Minimal conditions for additive conjoint measurement and qualitative probability

Axioms for additive conjoint measurement and qualitative probability are given. Representation theorems and uniqueness theorems are proved for structures that satisfy these axioms. Both Archimedean and nonarchimedean cases are considered. Approximations of infinite structures by sequences of finite structures are also considered.     

Utility-uncertainty trade-off structures

A qualitative axiomatization of a generalization of expected utility theory is given in which the expected value of simple gambles is not necessarily the product of subjective probability and utility. Representation and uniqueness theorems for these generalized structures are derived for both Archimedean and nonarchimedean cases. It is also shown that a simple condition called distributivity is necessary and sufficient in the case of simple gambles for one of these generalized expected utility structures to have simultaneously an additive subjective probability function and a multiplicative combining rule for expected values.     

Reducing cigarette smoking in a retarded adult: An application of self-management procedures

An attempt was made to reduce the overall number of cigarettes smoked per day with a mildly retarded adult. Self-monitoring was compared to self-monitoring plus self-graphing and goal setting procedures in reducing the number of cigarettes smoked. Self-monitoring plus self-graphing and goal setting was superior to self-monitoring alone when the goal was set at 15 cigarettes per day, but the actual number of cigarettes smoked increased when the goal was set at 12. The number of cigarettes smoked during all treatment conditions was lower than either baseline conditions. The therapist also reduced the patient's caffeine intake and switched the client's brand of cigarettes to a low “tar”/nicotine brand. The reduction in caffeine and “tar”/nicotine was related to a small and transient increase in somatic complaints and verbal abuse, as well as the complete elimination of nocturnal enuresis. Brand switching to low “tar”/nicotine cigarettes did not result in an increase in the number of cigarettes smoked per day.     

A SELF-INSTRUCTIONAL PACKAGE FOR INCREASING ATTENDING BEHAVIOR IN EDUCABLE MENTALLY RETARDED CHILDREN

The purpose of this study was to develop a self-instructional package that would aid highly distractible retarded children in increasing their attending behavior in a training and two generalization (a one-to-one and a classroom) situations. Three untrained subjects were monitored for general comparison and social validation purposes. One of these control subjects was distractible and the other two (criterion comparison) were evaluated as not having attentional problems. A multiple baseline design was employed in which training was sequentially introduced across subjects. During training, the experimental subjects were taught through self-instruction to focus their attention and to cope with two tasks, math and printing. After learning the self-instructions the subjects were systematically and sequentially exposed to photo-slides of distracting situations, to audio-distractors composed of noisy lunchroom verbal peer interactions, and to in vivo distractors provided by kindergarten children playing with wooden blocks in the training setting. The entire training procedure was handled in a game-like context to maintain subject interest and to facilitate generalization. The results suggested that the training package produced direct and generalized changes in self-instructional behavior. In addition, a decrease in off-task behavior occurred during math, printing, and also during a phonics program in the one-to-one and classroom situations. However, reliable changes in academic task performance were not observed. Finally, no systematic changes on any of the dependent measures occurred for the three untrained subjects.     

A general nonmetric technique for finding the smallest coordinate space for a configuration of points

LetA ₁,A ₂, ...,A _n be anyn objects, such as variables, categories, people, social groups, ideas, physical objects, or any other. The empirical data to be analyzed are coefficients of similarity or distance within pairs (A _i,A _i ), such as correlation coefficients, conditional probabilities or likelihoods, psychological choice or confusion, etc. It is desired to represent these data parsimoniously in a coordinate space, by calculatingm coordinates {x _ia } for eachA _i for a semi-metricd of preassigned formd _ij =d(|x _i1 -x _j1 |, |x _i2 -x _j2|, ..., |x _im -x _jm |). The dimensionalitym is sought to be as small as possible, yet satisfy the monotonicity condition thatd _ij <d _kl whenever the observed data indicate thatA _i is closer toA _j thanA _k is toA _l . Minkowski and Euclidean spaces are special metric examples ofd. A general coefficient of monotonicity is defined, whose maximization is equivalent to optimal satisfaction of the monotonicity condition, and which allows various options both for treatment of ties and for weighting error-of-fit. A general rationale for algorithm construction is derived for maximizing by gradient-guided iterations; this provides a unified mathematical solution to the basic operational problems of norming the gradient to assure proper convergence, of trading between speed and robustness against undesired stationary values, and of a rational first approximation. Distinction is made between single-phase (quadratic) and two-phase (bilinear) strategies for algorithm construction, and between hard-squeeze and soft-squeeze tactics within these strategies. Special reference is made to the rank-image and related transformational principles, as executed by current Guttman-Lingoes families of computer programs.This research was supported in part by the National Science Foundation of the United States Government, through Grant No. GS 929 to the University of Michigan.I am deeply indebted for many helpful comments on earlier drafts of this paper received from Joseph Kruskal, James Lingoes, and the managing editor.     

La Signifique De Mannoury Comparee A La Physique Quantique Et A La Cybernetique

Sans résumé     

The test-retest reliability of qualitative data

The test-retest reliability of qualitative items, such as occur in achievement tests, attitude questionnaires, public opinion surveys, and elsewhere, requires a different technique of analysis from that of quantitative variables. Definitions appropriate to the qualitative case are made both for the reliability coefficient of an individual on an item and for the reliability coefficient of a population on the item. From but a single trial of a large population on the item, it is possible to compute alower bound to the group reliability coefficient. Two kinds of lower bounds are presented. From two experimentally independent trials of the population on the item, it is possible to compute anupper bound to the group reliability coefficient. Two upper bounds are presented. The computations for the lower and upper bounds are all very simple. Numerical examples are given.