magnitude-estimation (AME) judgments was examined by determining whether the loudness judgment of a tone is influenced by the intensities of other tones presented within the session. A group of 18 subjects was tested in separate sessions in which they judged stimuli within either a low (10-60 dB SL) or a high (40-90 dB SL) range of intensities. Examination of the results of individual subjects revealed that judgments of stimuli common to the two ranges were, in most subjects, unaffected or only slightly affected by the position of the range. The judgments of 2 subjects who failed to follow the instructions, however, showed very large context effects due to changing the stimulus range. The results of a second experiment, in which 22 subjects judged the loudness of tones within either a narrow (35-65 dB SL) or a wide (20-80 dB SL) range, revealed that, in all but 1 subject, the width of the range had no systematic effect on the loudness judgments of stimuli common to both ranges. This was also true 1 month later when 16 of the subjects returned to the laboratory to judge the loudness of tones within an even wider range of 10-90 dB SL. It was concluded that AME judgments are relatively insensitive to the potential biasing influences of stimulus context.     

Further evidence of the invalidity of the magnitude estimation method

IntroductionThe magnitude estimation method is widely applied in diverse areas of psychology. However, Weiss (1972) found that this method may produce judgments that inaccurately represent subjective magnitudes: constructing the stimuli according to a factorial design allowed the bias caused by magnitude estimation to be exposed as a spurious divergence of factorial curves.ObjectiveThe present study experimentally compared magnitude estimation with graphic rating and ratio estimation. The comparison of magnitude estimation with graphic rating retested Weiss's finding. The comparison of magnitude estimation with ratio estimation explored the hypothesis that magnitude estimation may cause a divergence of factorial curves due to the requirement of magnitude estimation to multiply and divide numbers—both ratio estimation and magnitude estimation required participants to judge ratios, but only magnitude estimation required mental multiplication and division.MethodUsing a 3 × 4 factorial experimental design, an achromatic disk was presented concentrically with a larger achromatic square. The brightness of the disk varied with the luminance of the disk and, due to simultaneous contrast, with the luminance of the square. Three different groups of participants judged the brightness of the disk: one group by graphic rating, another by ratio estimation, and the third by magnitude estimation.ResultsIn accord with Weiss's results, graphic rating yielded roughly parallel factorial curves whereas magnitude estimation yielded diverging factorial curves. Ratio estimation also yielded roughly parallel factorial curves, supporting the hypothesis that the magnitude estimation task itself may cause divergence of factorial curves due to the requirement of this method to mentally multiply and divide numbers.ConclusionCaution should be taken in using magnitude estimation, especially in factorial experiments, because this method is likely to cause the researcher to make incorrect inferences about the functional relations between the variables involved in mental information integration. Ratio estimation yields a pattern of factorial curves essentially equivalent to that obtained by graphic rating.     

A behavioristic analysis of Stevens magnitude estimation method

A procedure independently proposed by Oyama and Lewis for treating the data of magnitude estimation is discussed in relation to the Graham-Stevens controversy on the psychophysical methods. In this procedure, the critical value of the stimulus needed to make the subject report numbers equal to or greater than each integral number is sought, instead of the median or geometrical mean of numbers reported for each level of stimulus intensity. Stevens’ magnitude estimation method has no special advantage over the other cross-modality matching methods, and the subjective magnitude of number should be estimated if one wants to know real relations between stimulus intensities and sensory magnitudes in various modalities.     

Stability of individual loudness functions obtained by magnitude estimation and production

A correlational analysis of individual magnitude estimation and production exponents at the same frequency was perfor.med, as well as an analysis of individual exponents produced in different sessions by the same procedure across frequency(250, 1, 000, and 3, 000 Hz). Taken together, results show, first, that individual exponent differences do not decrease by counterbalancing magnitude estimation with magnitude production, and, second, that individual exponent differences remain stable over time despite changes in stimulus frequency. Further results disclose that although individual magnitude estimation and production exponents do not necessarily obey the .6 power law, it is possible to predict the slope (exponent) of an equal-sensation function averaged for a group of listeners from individual magnitude estimation and production data. Assuming that individual listeners with sensorineural hearing loss also produce stable and reliable magnitude functions, it is also shown that the slope of the loudness-recruitment function measured by magnitude estimation and production can be predicted for individuals with bilateral losses of long duration. Thus, results obtained in normal and in pathological ears suggest that individual listeners can produce loudness judgments that reveal, albeit indirectly, the input-output characteristic of the auditory system.     

Unmasking the magnitude estimation response

The fuzzy judgement model of Ward (1979) predicts an inverse relation between the amount of stimulus information available to subjects and the magnitude of sequential dependencies on previous stimuli and responses in psychophysical scaling tasks. Ward confirmed this prediction for magnitude estimations of interdot distance for previous responses but not for previous stimuli, although the inverse relation has been repeatedly reported for both the previous stimuli and responses in absolute identification (e.g., Mori, 1989). This paper further explores this seemingly puzzling contradiction. A magnitude estimation of loudness experiment was conducted in which the amount of stimulus information available to subjects was manipulated by a modified version of informational masking (Watson, 1987). An absolute-identification-with-feedback experiment was also conducted to check the effectiveness of the informational masking in reducing the amount of stimulus information. The results of the magnitude estimation experiment show a striking similarity with those of Ward and generalize the failure of sequential dependencies on previous stimuli to vary inversely with stimulus information. An additional assumption that judgement strategies are altered under low-information conditions is necessary to explain this result.     

Scaling clinical judgments of symptom pathology by means of the psychophysiological method of magnitude estimation

Summing scores across heterogeneous symptom items without consideration of their differing psychopathological significance has been criticized as producing an inadequate picture of an individual's clinical status. The purpose of this study was to derive symptom item weights representing clinically judged seriousness of each symptom through the application of Stevens's psychophysical method of magnitude estimation. A nationwide sample of 129 clinicians rated the pathological significance of 221 symptom items in a design such that every rater rated 121 items, 21 of which were rated by all raters and 100 of which were rated only by the A or B subgroup to which each rater was randomly assigned. Each item was rated as to the seriousness of the pathology it would represent if manifested by either a boy child, girl child, boy adolescent, or girl adolescent, with one-fourth of the raters assigned to each condition. The results of 211 two-way analyses of variance revealed that age and age and sex in interaction, but not sex alone, significantly influenced the clinical ratings. The resulting magnitude estimation ratings of symptom pathology ranged from 1.0 to 9.9. They were demonstrated to have satisfactory reliability and convergent validity and to have the psychophysical characteristics of a prothetic continuum.A preliminary version of this paper was presented at the 85th Annual Convention of the American Psychological Association, San Francisco, August 1977. The research was supported by HEW grant MH24886. The authors wish to express appreciation to Walter W. Wengel for his work in developing the median quotient ratings used in the study, to Terrance Auger for making available unpublished raw data, and to Merton S. Krause for helpful suggestions regarding the interpretation of results.     

The occurrence of the filled duration illusion: A comparison of the method of adjustment with the method of magnitude estimation

A time interval between the onset and the offset of a continuous sound (filled interval) is often perceived to be longer than a time interval between two successive brief sounds (empty interval) of the same physical duration. The present study examined whether and how this phenomenon, sometimes called the filled duration illusion (FDI), occurs for short time intervals (40–520 ms). The investigation was conducted with the method of adjustment (Experiment 1) and the method of magnitude estimation (Experiment 2). When the method of adjustment was used, the FDI did not appear for the majority of the participants, but it appeared clearly for some participants. In the latter case, the amount of the FDI increased as the interval duration lengthened. The FDI was more likely to occur with magnitude estimation than with the method of adjustment. The participants who showed clear FDI with one method did not necessarily show such clear FDI with the other method.     

Individual magnitude estimates for various distributions of signal intensity

Magnitude estimates of loudness were collected for several variations in the schedule of signal presentations. For wide ranges (about 50 dB centered at 65 dB), the conditions were: random selection of 21 signals equally spaced in decibels, constrained selection so that each signal was used equally often but successive signals were always close together, constrained selection in which successive signals were always far apart, and random selection from a nonuniform distribution that consisted of two groups of equally spaced signals separated by a gap of 24 dB. In addition, two other ranges, 10 and 30 dB, were run with random selection of 21 equally spaced signals. The measures examined were: mean magnitude estimate as a function of signal intensity, coefficient of variation of the ratio of successive responses as a function of signal separation, and the correlation of the logarithm of successive responses as a function of signal separation. The basic question was whether all of the different schedules of signal presentation produce data that can be viewed as selections from appropriate regions of the 50-dB random signal selection data. To a degree, this was found, but with systematic exceptions.     

Variability of magnitude estimates: A timing theory analysis

Three procedures for magnitude estimation were investigated, and a sufficient number of responses were obtained to make reasonable estimates of both the mean and variance of the responses. The conventional magnitude estimate procedure, without a standard signal, appeared to produce the most sensible data. The best method of establishing the central tendency of the data appears to be the plot of the mean ratio of successive responses against the intensity ratio of the corresponding signal intensities. When this is done, the average response ratio increases roughly as a power function of the signal ratios. The coefficient of variation, σ/m, varies from about 0.1 for small signal ratios and increases to 0.3 at about 20 dB and greater signal separations. The distribution of response ratios appears to be reasonably well approximated by a beta distribution. The change in σ/m with signal ratio is suggestive of an attention mechanism in which the sample size depends on the location of the attention band. The ratio estimation procedure suffers badly from discrete number tendencies.     

Effect of reference number on magnitude estimation

The psychophysical function obtained by the method of magnitude estimation was influenced by the reference number (modulus) assigned to a “standard” line and the position of this standard in the range of comparison stimuli. Data from two experiments with judgments of apparent length of lines show how both variables systematically affect the slope of the power function. AllowingO to choose his own reference numbers, even though these numbers varied among as, tended to produce less variability in slope than ifE imposed fixed reference numbers forO to use.     

Individual differences in magnitude estimation of loudness

Twenty-two male and female subjects, aged 15 to 31 years, participated in two sessions, 11 weeks apart, of magnitude estimations of loudness. Stable individual differences in the exponent of the psychophysical power law, ψ=k?ⁿ, were shown. The correlation between subjects’ exponents of the first and second sessions was +.59. The generality of these findings and the origin of the individual differences were discussed.