Clyde H. Coombs

The assessment of partial knowledge

THE general acceptance of the multiple-choice type test item as the best one for objective measurement of aptitude or achievement does not imply that its merits are optimal. Any variation upon an already widely accepted and useful technique which indicates promise of improved measurement is deserving of further investigation. A response method3 for multiple-choice items which has certain theoretical advantages over the conventional response method is considered here, and this study is an empirical investigation of some of its relative merits. The conventional response method (C method) for multiplechoice items requires selecting and marking the answer from among the choices offered. In this study it was to pick one of four. The conventional item score in a power test is one point when the answer is chosen and zero when a distracter is chosen. Complete information leads to an item score of one and misinformation to a score of zero. Partial information may lead to a score of either one or zero. The inability of the

Preference scales for number and sex of Children

Summary A measurement—theoretical approach to the scaling of preferences for number of children and sex composition is developed to provide a feasible field procedure for studying factors affecting size bias and sex bias and for studying the effects of such biases on realized family size. The measures, reflecting the individuals utility for number and sex of children, go beyond global stated preferences and are sensitive to deviations from a first choice. The procedures derive from a model based on developments in psychological measurement in unfolding theory and additive conjoint measurement. This model disentangles size and sex bias, giving independent measures of each. A methodological sample of University of Michigan students is used to test and illustrate various aspects of the model in some detail. Field pre-tests in Taiwan provide data from another culture for further testing of the model and method. In addition, simplified and abbreviated interview procedures were field-tested there. Two other se...

On a connection between factor analysis and multidimensional unfolding

Given the preference ordering of each of a number of individuals over a set of stimuli, it is proposed that if the preference orderings are generated in a Euclidean space ofr dimensions which can be recovered by unfolding the preference orderings, then a factor analysis of the correlations between individuals preference orderings will yield a space ofr + 1 dimensions with the originalr-space embedded in it, and the additional dimension will be one of social utility. The proposition is clearly shown to be satisfied by means of the Monte Carlo technique for both random and lattice stimuli in three dimensions and for two other examples with random stimuli in one and two dimensions.

Polynomial psychophysics of risk

Abstract Three mathematical transformations on two-outcome games are defined. It is assumed that these transformations induce corresponding transformations on perceived risk. The rule governing the joint effect of these transformations is assumed to be the distributive model. An experiment is reported in which a class of simple polynomials are compared using the measurement-free methods of polynomial conjoint measurement. Substantial support for the distributive model is obtained.

A test of ve-theories of risk and the effect of the central limit theorem

Abstract There are several theories of risk which indicate that risk could be a function only of variance and expectation. A transformation on odds or skewness was constructed which left the variance and expectation of a gamble unchanged. Perceived risk was clearly a function of this transformation as well as variance and expectation, even under multiple play in which the effect of the central limit theorem modifies the effect of skewness but it remains a relevant variable.

Testing expectation theories of decision making without measuring utility or subjective probability

Abstract Certain empirical implications of those decision-making theories which involve maximizing an expectation are derived. These implications are all measurement-free, so neither subjective probability nor utility need be measured. Two experiments are reported, the first exploratory and the second intensive and substantial. EV, EU, and SEV theory were inadequate to account for the behavior of 12% or more of the subjects in either experiment. SEU theory was inadequate in 10% or less of the cases in the first experiment and 5% of the cases in the second experiment.

A factorial study of number ability

In order to investigate certain hypotheses concerning the nature of number ability, and, secondarily, the nature of perceptual speed, a battery of thirty-four tests was given to 223 Chicago high school seniors and the data were factored by the centroid method. Seven primary factors were identifiable upon rotation. Several deductions are made relative to the interpretation of the factors and relative to the consistency of the data with the hypotheses which were to be tested.

Risk-preference in coin-toss games

It is hypothesized that an individual has a preferred unidimensional risk level in a coin-tossing game, and that his preferences are single-peaked over the risk scale. Risk was varied by increasing both the monetary denomination (D = le to

Tests of the betweenness property of expected utility

1) and number of tosses (N = 1 to 20) involved in a game. The rank order preference data of 30 subjects within sets of games having either constant D or N, single stimulus preference data, and pair comparison preferences between games supported these hypotheses. Data also supported the existence of a function R,[(D, N)] which maps games onto the risk scale and is monotone increasing in both arguments. However, the exact form of the function may vary, depending on the particular set of games from which the subject chooses. The prevailing expectation theories of individual decision making in a risky situation (Edwards, 1954, 1955) all avoid the subjective variable of riskiness. However, this variable has been given some attention as a stimulus dimension relevant to choice (Coombs and Pruitt, 1960; Royden, Suppes, and Walsh, 1959). In these experimental studies, the variance or some other parameter of the frequency distribution of a game’s possible outcomes was explored as a potential correlate of risk. The evidence supports the hypothesis that variance is a strong correlate of risk in simple game situations, but in more complex situations, the concept of risk is elusive and idiosyncratic (Wilcox, 1967). Thus we have chosen to treat the concept of risk as being undefined in a strict sense, although we do assume the existence of a variable which, in addition to expected value, mediates preferences in a consistent manner, can be experimentally manipulated in various ways, and for intuitive reasons might be identified as risk. The present study considers a number of coin-tossing games which vary in two aspects: the coin denomination (D) involved in a single toss, and the number of tosses (N) composing the complete game. As an example, the game (25@,5) represents a game in which 5 quarters are tossed all at once. For each coin landing heads, the game’s owner is paid a quarter by a bank. For each tail, the bank is paid a quarter by the owner.

Conjoint Design and Analysis of the Bilinear Model: An Application to Judgments of Risk

Abstract In order that maximizing some kind of an expectation be acceptable as a descriptive theory of risky decision making it is necessary that a gamble made up of a probability mixture of two others lie between them in the perference order. It should not be the most preferred nor the least preferred of the three. The two experiments reported here test that condition and find it is significantly violated. According to Portfolio theory and expected risk theory the mixture may be most preferred but not least preferred. This condition is found to obtain.