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.     

Response bias in category and magnitude estimation of difference and similarity for loudness and pitch

Interval scales of sensory magnitude were derived from magnitude and category estimates of loudness differences, loudness similarities, pitch differences, and pitch similarities. In each of the four loudness experiments, a loudness scale was constructed from a nonmetric analysis of the rank order of the judgments. The four loudness scales so constructed were found to be equivalent to one another and indicated that loudness was a power function of sound pressure with an exponent of .29. A similar analysis for the four pitch experiments found the pitch scales derived in each case to be equivalent to one another and linear with the mel scale of pitch. Thus the same sensory and similarities for two distinct perceptual continua. For both pitch and loudness, these sensory scales were used to generate scales of sensory differences. A comparison of the category and magnitude estimates of sensory differences with the scale of sensory differences derived from the nonmetric analyses indicated the presence of significant response biases in both category and magnitude estimation procedures.     

THE PROBLEM OF MAGNITUDE AND CATEGORY SCALES: INTERPRETATION OF RESULTS

J unge , K. The problem of magnitude and category scales: interpretation of results. Scand. J. Psychol ., 1962, 3 , 215–218.—It is proposed that three main factors are responsible for the relation between magnitude and category scales: (1) ratio judgments on a transformed category scale, (2) interval judgments, and (3) hybrid judgments. The last term refers to the tentative explanation that magnitude judgments are a cross between pure ratio and interval judgments.     

Direct psychophysical scaling of the olfactory pleasantness of diluted n-amyl acetate

A category and two magnitude scales were constructed from observations of 12 Os who judged the pleasantness of a geometric dilution series of n-amyl acetate. Pleasantness varied inversely with concentration and had a short subjective range for a fairly typical range of stimulus concentrations. Scales resembled power functions with negative exponents of .110 to .126. A concave upward relationship between the two types of scales, which was also found in previous experiments involving hedonic and oiliness attributes, suggests a nonprothetic continuum, although evidence was mixed.     

Scaling occupational prestige by magnitude estimation and category rating methods: A comparison with the sensory domain

In a field study, models for magnitude estimation and for category ratings are applied to the scaling of occupational prestige. The two respective models provide sufficient conditions for magnitude estimates to yield logarithmic interval scales and for category ratings to lead to interval scales. Both models are found to hold reasonably well for the majority of respondents. As implied by a third model, the relation between magnitude estimation and category rating scales can well be described by a generalized power function. Although overall results do not favour one method over the other individual data analyses reveal substantial interindividual differences with respect to the capability of performing magnitude estimates and category ratings, respectively. The findings are compared to results recently found in psychophysical laboratory experiments, and it is concluded that the individual scale properties the two methods provide do not differ across the attitudinal and the sensory domains.     

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.     

Relative olfactory intensity perception as mediated by ratio-range category scale responses

Scales whose categories are labeled with ranges of ratio values are compared with verbal category scales and magnitude estimation. Relative perceived intensities of Eugenol odor were scaled by power law methods, using 102 Ss, five scaling methods-one verbal, two numerical, and two magnitude estimation-and making comparisons against two alternate odor reference standards. Variations in the psychophysical exponent values derived under each condition were examined. Comparisons between scale types were made: numerical ratio-range category scales may behave as magnitude estimations or as category scales depending on the way responses are scored by the experimenter.     

METHODOLOGICAL NOTE ON SCALES OF GUSTATORY INTENSITY

E kman , G. Methodological note on scales of gustatory intensity. Scand. J. Psychol ., 1961, 2, 185–100.—The subjective salt intensity of seven concentrations of sodium chloride in water was measured by the method of ratio estimation and by three variants of the method of magnitude estimation. The four scales thus constructed were not in agreement. The magnitude scales varied systematically with the stimulus used as standard. The average magnitude scale was in good agreement with the scale constructed by the method of ratio estimation. A combined scale was constructed from all the data. This scale is a power function of stimulus concentration. The exponent of the function is 1.59. The function includes an additive constant, which may indicate either the lack of an absolute zero point of the scale, or the presence of a basic sensation without external stimulation.     

Judgments of average lightness and darkness: A further consideration of inverse attributes

Twenty subjects judged the average lightness and darkness of paired Munsell gray papers according to magnitude estimation and category rating instructions. The data from category rating were approximately consistent with an averaging model but those from magnitude estimation were not. An analysis in terms of a two-stage model suggested that category ratings and magnitude estimates of each attribute were produced on the basis of the same composition rule, but implicated different output transformations. In judging darkness, subjects appeared to have reversed the scales employed in judging lightness, by a linear transformation in the case of category rating and by a reciprocal transformation in the case of magnitude estimation. However, differences between the input parameters obtained from judgments of lightness and darkness suggested that the scales of these attributes constructed from judgments of average magnitude may be biased.     

Range and regression, loudness scales, and loudness processing: toward a context-bound psychophysics

How does context affect basic processes of sensory integration and the implicit psychophysical scales that underlie those processes? Five experiments examined how stimulus range and response regression determine characteristics of (a) psychophysical scales for loudness and (b) 3 kinds of intensity summation: binaural loudness summation, summation of loudness between tones widely spaced in frequency, and temporal loudness summation. Context affected the overt loudness scales in that smaller power-function exponents characterized larger versus smaller range of stimulation and characterized magnitude estimation versus magnitude production. More important, however, context simultaneously affected the degree of loudness integration as measured in terms of matching stimulus levels. Thus, stimulus range and scaling procedure influence not only overt response scales, but measures of underlying intensity processing.     

A comparison of MMPI-2 validity in African American and Caucasian psychiatric inpatients

This study investigated ethnic differences on the Minnesota Multiphasic Personality Inventory-2 (MMPI-2) in 229 African American and 1,558 Caucasian psychiatric inpatients. Mean differences were found on several MMPI-2 validity and clinical scales. These were generally consistent with differences between the groups, indicated by the available extratest criterion data. To identify potential bias, the authors conducted 65 step-down hierarchical multiple regression analyses, predicting conceptually relevant clinical criteria from either MMPI-2 clinical or content scales for each gender. A number of MMPI-2 scales evidenced bias reflecting minor underprediction of psychopathology in African Americans. It is important to note that, in almost all cases, the magnitude of these differences was small and not clinically significant.     

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.     

MEASUREMENT OF 'POLITICAL.' PREFERENCES: A further study of direct and indirect scaling methods

The direct methods of ratio estimation and magnitude estimation and the indirect method of pair comparison were used to construct scales of liberalism and conservatism. It was found ( a ) that the scales of conservatism are linearly related to each other and ( b ) those of liberalism are also linearly related to each other but with a discontinuity in the middle of the range; one linear function for the conservative statements and another for the liberal statements, with the discontinuity occurring in the middle of the subjective scale. Liberalism vs. conservatism was found to be reverse. The linear function between all kinds of scales as well as the reverse relation between liberalism vs. conservatism suggest that the continuum of political preferences is metathetic.     

Relationships Between Inventoried Interests and Inventoried Needs

The primary purpose of this study was to investigate the relationship of interests, as defined by the Strong Vocational Interest Blank (SVIB) scales, to psychological needs, as defined by the Minnesota Importance Questionnaire (MIQ) and the Edwards Personal Preference Schedule (EPPS) scales. The 3 instruments were administered to a group of 279 University of Minnesota male student volunteers. A correlational analysis disclosed about one-third of the relationships between the SVIB and the two needs measures significant at the .01 level. Of the MIQ scales, Advancement, Authority, Security, Social Service, Social Status, and Working Conditions were most often related to the SVIB; while of the EPPS scales, Dominance clearly had the most numerous and the highest relationships with SVIB groups, and Order, Exhibition, Autonomy, Abasement, and Endurance also had some relationships. Although relatively low in magnitude, the results of this study tend to support 5 previously identified occupationally related personality need dimensions.     

Psychophysical scales of the olfactory pleasantness of homologous alcohols

A category, a ratio estimation, and three magnitude scales were constructed from the observations of 10 Os who judged the pleasantness of a homologous series of n-aliphatic alcohols. Magnitude scaling indicated that pleasantness generally varies inversely with chain length, which is consistent with the findings of earlier investigators who used different methods; ratio estimation also indicated an inverse relationship. Stable magnitude scales resembled power functions with exponents of ?0.262 to ?0.587; the adjusted ratio estimation’s was ?0.138. Pleasantness seemed to be unexpectedly prothetic, some evidence of which had also been reported in an earlier study involving a more diverse set of odorants. Yet in the present study the hedonic range was small and in the earlier, large. More than the size of range appears to account for the puzzling prothetic evidence.     

A GENERAL DIFFERENTIAL EQUATION IN PSYCHO-PHYSICS: DERIVATION AND EMPIRICAL TEST

By a reasoning similar to Fechner's a general psychophysical differential equation is developed. Its integration allows the calculation of intrasubjective relations, provided the Weber functions of the two pertinent variables are known. The method is empirically validated for the relation between category and magnitude scales and for the similarity function. Theoretical implications are discussed.     

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.     

Ipsative and Normative Scales in Adjectival Measurement of Personality: Problems of Bias and Discrepancy

887 respondents completed ipsative and normative versions of the PAL-TOPAS personality questionnaire. Data were analysed to test for (1) systematic bias in scores associated with the two response formats and (2) predictors of the magnitude of the discrepancy in the individual's ipsative and normative scores. Discrepancy was assessed for both item responses and scale scores. Sources of biases investigated included ipsative scaling artifact, extremeness of scores on the normative scales and response variability. Results showed that systematic bias in scale scores and magnitude of discrepancy were predicted by different factors. One source of systematic bias was associated with ipsative scaling artifact: the ipsative scales measure both the scale itself and rejection of other alternatives. A second source of systematic bias was acquiescence in response to normative items. A confirmatory factor analysis showed that a good but imperfect fit to the data may be obtained by constructing a structural model of the inter-relationship between normative and ipsative scores which accommodates both sources of bias. The strongest influence on discrepancy in scale scores was extremeness of normative scoring, associated with a bias towards either general acceptance or rejection of trait adjectives. It is concluded that both normative and ipsative response formats have limitations, and it may often be desirable to assess both.     

Magnitude effects for experienced rewards at short delays in the escalating interest task

A first-person shooter video game was adapted for the study of choice between smaller sooner and larger later rewards. Participants chose when to fire a weapon that increased in damage potential over a short interval. When the delay to maximum damage was shorter (5–8 s), people showed greater sensitivity to the consequences of their choices than when the delay was longer (17–20 s). Participants also evidenced a magnitude effect by waiting proportionally longer when the damage magnitudes were doubled for all rewards. The experiment replicated the standard magnitude effect with this new video game preparation over time scales similar to those typically used in nonhuman animal studies and without complications due to satiation or cost.     

Assessing parent-child relationships: a report of normative scores and revalidation of two clinical scales

Normative score performances on the Child's Attitude toward Mother and Child's Attitude toward Father scales by several adolescent subpopulations important to family therapists and researchers are reported for use in clinical assessment and future research. The instruments were administered to a representative sample of 2,419 Florida adolescents, and subpopulations were constructed based upon parental structure and sex. A previous study investigating psychometric properties of the two instruments was partially replicated. Results indicated that both scales are reliable and valid measures of the magnitude of problems in parent-child relationships from the child's point of view. The scales are recommended for both clinical and research applications.