ON THE DANGERS OF AVERAGING ACROSS SUBJECTS WHEN USING MULTIDIMENSIONAL SCALING OR THE SIMILARITY-CHOICE MODEL

Abstract— When ratings of judged similarity or frequencies of stimulus identification are averaged across subjects, the psychological structure of the data is fundamentally changed. Regardless of the structure of the individual-subject data, the averaged similarity data will likely be well fit by a standard multidimensional scaling model, and the averaged identification data will likely be well fit by the similarity-choice model. In fact, both models often provide excellent fits to averaged data, even if they fail to fit the data of each individual subject. Thus, a good fit of either model to averaged data cannot be taken as evidence that the model describes the psychological structure that characterizes individual subjects. We hypothesize that these effects are due to the increased symmetry that is a mathematical consequence of the averaging operation.     

THE EFFECT OF FACTOR SCORES,GUTTMAN SCORES,AND SIMPLE SUM SCORES ON THE SIZE OF F RATIOS IN AN ANALYSIS O F VARIANCE DESIGN

Many questions in the social sciences reduce to a comparison of mean values across groups in a classical analysis of variance F test. Often the original data my come from a set of items in a questionnaire or personality inventory. When this occurs, some sort of data reduction, combining of items, or scaling procedure is first performed before the hypothesis of no difference in mean values across groups can be made. In many cases, this problem causes undue concern t0 a researcher because the effect of the scoring procedure on the distribution of F is not clear. To help solve this problem, this study was undertaken to investigate whether the method used to calculate scores has any effect on the magnitude of the F ratio in an analysis of variance, for, if it were shown that no statistical difference existd, then a researcher would have some justification for showing the procedure having minimal messes. On the other hand, if statistical differences were b arise because of the kind d scaling procedure employed, then a researcher would have to be more cautious in his choice. For this empirical investigation, Guttman, Saaotor, and simple sum scores were generated using item responses from a large pool of high school seniors. No difference in scoring method was detected when the F ratios resulting from each of the three scoring methods were analyzed. This suggests that, for chin analyses, a simple sum score may be as effective as mres derived by more complicated methods.     

THURSTONIAN METHODS IN THE MEASUREMENT OF LEARNING

A distinction is discussed between manifest and latent concepts on the one hand and observable and unobservable psychological processes (of which learning is one) on the other. Previous attempts at measurement by Hull and Björkman are briefly reviewed. An analysis is presented of improved performance in terms of the latent variables of the Law of Comparative Judgment. Finally, the author's method for successive intervals scaling is applied to some paired associate learning data.     

DIMENSION ANALYSIS OF THE PERCEPTION OF INSTRUMENTAL TIMBRE

W edin L. & G oude G. Dimension analysis of the perception of instrumental timbre. Scand. J. Psychol ., 1972, 1 3 , 228–240.—The dimensionality of the perception of instrumental timbre for single tones was investigated through multidimensional scaling according to Ekman's vector model of similarity. Three factors were extracted and they were identified with certain characteristics of the spectrum envelopes. It was found that initial transients were important for the identifiability of instrumental tones but their presence or absence did not influence the dimensional structure. The "perceptual structure" was found to be different from the "cognitive structure" (= knowledge about the classification of the instruments), and the results are general for both trained and naive listeners.     

THE USE AND UTILITY OF THE MONOTONE CRITERION IN MULTIDIMENSIONAL SCALING

The monotone criterion as a multidimensional scaling technique is theoret- ically and empirically evaluated using the algorithms of Kruskal (MDSCAL) and Guttman-Lingoes (SSA-1). Geometric configurations are used to test the recovery capabaty and other aspects of MDSCAL and SSA-1. In addition to theoretical shortcomings, the monotone criterion permits results which do not correspond to the shape of the input data. Because of its deficiencies, alterna- tive goodness-of-fit criteria are suggested in preference to the monotone criterion.     

THE DEVELOPMENT OF BEHAVIORAL OBSERVATION SCALES FOR APPRAISING THE PERFORMANCE OF FOREMEN

Behavioral observation scales (BOS) were developed for first line foremen. BOS are similar to behavioral expectation scales (BES) in that both are based on a job analysis procedure known as the critical incident technique. However, the BOS differ from BES in that, in developing BOS, (a) a group of individuals is observed and rated on a five-point scale as to the frequency with which they engage in the behavior described by each incident/statement, (b) a total score for each individual is determined by summing the observer's responses for each behavioral item, and (c) an item analysis (or factor analysis, depending upon the sample size) is conducted to select the most discriminating items. Those items with the highest correlations with the total score on a scale are retained to form one behavioral criterion or scale (BOS).     

SCALING THE EPISODIC FAMILIARITIES OF PICTURES AND WORDS

Abstract— Most current memory theories assume that judgments of past occurrence are based on a unidimensional familiarity signal In a test of this hypothesis, subjects studied mixed lists of pictures and words that occurred up to three times each They then were given two tests a forced-choice frequency discrimination test including all pairs of conditions (e g., picture seen twice vs word never seen) and a numerical frequency judgment test on individual items Forced-choice proportions for all pairings (picture-picture, word-word, and picture-word) were well fit by a one-dimensional scaling solution, suggesting a common basis of recognition and frequency judgments for both pictures and words Both forced-choice and numerical judgment data indicated that familiarities of pictures started lower than those of words but increased more rapidly with repetition Results are discussed in connection with the distinction between familiarity and recall, and the possible role of rescaling in the mirror effect.     

THE EFFECT OF CORRELATED ARTIFACTS AND TRUE VALIDITY ON THE ACCURACY OF PARAMETER ESTIMATION IN VALIDITY GENERALIZATION

The effect of non-zero intercorrelations among the three artifacts (criterion reliability, predictor reliability, and range restriction on the predictor) and true validity on the accuracy of estimation in two validity generalization models (Model 1and Model 2) was investigated. Only the Thylor Series Approximation 1(TSA1) procedure from Model 1 and the procedure with complete sample-based artifact data from Model 2 were included in this study. Six intercorrelation conditions (zero, low positive, medium positive, low negative, low negative and positive, and medium negative and positive) and two distributions of artifacts were used in this investigation. The two major conclusions from this study are: (a) Both models yielded reasonably accurate estimates of the mean of true validities (M_ρ) and (b) only Model 2 produced accurate estimates of the variance of true validities (V_ρ). The need for additional research for accurately estimating V_ρ when the three artifacts and true validity are correlated is recommended.     

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.     

CONSTRUCTING THE LAW OF PEOPLES

In this paper I shall argue that due to the constructivist procedure which John Rawls employs in “The Law of Peoples,” he is unable to justify his claim that there is a relationship between limiting the internal and external sovereignty of states. An alternative constructivist procedure is viable, but it extends the ideal theory of international justice to include liberal democratic and egalitarian principles. The procedure and principles have significant implications for non-ideal theory as well, insofar as they justify a principle of international resource redistribution and weaken general prohibitions against intervention.     

LOUDNESS AS A FUNCTION OF THE DURATION OF AUDITORY STIMULATION

The perceived loudness of a 1000 c/s tone was measured by a direct scaling method under different conditions of intensity (19–35 db) and duration (50–500 msec) of stimulation. It was found that loudness grows as a logarithmic function of stimulus duration; the relation was verified for ten individual subjects and four levels of intensity. In addition, the relation between temporal threshold and level of intensity was tentatively described.     

THE EFFECTS OF FEEDBACK ACCOUNTABILITY ON UPWARD APPRAISAL RATINGS

Do subordinates feel and respond differently to upward appraisal procedures depending on whether they are accountable or anonymous? Accountability requires subordinates to identify themselves on the upward appraisal questionnaires they complete. In an experimental field study, 38 managers and their subordinates from an insurance company were randomly assigned to use one of the appraisal procedures. As hypothesized, managers who received feedback from specific individuals in the accountability procedure viewed the upward appraisal process more positively than did managers in the anonymity procedure. However, subordinates felt more comfortable giving anonymous responses. As a result, subordinates who used the accountability procedure rated their managers significantly higher than the subordinates who responded anonymously. Therefore, the results of this study suggest that an upward appraisal procedure in which individuals are accountable for their responses may produce inflated ratings of managers' performance. Further research should compare the accountability and anonymous upward appraisal procedures to determine which procedure produces more accurate ratings.     

Evidence against “absolute” scaling

Zwislocki and Goodman (1980) argue that there exists an “absolute coupling” of numbers to sensation magnitudes and conclude that, when subjects are left unconstrained by a designated stimulus-number pair, they may use this “absolute” scale. The purpose of the studies reported here was to test whether Zwislocki and Goodman’s (1980) absolute scaling procedure reduces contextual effects due to variations in the stimulus spacing. It was found that magnitude estimations vary as a function of the stimulus spacing, regardless of whether subjects are instructed to use a standard and modulus, and, furthermore, that category ratings yield effects of the stimulus spacing comparable to those obtained with magnitude estimations. It is argued that removing the so-called constraints of a standard and modulus does not yield an “absolute” scale of sensation. The absolute scaling procedure increases response variability and thereby lowers the power of a test for contextual effects.     

PERCEPTION AND JUDGMENT OF FACIAL EXPRESSIONS AMONG THE CHINESE

Perceived relationships among nine facial expressions were structurally represented in a two-space configuration by multidimensional scaling procedure. The two dimensions operative for Chinese judges were interpreted as positive versus negative emotions and open versus controlled styles of expressions. While there was some consensus in identifying seven of the nine intended emotions, interest-excitement and disgust-revulsion were often not recognized. Implications of cross-cultural comparisons in identification rates were discussed.     

THE SEMANTICS OF FACIAL EXPRESSIONS AND THE PREDICTION OF THE MEANINGS OF STEREOSCOPICALLY FUSED FACIAL EXPRESSIONS

Two experiments were concerned with scaling affective meanings of posed facial expressions using a specially devised form of semantic differential and with determining the extent to which the meaning of stereoscopically fused facial expressions could be predicted. Both experiments provided evidence for at least three dimensions. High reliability for scaling the affective meanings of facial expressions was demonstrated. Two methods were employed for predicting the meaning of a composite expression. The results indicated that the predictions based on the congruity principle do no better than those based on a simple algebraic mean of the two components.     

THE EFFECTS OF SELF-MONITORING AND SUPERVISOR FEEDBACK ON STAFF PERFORMANCE IN A RESIDENTIAL SETTING

We evaluated the effects of a self-monitoring procedure to increase staff on-task behavior and adherence to scheduled activities. Self-monitoring involved the use of activity cards that staff members completed and carried with them to assist in determining the activities for which they were responsible at any given time. Increases in both on-schedule and on-task behavior resulted. Supervisor feedback was subsequently added because some staff members did not maintain consistently high levels of performance. Generalization data indicated that staff members implemented the procedure during evening hours without specific programming. The advantages and limitations of using a self-monitoring procedure for improving performance of staff members in residential settings are discussed.     

Interactive scaling with individual subjects

A metric multidimensional scaling (MDS) procedure based on computer-subject interaction is developed, and an experiment designed to validate the procedure is presented. The interactive MDS system allows generalization of current MDS systems in two directions: (a) very large numbers of stimuli may be scaled; and (b) the scaling is performed with individual subjects, facilitating the investigation of individual as well as group processes. The experiment provided positive support for the interactive MDS system. Specifically, (a) individual data are amenable to meaningful interpretation, and they provide a tentative basis for quantitative investigation; and (b) grouped data provide meaningful interpretive and quantitative results which are equivalent to results from standard paired-comparisons methods.This report was supported in part by a PHS research grant, No. M-10006, from the National Institute of Mental Health, in part by a Science Development grant, No. GU-2059, from the National Science Foundation, both granted to the Psychometric Laboratory at the University of North Carolina, and in part by a PHS research grant, No. MH-16474, from the National Institute of Mental Health, Public Health Service, granted to the second author. The major portion of this research was performed while the second author was the L. L. Thurstone Distinguished Fellow at the Psychometric Laboratory of the University of North Carolina while on leave from the University of Southern California. The authors are indebted to Amnon Rapoport and Thomas S. Wallsten for their critical evaluations of an earlier version of this report. While this paper was entirely a cooperative effort on the part of both authors, the first author was primarily responsible for the algorithms, and the second for developing the mathematical model.     

Loudness bisection and masking in the rat (Rattus norvegicus).

The bisection method of animal psychophysical scaling was examined as a measurement procedure. The critical assumptions of bisection scaling, as described by Pfanzagl (1968), were tested to determine if a valid equal-interval scale could be derived. A valid scale was derived in which loudness for the rat (Rattus norvegicus; n = 13) was a power function of sound pressure for 4-kHz tones. Masking noise reduced the discriminability of tonal stimuli but did not affect the bisection point. This result is consistent with an interval scale representation of loudness and demonstrates scale meaningfulness. Loudness bisection data that have been reported in the literature for 3 species (humans, rats, and pigeons) are in substantial agreement with our results.     

独体汉字的字形相似性研究

本文以速示呈现方式获得了一系列独体汉字和字符的混淆矩阵。用Luce（1963）的选择模型特混淆矩阵分解为对称的相似矩阵和反应倾向矢量。基于相似矩阵,以聚类分析和多维量表法探索了汉字和字符的视觉特征及其表征形式,为揭示汉字视觉特征的几何特性和潜在结构,在研究方法上作了有意义的偿试、此外,本研究的结果支持了作者（1995）关于在含“十”或“口”的独体汉字中,“十”与“口”是该类汉字的突出视觉特征的结论。