Direct Magnitude Estimation Research Articles

Direct magnitude estimation and interval scaling of stuttering severity.

The appropriateness of direct magnitude estimation and interval scaling for assessing stuttering severity was investigated by determining whether the continuum of the stutterers' judged severity was prothetic or metathetic. As operationally defined by Stevens, prothetic continua show a curvilinear relation between magnitude estimates and interval scale values of the same set of stimuli, whereas metathetic continua show a linear relation between these scale values. The stuttering severity of 20 stutterers was scaled by three groups of 15 listeners who used interval scaling, direct magnitude estimation with standard/modulus, and direct magnitude estimation without standard/modulus. The results indicated that the two sets of direct magnitude estimation scale values were related to the interval scale values in the curvilinear fashion that is typical of prothetic continua. These findings suggest that direct magnitude estimation is preferable to interval scaling for measuring stuttering severity.

Judgments of sound volume: effects of signal duration, level, and interaural characteristics on the perceived extensity of broadband noise.

While auditory stimuli are often described in terms of their apparent extensity, such descriptions have usually not been collected systematically. Moreover, the few deliberate attempts to evaluate image size have rarely gone beyond the classic parameters of stimulus frequency and intensity. In the present study a direct magnitude estimation procedure was employed. Seventeen subjects numerically estimated the apparent size of images produced by broadband noise stimuli. Under earphone listening conditions, signals were presented either dichotically (uncorrelated noise), diotically (correlated noise), or monaurally (noise led to a single earphone). The signals in each of these modes varied in duration (100, 300, 1000, and 3000 msec) and intensity level (60, 75, and 90 dB A weighted). Size estimates were plotted as power functions and analyzed with a repeated measures design analysis of variance. Consistent with previous research, the main effects of duration and intensity were both highly significant (p less than 0.001). In addition, a highly significant effect for mode of presentation was found (p less than 0.001). Across conditions, dichotic stimulation produced the largest images and monaural stimulation the smallest (about half the size of the diotic images). This last result is the first quantification of previous anecdotal observations. General implications of these results were discussed.

Construct validity of direct magnitude estimation and interval scaling of speech intelligibility: evidence from a study of the hearing impaired.

The appropriateness of direct magnitude estimation and interval scaling procedures for assessing the speech intelligibility of hearing-impaired adults was investigated by determining whether the continuum of the talkers' intelligibility was prothetic or metathetic. The intelligibility of 20 hearing-impaired talkers was scaled by 20 listeners using direct magnitude estimation and by 20 listeners using interval scaling. The two sets of scaling data were related in the curvilinear fashion that is typical of prothetic continua, indicating better construct validity for direct magnitude estimation than for interval scaling of speech intelligibility.

Brightness exponent as a function of flash duration and retinal eccentricity.

The effect of flash duration on the exponent of the brightness power function was investigated in the fovea and 20-deg periphery using a method of direct magnitude estimation. The flash duration employed covered a 5-log-unit range between .001 and 100 sec. The results showed that the exponent is clearly time-dependent for both extremes of the duration—that is, very short (.001 to .1 sec) and prolonged (3 to 100 sec) durations—but not for the medium flash durations between .1 and 3 sec. Furthermore, the exponent is a little larger for peripheral viewing than for foveal viewing except for the durations below approximately .03 sec. The systematic change of the exponent as a function of duration is discussed in terms of retinal and postretinal intensity coding functions.

Variations in brightness at two retinal locations

The brightness of foveal flashes was compared to flashes presented 4° temporal to the fovea using two psychophysical procedures, direct magnitude estimation and brightness matching and two levels of adaptation. For both procedures over a wide range of intensities, foveal flashes appeared brighter than parafoveal flashes. However the two procedures did not produce identical results. Changing adaptation level did not affect these findings. The differences in the results due to psychophysical procedure are related to the discrepancies found among previous studies.

Direct magnitude estimation of salt taste intensity with continuous correction for salivary adaptation

Direct magnitude estimation of salt taste intensity with continuous correction for salivary adaptation

Scaling of color sensation by magnitude estimation: a contribution to opponent-colors theory.

Saturation and hue perceived in monochromatic stimuli and in light mixtures were scaled psychophysically by a direct magnitude estimation method. The colors were of aperture mode and were presented against a dark background. As a result opponent-colors functions were obtained which show the hue sensations produced by the lights of the visible spectrum (under the observing conditions used). Compared to the opponent-colors functions of Hurwich and Jameson, obtained by a cancellation technique, the subjective hue sensation differed significantly. It may be concluded that these cancellation functions describe an earlier, probably a retinal level of data processing, while our results may be regarded as a description of the output of the color vision system.

Loudness magnitude adaptation at 60 dB SPL

Fishken et al. [J. Acoust. Soc. Am. 61, S61 (1977)], Scharf and Horton [J. Acoust. Soc. Am. 63, S16 (1978)], and Canevet et al. [J. Acoust. Soc. Am. 67, S21 (1980)] report that direct magnitude estimation of a continuous sound does not yield adaptation above 30 dB SL. To investigate the phenomena further, we presented a 1 kHz 60‐dB SPL tone to the right earphone of ten listeners for a 7‐min period, with and without an additional ipsilateral (reference) intensity. The initial 60‐dB intensity was defined as a magnitude of 60. Using the method of successive magnitude estimations at 30‐s intervals, there was found to be no consistent or significant change in the judged magnitude of a continuous 60‐dB sound. This agrees with the above referenced studies. However. when a 20‐dB increment (80 dB SPL) was added for 5 s every 30 s, subsequent magnitude estimations declined immediately, permanently, progressively, and significantly (p < 0.01) for the majority of subjects. It had been hypothesized that the “reference” intensity would allow for a perceptual cue to the declining sensation of a stimulus otherwise “known” to be unchanged. The results do not rule out the possibility of direct effects induced by the 80‐dB “reference.” Either explanation concludes that loudness magnitude adaptation can be measured above 30 dB, and at 60 dB specifically, with the modification of technique described.

Brightness exponent as a function of retinal eccentricity in the peripheral visual field: effects of dark and light adaptation.

Using a method of direct magnitude estimation, the exponent of the brightness power function was determined under dark and light adaptation at luminance levels well above threshold. The exponent was estimated for functions describing the brightness of stimuli presented at the fovea and the following peripheral retinal loci: 10, 20, 30, 40, and 50 deg nasally eccentric to the fovea along the horizontal meridian of the right eye. The exponent for a 1-sec flash was found to be approximately .33 at the fovea and increased slightly with increasing retinal eccentricity.The effect of adaptation on the brightness exponent was not so large when the target luminance was set well above threshold.

Eliminating subjective biases in judging the loudness of a 1-kHz tone.

It is possible to eliminate most of the known subjective biases that affect judgments of sensory magnitude using numbers. Experiments are described which do this, and which also investigate some of the biases. The least biased estimate for doubling the loudness of a 1-kHz tone is found to be about 11.5 dB. This value is still slightly affected by the logarithmic bias, although the bias could be eliminated. It is also affected by the stimulus equalizing bias, produced by the inequality between the finite range of loudnesses to which the ears are sensitive and the infinite range of numbers to which the loudnesses are matched. This last bias cannot be eliminated completely in direct magnitude estimation.

Direct Magnitude Estimation Scales in Public Opinion Surveys

Direct magnitude estimation scales, patterned after S. S. Stevens's work in psychophysics, provide precise, reliable measures. The use of the scales in three surveys demonstrates that they can be used in telephone surveys of a general population. Because the scales are relatively easy to construct, the researcher is able to go into the field more quickly than if he had developed scales through other methods. Since respondents arrange the stimuli on the scale, rather than have the researcher structure the stimuli into categories for respondents, the measures are relatively free of researcher predispositions and bias. The scales' most important use is in providing measures that can be used in theory building. Researchers should benefit from data that allow one to use powerful statistical techniques without violating data assumptions. Diana Stover Tillinghast is an Assistant Professor of Communication at Stanford University. The author is grateful to Kay Magill, Stanford Ph.D. candidate, for her substantial contribution to the work reported here. The surveys were conducted for the San Jose Mercury News. Public Opinion Quarterly ? 1980 by The Trustees of Columbia University Published by Elsevier North-Holland, Inc. 0033-362X/80/0044-377/$1.75 This content downloaded from 207.46.13.129 on Mon, 27 Jun 2016 05:25:02 UTC All use subject to http://about.jstor.org/terms 378 DIANA STOVER TILLINGHAST ducted by the University of Michigan's Survey Research Center. The Laboratory for Behavioral Research at the State University of New York at Stony Brook developed the scales used in one wave of a national panel study designed to test a learning model of support for the U. S. Supreme Court (Lodge et al., 1976). The researchers validated adjectival descriptor scales by using three cross-modality matching procedures-magnitude estimation, hand grip intensity, and sound pressure intensity-demonstrating not only that researchers can build regression-free, psychophysically valid ratio scales to measure the intensity of opinion, but also that these scales can be used in field surveys. The scales discussed in this article were adapted from Stevens's direct, subjective magnitude estimation scale for use in telephone surveys of a general population. In Stevens's early loudness experiments, a subject was presented with a standard tone, which had been assigned a numerical value, and was asked to judge the loudness of other tones in relation to the fixed standard (Stevens, 1956). Later, Stevens (1975) adopted a no-standard procedure, in which subjects assigned any number to the first stimulus and assigned successive numbers in such a way that they reflected their subjective impressions. Although the no-standard procedure is preferred by psychophysicists, the lack of a flxed standard bothers many social scientists (Hamblin, 1974). The scales have the following ratio-scale properties: (1) respondents use the scale to rank order the stimuli, (2) the size of the distances between numbers is known and has meaning, and (3) the scale has an absolute zero, meaning that the number zero is assigned when none of the property being measured is possessed (Nunnally, 1967; Torgerson, 1958). However, some researchers argue that subjective magnitude estimation scales provide only interval level measures. For example, Krantz et al. (1971) contend that subjective intensity is an interval scale. The scale provides researchers with two advantages: (1) fundamental measurement and (2) the ability to use the more powerful methods of statistical analyses without violating assumptions of the data (see Torgerson, 1958, and Hamblin, 1974). For more than three decades, researchers have argued whether Likert-type ordinal scales, the most common ordinal scales used in surveys as well as in much social science research, should be treated like interval scales for purposes of analysis (see Hewes, 1978). The beauty of the magnitude estimation scale is that the question of whether it is an interval scale does not arise because the distances between points on the scale are known and represent equal psychological distances along the continuum being measured. This content downloaded from 207.46.13.129 on Mon, 27 Jun 2016 05:25:02 UTC All use subject to http://about.jstor.org/terms DIRECT MAGNITUDE ESTIMATION SCALES 379

Brightness exponent for the periphery in the Bloch region

Using a method of direct magnitude estimation, perceived brightness was measured in the dark-adapted eye with brief flashes of varying duration in the Bloch region (1-100 ms) and retinal lock (0 degrees-40 degrees) for the photopic luminance levels covering the range between 140 and 0.14 cd/m2 in steps of 1 log unit. Perceived brightness increased as a function of flash luminous energy (product of luminance and duration) up to critical duration of approximately 100 ms. The brightness power exponent for brief flash was found to be 0.48 +/- 0.01 in the fovea, whereas about 0.44 +/- 0.01 in the periphery.

Quantitative subjective assessments are almost always biased, sometimes completely misleading*

Subjective assessments are used widely in civilized societies for evaluating people, the work they do, and the stresses they work under. Yet most of the people who use subjective assessments are probably not aware of the pitfalls which they involve.Range effects introduced by the investigator almost inevitably bias quantitative subjective assessments, unless very special precautions are taken to prevent or eliminate the bias. Stevens' method of direct magnitude estimation is always biased by range effects. The international standard for calculating the loudness of noise corresponds to a 30 decibel range of sound intensity.When the investigator takes special precautions not to introduce bias, the observers may use their own well‐known standards which they bring with them to the investigation. In a height constancy investigation conducted in a field, the well‐known standard is the height of a hedge or fence. In judging just acceptable noise levels, the well‐known standards used by the observers must depend upon the noise levels which they are accustomed to.The chief danger of subjective assessments is that they may be based upon a well‐known rule which does not happen to apply in the particular circumstance of the investigation. A result may then be obtained which is the direct opposite of the truth. Examples are the well‐known rules that noise and heat interfere with work. Yet performance can improve in both noise and heat. Results of this kind are revealed by measuring performance, not by asking people how noise or heat affects them. Subjective assessments should be used to complement measures of performance, not to replace them.

Perceived brightness as a function of flash duration in the peripheral visual field

Using a method of direct magnitude estimation, perceived brightness was measured in the dark-adapted eye with brief flashes of varying duration (1–1,000 msec), size (16’–116’), and retinal loci (0°–60°) for the lower photopic luminance levels covering the range between 8.60 and 86 cd/m2 in steps of .5 log units. Perceived brightness increased as a function of flash duration as well as luminance up to approximately 100 msec, then remained constant above 100 msec. The enhancement of brightness at about a 50-msec flash duration has been observed not in the fovea but in the periphery. Target size also has been found to be effective on brightness.

Direct Interval-Estimation: A Ratio Scaling Method

A variation of S. S. Stevens's direct magnitude-estimation scaling procedure is described in which the standard stimulus consists of an “interval” rather than a “point.” Data suggest this variation requites considerably fewer judges than direct magnitude-estimation to produce scale values possessing a given level of reliability.

A psychophysical study of rate of continuous speech stimuli by means of direct magnitude estimation scaling.

The psychological scaling procedure of direct magnitude estimation was employed to establish the relationship of measured and perceived rate of continuous speech stimuli. Time-altered recordings of a standard prose passage were prepared with a speech compressor to provide six variable rates: 75, 125, 175, 225, 275, and 325 w.p.m. A total of 30 master tapes were constructed, one for each of the 30 subjects who participated in the study. Each tape included the six variable stimuli and the standard stimulus to be used in each of three experimental sessions. For each session, one standard stimulus (125, 175, or 225 w.p.m.) and a total of three randomized series of six variable stimuli were used. Results of subjects' magnitude estimations indicate that although a linear trend is evident, there is no one-to-one relationship between measured and perceived rate of continuous speech stimuli. Stevens' power function law appears applicable in describing this relationship. Comparisons of the present results with previous findings using different scaling techniques and different stimuli are discussed.

Context effects on silent interval estimation in speech and nonspeech environments

The speech stimuli for this experiment were derived from two sentences, each containing the words free criminals. In one sentence, the words free criminals occurred intraphrase and in the other sentence they occurred interphrase. The vowel duration in free and the silent interval preceding criminals were systematically and independently varied. Vowel durations of 100, 200, 300, 400, 500, and 600 msec were paired with silent intervals of 0, 50, 100, 150, 250, and 500 msec. Subjects were asked to make direct magnitude estimates of the silent interval duration between free and criminals. Power-law scaling exponents for judgments versus vowel duration and silent interval duration were 0.29 and 0.48, respectively. The above experimental procedure was repeated in two experiments using nonspeech stimuli with temporal characteristics similar to the two sentences. In particular, the silent interval to be estimated occurred between two 1000-Hz tones. In Experiment 1 the duration of the tone preceding the silent interval was varied, while in Experiment 2 the tone following the silent interval was varied. Power-law scaling exponents for judgments versus tone duration and silent interval duration were 0.45 and 0.36, respectively, for Experiment 1 and 0.24 and 0.45, respectively, for Experiment 2.

The effect of interstimulus procedures on salt taste intensity functions

Taste intensity functions were constructed for the salt taste, using variations of the method of direct magnitude estimation, to study the effects of adaptation to residuals from prior tastings. The prediction that mouthrinsing would reduce residuals, lower the level of adaptation, and thus yield lower exponents was confirmed. The effect of the residuals tended to be reduced, tiowever, when the power functions were adjusted for such threshold changes. Power function deviations from linearity were also discussed. The literature on intensity scaling for the salt taste was examined and seen to support these findings. It was concluded that the interstimulus procedure, by altering residual stimulus levels, played a major role in determining salt taste intensity functions.

Empirical Approach to Testing Equal-Interval Assumption of Equal-Appearing-Interval Scales

The method of equal-appearing intervals offers no direct check of the assumption that the intervals between points on equal-appearing-interval scales are, in fact, equal appearing. An approach is described for checking this assumption that has much in common with Stevens' method of direct magnitude-estimation.

Silent Interval and Vowel Duration Effects on Pause Magnitude Estimation in Intrapause and Interpause Environments

The stimuli for this experiment were derived from two sentences, each containing the words free criminals. In one sentence these two words occurred within a phrase, and in the other sentence a phrase boundary occurred between the words. The vowel duration in free and the silent interval preceeding criminals were systematically and independently varied. Vowel durations of 100, 200, 300, 400, 500, and 600 msec were paired with silent intervals of 0, 50, 100, 150, 250, and 500 msec for both sentences. Subjects were asked to make direct magnitude estimates of the perceived pause between free and criminals in each of the stimulus sentences. Results indicated that given durations of vowel and silent interval result in similar perceived pauses in intraphrase position than in interphrase position. Power law scaling exponents were larger for vowel duration than for silent interval in all conditions. [This research supported by the National Institutes of Health.]