Method Of Successive Intervals Research Articles

Verb tense, negatives, and other determinants of the intensity of evaluative meaning

Fourteen adjectives were rated along an 11-point scale of (Un) Favorableness, both singly and when preceded by each of 21 Quantifiers. The Quantifiers consisted of: eight adverbs denoting Frequency (e.g., Often ); severn adverbs denoting Temporal proximity (e.g., Soon ); three Verb Tenses ( Is, Was, Will be ); and three Negatives ( Not, Un —, and Not un —). Data from 88 S s were scaled by a successive intervals method. Empirical scale values for all Quantifier-Adjective pairs were tested against a linear model. All four categories of quantifiers exert decremental effects on the degree of evaluative polarization of the adjectives, to comparative extents which are consistent with a priori and theoretical expectation. Some implications of the findings for measurement and development are briefly discussed.

RELIABILITY ESTIMATE FOR FAVORABILITY (SOCIAL DESIRABILITY) RATINGS OF MMPI ITEMS.

items. A product-moment correlation coefficient was computed between the two different sets of favorability ratings for these 16 items. The resulting coefficient was ,987. While these 16 items may not be regarded as representing a random sample of MMPI items, they are quite heterogeneous regarding content when compared with the MMPI item content categories described by Wiggins and Vollman (1959). Messick and Jackson (1961), using the method of successive intervals, developed SD scale values for MMPI items and found a similar correlation coefficient (.984) between the two sers of SD scale values for these duplicate items. There has been a surprising degree of similarity among the various sers of SD scale values developed for MMPI items. Messick and Jackson found that their SD values for MMPI items correlated ,964 with the Heineman values. Mees, Gocka, and Holloway (1964) reported a correlation of .35 between their SD scale values for those 178 California Personality Inventory items identical with MMPI items and the Messick-Jackson SD scale values for these 178 items. As Messick and Jackson have suggested, regarding MMPI items, [here appears to be extremely high stability of average desirability judgments and their comparability across samples (p. 413). It appears, if we generalized €tom the high similarity of reported MMPI item SD values and from the studied 16 items, thar the Heineman favorability (desirability) ratings for MMPI items possess high reliability.

Psychological Study on Optimal Levels of Illumination

The previous studies on the optimal levels of illumination [1, 2, 3] have been based on the data of the threshold. But the threshold itself has no connection with the optimal levels of illumination. This study purports to construct a scale for easiness of reading a letter (which we shall hereafter call “readability”) without referring to the threshold data, and express the “readability” as a function of the size, contrast and brightness of the letter.The objects used in the experiments (Exp. I and Exp. II) were Chinese characters with various sizes (Table 1) and contrasts (Table 2). Here the contrast was defined by the logarithm of the ratio of the brightness of the object to that of the background. In Exp. II Chinese characters printed on a newspaper and a dictionary were also used. Subjects (4 persons) observed the object under various levels of illumination (Table 3) from the distance of 2 m in Exp. I and from the distance of 30 cm in Exp. II. The experiments were designed so that every letter might be observed under every level of illumination. The subjects were required to evaluate the “readability” of each letter by categories shown as follows.0 cannot see it at all.1 can see something but cannot read it.2 can guess the letter.3 can read with effort.4 can read but cannot see the fine structure of the letter.5 can read and see the fine structure of the letter but feel tiresome to read a number of such letters for a long time.6 can read easily but not easily enough.7 can read very easily and feel just right.8 feel too much brightness and/or too much contrast.9 feel unpleasant because of too much brightness and/or too much contrast.By the method of successive intervals [4] the subjective scale of “readability” was constructed from the data obtained. The principle of the method may be outlined as follows. The “readability” is assumed to be one-dimensional continuum S. In Fig. 3, S is represented on the abscissa. Then, the probability distribution of the “readability”S for a given level of illumination E, for all the possible grades of size, contrast and complexity of the object will look like the solid curve below E in Fig. 3. In the present paper the distribution is assumed to be normal.Now the categories mentioned before are assumed to correspond to nine consecutive and nonoverlapping intervals, -L0-L1-L2-...L8-, on the S-axis. The determination of the location of these intervals on the S-axis will lead to establishing a scale of “readability”. For this purpose the location (and hence the lengths) of the intervals were adjusted so that the probability distribution of S might become normal for all levels of Ei (i=1-7).The results and consideration. The method of successive intervals described in the preceeding paragraph can be applied to the data of the present experiment very well as is shown in Fig. 5. One can, therefore, define a scale of “readability” as follows. The “readability” 0 corresponds to the situation where one can not read the object. The “readability” 100 corresponds to the situation where one can read the object very easily and feels just right. The intermediate values of the “readability” are defined by dividing the distance between 0 and 100 on the abscissa of Fig. 5 into 100 equal parts. Actually, the origin of the scale is arbitrary since the scale is a so called interval scale, hence, only the difference of “readability” is meaningful.

Probabilistic adverbial qualifications of adjectives

Summary These two inquiries are concerned with the effects of probabilistic adverbs (e.g., possibly, definitely ) upon evaluative ratings of adjectives. In Study I, 14 adjectives were rated, along a Pleasant-Unpleasant scale, both in unqualified form and when qualified by each of 10 probabilistic adverbs. Data were scaled by the method of successive intervals. The scale values were then tested against a linear model originally proposed by Cliff to account for the effects of intensive adverbs upon adjectives. This model states that the scale value of an adverb-adjective phrase equals the product of the psychological scale value of the unqualified adjective and an empirical “multiplying value” for the adverb, plus a general constant, K . It was found that the effects of probabilistic adverbs are highly consistent. The correlation between empirical scale values and theoretical ones derived from the model was .987 ( df = 138). It was shown that while the majority of variance is accounted for by adjectives rather than adverbs, nevertheless the high correlation cannot be considered artifactual and thus be attributed to chance effects of the adverbs. In Study II, 7 adjectives from Study I were rated along the same Pleasant-Unpleasant scale both in unqualified form, and when qualified by: (1) each of 4 discriminable probabilistic adverbs from Study I; (2) each of 4 discriminable intensive adverbs from Cliff's study; (3) each of the 32 possible combinations of 1 probabilistic and 1 intensive adverb. Data were again scaled by the method of successive intervals. This study posed two questions. (1) Can the empirical effects of double adverbial qualification be predicted from the observed effects of the two constituent adverbs when used singly? (2) Does the Adverbial Order variable yield differences in the scale values (e.g., definitely rather scared vis-a-vis rather definitely scared )? Five extensions to the basic model, designed to take account of double qualifications, were derived. The effects of double adverbial qualifications were excellently predicted using empirical data derived only from instances of single qualification. The two highest, linear correlations between empirical and theoretical scale values ( r = .991 and .987) for the 224 instances of double qualification were obtained using, as the multiplying value for double adverbial qualifiers, the geometric mean of the multiplying values for the two individual adverbs. The effect of the Adverbial Order variable was negligible. While the majority of variance was again attributable to the adjectives, the superior predictability of the data could not be accounted for by appeal to chance effects of the adverbs. It was also established that an interaction occurs between the effects of the two classes of adverbs. Psychological implications of the relative equivalence of intensive and probabilistic adverbs, of their interaction, and of the non-significant Adverbial Order variable are discussed.

絶対尺度構成による児童の9学年にわたる知能発達に関する考察

The data analysed in the present study were laboriously collected for ten years by Dr. Hiroshi Kano and other members of the Institute for Science of Labour, and the author is much obliged to Dr. Kano for making the data available for her analysis. The main purpose of the present study is to construct the absolute scale of intelligence developed by Thurstone, L. L., on the basis of raw scores of Suzuki-Binet Intelligence Test administered once a year to apprroximately four or five hundred children for nine successive years since they entered a elementary school in Tokyo in 1946 (first group) and in 1947 (second group) till they graduated from the adjacent junior high school. The original data were rescored for the sake of convenience according to new criteria, among which the following one is important: an item is regarded to be solved by an examinee if it has been solved by him at least once in the preceding testings no matter it is practised to him this time or not.In the absolute scale construction it is assumed that the variable x, representing the mental ability required in solving Suzuki-Binet items, is normally distributed for the examinees at each grade level i, on one dimension with Mi as the mean and σi as the standard deviation, and the critical value ls corresponding to each raw score s is also located on the same continuum, and that only those examinees who possess more or less higher values of x than ls get higher marks than s in testings. However, in the course of analysis it was discovered that the assumption of normality was needed to be slightly modified as it was the case in the author's previous study of absolute scale construction of the same Suzuki-Binet Test data collected by Dr. Jisaburo Suzuki. The two distributions were contrasted and the present one proved to be more leptokurtic (see Fig. 4). The scaled values for ls, Mi and σi were obtained by using the method of successive intervals and the graphical least squares solution developed by Diederich, G. W., and those values were converted to l′s, M′a and σ′a with newly defined origin and unit for being compared with the values ls, Ma and σa obtained from Dr. Suzuki's data (see Table 5, 6 and 7, and Fig. 5).The average growth curve of intelligence developed from the values of M′a and the standard deviation as a function of age were illustrated and compared with those obtained from Dr. Suzuki's data respectively (see Fig. 6 and 7). The two growth curves coincide with each other in spite of the fact that the two samples differ in various respects, in time and district and that the former consist for the most part of the same examinees throughout all the grade levels while the latter consist of different examinees at each age level. The standard deviation σ′a was found to be more invariant from age to age than in the case of σa obtained from Dr. Suzuki's data, and this fact seems to have some connection with the slightly different definitions of the raw scores in the two cases.

An Application of the Method of Successive Intervals to the Study of Fear-Arousing Information

An Application of the Method of Successive Intervals to the Study of Fear-Arousing Information

CONSTRUCTION OF SOME JUDGMENT SPACES

ABSTRACTCritical factors in the differing reactions of observers toward known persons, and thus important ones for interpersonal relations, are the preconceptions which observers bring to particular social situations. Because of inherent difficulties in communicating through language the organization of these preconceptions, use of dimensional judgment models for studying these preconceptions is proposed. These dimensional models require estimation on an interval scale of interstimulus distances (relative interpoint distances). Measurement of relative interpoint distances may be achieved using judgments of relative similarity of stimulus pairs.Multidimensional scaling studies of a variety of stimulus types have been conducted in the past. In none of these have the assumptions required been tested in applications where known persons are the stimuli. Hence, the general objective of the present experiment is the application of two multidimensional scaling methods to construction of judgment spaces where the points are known persons, and that testing of the assumptions required may be accomplished. To this end specific objectives of the present study are: to determine whether the Complete Method of Triads and the Method of Successive Intervals yield similar results in terms of interpoint distance differences; to determine whether in terms of relative interpoint distances judgments of similarity with respect to a general trait yield results similar to those when judgments of similarity are made with respect to a domain defined by specific instances of relevant behavior; to determine whether the body of assumption agrees with observed data in terms of goodness of fit; and to determine the dimensionality of the space, observing whether coordinates on the respective dimensions relate to peer nominations of the trait judged. To accomplish these specific objectives two experiments were conducted. In the first of these, 86 first classmen (seniors) from the United States Coast Guard Academy provided judgments of similarity with respect to Adaptability using the Complete Method of Triads and the Method of Successive Intervals. In addition, Successive Intervals judgments of similarity with respect to a behavioral domain defined by a list of specific behaviors (all behaviors were, in the experience of the Cadets, related to the concept of Adaptability) were obtained. Finally, peer nominations of “most adaptable” and “least adaptable,” gathered several weeks prior to the conduct of the scaling experiment, were obtained.In the second experiment, two groups of Naval Aviation Cadets provided judgments of similarity with respect to Leadership. There were 20 judges in one group and 21 judges in the other. The Cadets had known each other for about fourteen weeks.In terms of the specific objectives, the results of the studies conducted were that: interpoint distance differences obtained by the Complete Method of Triads and the Method of Successive Intervals correlated .88, indicating that the underlying spaces are essentially the same; relative interpoint distances obtained using the general term “adaptability” and those obtained using a specific set of behaviors to define the trait domain correlated .93, indicating that the underlying spaces are essentially the same; theoretical proportions, computed using parameters obtained through the scaling, have a good approximation to the observed proportions; and the dimensionality of the obtained spaces was three—one with large variation and the other two with less variation than the large one but about equal to each other. The first dimension in the Adaptability space correlated −.92 with peer nominations of adaptability while the other two dimensions were essentially unrelated to the peer nominations. These results supported acceptance of the dimensional model, together with the scaling techniques. It is not felt, however, that the adaptability concept was resolved into component parts. Implications of these results are discussed.

A Patient Progress Scale

In evaluating effectiveness of treatment programs for psychiatric inpatients, it is often desirable to supplement symptom ratings with more global estimates of change. Psychiatrists in particular complain that the subtle, rare, and complexly integrated aspects of the clinical picture are not captured by discrete symptom or behavioral ratings. Overall clinical impression is often considered unsatisfactory for other reasons. During treatment, psychiatrists continually make decisions about individual patients, predicated upon a coral impression of the patient and knowledge of him as a person, his strengths as well as his weaknesses. Statements representing typical clinical decisions, such as type of ward placement, pass and privilege status, and the like were prepared and submitted to 55 psychiatrists to be judged on a nine-point scale along the continuum of of functional adjustment. Scale values of the items, obtained by the method of successive intervals, ranged from .246 (Has been placed on a suicide observation status) to 6.326 (Has resumed his customary social role in his community). Examples of intermediate items are: No-privilege scam (1.445), Limited ground privileges (2.907), Full ground privileges (3.869), Maximum security ward (.289), Closed ward 1.309), Supervised open ward (3.811), and Open ward (4.540). For our initial purposes, all 45 items were retained and psychiatrists are asked to check all items tha: pertain to a patient at a given time. The average scale value of the items checked (usually 4 to 8) is taken as an indication of the patient's status wichin the hospital at the time of rating and the difference between two such values as an indication of his progress. Although many subjective factors enter into a clinical decision, once made it is concrete and can be rated objectively without these judgments being involved. This should curtail the bias toward rating improvement that sometimes occurs when therapists rate their own patients. Data from 233 newly admitted schizophrenic patients showed a shift in the means from 1.742 to 2.485 after one month of hospitalization, a difference significant beyond the ,001 level (analysis of variance). Whether the scale will be successful in distinguishing berween differentially treated groups remains to be seen. As additional data are obtained some items may be discarded and alternative scoring procedures adopted but preliminary experience suggests that this may be a useful way to record a patient's progress wichin the hospital. The approach is similar to that of Gordon, et al. (1957), who scaled ward membership, but may have wider application because the clinical decisions are similar from hospital to hospital. REFERENCE GOWN, M. H., LINDLFI, S. B., & my, R. B. A criterion measure of within-hospita1 change in psychiatric illness. I. din. Psychol., 1957, 13, 145-147.

Some Invariant Findings under the Method of Successive Intervals

Some Invariant Findings under the Method of Successive Intervals

鈴木ビネー知能測定法における素点に立脚した絶対尺度の構成

The purpose of this study is to construct the absolute scale of mental abilities developed by L. L. Thurstone on the basis of the raw scores of the Suzuki-Binet Intelligence Test given to 15, 820 children by Dr. J. Suzuki. The age of the children whose scores were used in this study ranged from 4 years to 12 years and 6 months, and they were classified into 18 age groups. The method of successive intervals developed by G. W. Diederich was applied in the course of scaling.It was assumed that the variable x, the mental ability required in solving the problems, was normally distributed for each age group, i, on the continuum with Mi as the mean and σi as the standard deviation. It was also assumed that there existed the critical value, tg, on the same continuum corresponding to each raw score, g, and that only those who had higher values of x than tg could get higher marks than g (see Fig. 1).However, in the course of analysis it was discovered that the assumption of normal distribution of x was somewhat inadequate and needed to be modified. The new distribution thus derived was much the same as normal distribution, but was slightly skewed to the right (see Fig. 4).The relationship among tg, Mi, σi and Z′ig, the deviate value of the new distribution corresponding to the distance from Mi to tg, is shown by the equation: tg=Mi+σiZ′ig. The values of tg, Mi and σi were obtained by the graphical solution developed by Diederich (See Fig. 5, Table 3 and Table 4).There was some variation in the values for t(g+1)-tg, but, where more than 30 children were available for obtaining a tg, the range of the variation was between .04 and .07 (see Table 3). This fact shows that the difference between the mental abilities required to get any 2 successive scores, g and (g+1), in the Suzuki-Binet Intelligence Test is almost the same regardless of the g value.From the values of Mi thus obtained the growth curve of intelligence was developed. It was slightly different from the growth curve obtained by Yokoyama and Indow (1), in which the absolute scale of the same data was constructed by using, as the landmark, the proportion of the right answers to each item of the test, though the amount of data available was 1/4 of that of the present study' the previous curve was almost a straight line while the present one proved to be slightly convex (see Fig. 6).As to σi as a function of age, a more remarkable difference was discovered between the results of the present study and those of the previous one (Yokoyama and Indow). In the previous study there appeared a tendency for the value of σi to become larger as the age increased. However, in the present study, no such tendency was discovered; the values of the standard deviation proved to be almost the same for all ages. The location of the absolute zero point, which was suggested by L. L. Thurstone, therefore, could not be determined from the results of the present study (see Fig. 7).

An axiomatic formulation and generalization of successive intervals scaling

A formal set of axioms is presented for the method of successive intervals, and directly testable consequences of the scaling assumptions are derived. Then by a systematic modification of basic axioms the scaling model is generalized to non-normal stimulus distributions of both specified and unspecified form.

Applicability of the Edwards Personal Preference Schedule to Nisei

The Edwards Personal Preference Schedule (EPPS) is designed to measure 15 personality variables by forced choices between pairs of statements. Statements in the EPPS were scaled for social desirability by college students. Statements representing different needs were then matched for social desirability. This technique reduced the correlation between social desirability and the probability of endorsement in normal college populations from .87 to .40. The purpose of the present study was to investigate the applicability of the EPPS to a cultural subgroup of Nisei students. Specific hypotheses investigated were: ( a ) The social desirability scale values of the EPPS items for the Nisei group will not differ significantly from those of the normative group. ( b ) The social desirability matching of paired items in the EPPS is adequate for the Nisei population. Ss were 50 men and 50 women Nisei students enrolled at the University of Washington. Group I, 25 of each sex, scaled the EPPS items for social desirability. Group 11, 25 of each sex, were administered the EPPS. For Group I the original list of 140 items used in constructing the EPPS was presented. A 9-point scale was used to obtain ratings of social desirability for each statement. Scale values were obtained by the method of successive intervals. The product moment correlation between these values and the scaled values of the normative group, obtained by the same method, was 95. To determine if the paired statements were matched adequately for Nisei, Fisher's intra-class correlation was calculated. The obtained value of .76 for the Nisei group compares favorably with the .85 correlation for the normative group given by Edwards. The results of giving the EPPS to Group I1 showed no significant differences, at the 1% level, between individual trait means of like sexes for the Nisei and the normative group. A rank order correlation of the means was calculated between like sexes. Correlation between the means for men was .44. This low rank order correlation indicates some difference in the organization of variables for the Nisei men as compared to the normative group men. The rank order correlation between the variable means for Nisei women was .79. This correlation, plus the lack of significant differences of means, supports the interpretation that Nisei women represent a sample from the general college population.

An empirical evaluation of multidimensional successive intervals

The multidimensional method of successive intervals and the method of complete triads are applied to similarity judgments of Munsell colors varying in brightness, saturation, and hue. Both methods yield configurations that correlate highly with the Munsell color structure. This validation of these scaling methods in an area of known dimensionality indicates their applicability for exploration in areas of unknown dimensionality.

The validity of the successive intervals method of psychometric scaling

The degree to which scale values computed by the method of successive intervals diverge from theoretically “true” values is seen to be due to three types of error: error due to inequalities in variances of the distributions from which the scale values are computed, error due to non-normality of the distributions, and sampling error. The contribution of each type of error to the total error is evaluated; the latter is seen to be surprisingly small under appropriate conditions. Certain aspects of the formal methodology underlying scaling procedures are also briefly considered.

The estimation of the discriminal dispersion in the method of successive intervals

A new algebraic formula is derived for estimation of the discriminal dispersion in the method of successive intervals. The legitimate use of the formula requires that as many normal deviates as possible be present in the matrix. For this reason, it is recommended that deviates corresponding to the interval (0.01, 0.99) of the cumulative proportions be used, instead of those corresponding to (0.05, 0.95), the interval used by Edwards and Thurstone. Computations on data published by Edwards and Thurstone showed that when adjustment was made for variability in dispersions calculated by the formula of this paper, a reduction of fifty per cent in mean absolute discrepancy was produced. Since the formula is easy to use and avoids the disadvantages of its predecessors, it should have fairly wide applicability in psychological research.

THE PERCEPTION OF ATTITUDE RELATIONSHIPS: A MULTIDIMENSIONAL SCALING APPROACH TO THE STRUCTURING OF SOCIAL ATTITUDES

ABSTRACTThe primary purpose of this study was to see whether a set of perceived attitude relationships could be adequately represented by a dimensional model. The particular attitude area selected for this purpose was composed of attitudes toward war, capital punishment, and the treatment of criminals. A multidimensional method of successive intervals based upon the Euclidean model of multidimensional psychophysics was developed. If this model satisfactorily accounted for perceived relationships among statements of the three attitudes, it would also be possible to discover the number and the nature of the relevant dimensions involved. A secondary purpose of the experiment was to investigate judgments made by two diverse groups in order to discover whether they perceive attitudes as being structured in different ways.However, since the multidimensional method of successive intervals had not yet been applied even in the area of psychophysics, it was felt that an empirical evaluation of the method in an area of known dimensionality would be appropriate before any conclusions could be legitimately drawn concerning areas of unknown dimensionality. Accordingly, both multidimensional successive intervals and the previously validated method of complete triads were applied to judgments of color similarity obtained from 42 subjects. The stimuli were a set of Munsell colors of the same red hue, but differing in brightness and saturation. Both the multidimensional successive intervals and the complete triads structures, which were essentially identical, correlated highly with the Munsell color structure as an approximation to psychological color space. There were also indications of high reliability for the multidimensional successive intervals technique.In view of its validation in an area of known dimensionality, multidimensional successive intervals was applied to judgments of attitude relationships. Seven statements were selected from each of the three Thurstone scales on attitude toward war, capital punishment, and the treatment of criminals, and these 21 statements were set up in booklet form for group presentation. The attitude booklets were administered to 40 third‐year, male students at the Princeton Theological Seminary and to 82 male Air Force officer candidates at Lackland Air Force Base.The multidimensional attitude structures perceived by the two diverse groups were essentially identical, the relationships among statements of the three attitudes being adequately represented in terms of two oblique dimensions, a war dimension and a punishment dimension. Apparently individuals do perceive attitudes, at least in this particular attitude area, in terms of a definite structure, and when called upon to make judgments concerning attitude relationships, they respond in terms of this dimensional frame of reference.

A least squares solution for successive intervals assuming unequal standard deviations

A least squares solution has been presented for the Law of Categorical Judgment and the Method of Successive Intervals, which is formally equivalent to Horst's solution for the matrix of incomplete data. A simplified approximation which is recommended for use with any matrix of complete data is also given. A procedure, analogous to that originally devised by Thurstone and presented by Saffir, is outlined for the typical experimental matrix of incomplete data. It is essentially a “point and slope” method of fitting a straight line which comes rather directly from the least squares solution.

An internal consistency check for scale values determined by the method of successive intervals

The method of successive intervals is a psychological scaling procedure in which stimuli are classified into successive intervals according to the degree of some defined attribute which they are judged to possess. A psychological continuum is defined and the scale values are then taken as the medians of the distributions of judgments on the psychological continuum. It is assumed that the distributions of judgments for each stimulus are normal on the psychological continuum as defined.

The scaling of stimuli by the method of successive intervals.

The scaling of stimuli by the method of successive intervals.

A modification of the method of successive intervals

A modification of the method of successive intervals is presented which yields scale values correlating .995 with those from Thurstone's method described by Saffir. Values yielded by the present method can be obtained in 25 per cent of the time required by the older method and are shown to be, on apriori grounds, more reliable as well.