Test theory without an answer key

A general model is presented for homogeneous, dichotomous items when the answer key is not known a priori. The model is structurally related to the two-class latent structure model with the roles of respondents and items interchanged. For very small sets of respondents, iterative maximum likelihood estimates of the parameters can be obtained by existing methods. For other situations, new estimation methods are developed and assessed with Monte Carlo data. The answer key can be accurately reconstructed with relatively small sets of respondents. The model is useful when a researcher wants to study objectively the knowledge possessed by members of a culturally coherent group that the researcher is not a member of.This research was supported by NSF Grant No. SES-8320173 to the authors. We gratefully acknowledge comments and suggestions from John Boyd, Tarow Indow, and Kathy Maher as well as the editor and several anonymous referees.     

Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

Functional measurement approach to self-estimation in multiattribute evaluation

Multiattribute analysis depends on measurement of values and weights. Unless these measures reflect the decision maker's true values and weights, the multiattribute formula may put a less-preferred alternative in first place. To avoid such disordinality requires stringent measurement conditions: First, the values and weights must be on linear (equal interval) or ratio (known zero) scales. Second, these scales must satisfy a condition of common unit across disparate attribute dimensions. Most methods of range adjustment beg both of these measurement questions. Functional measurement theory can solve both problems and so can be useful in multiattribute analysis. Past work has established the operation of a general cognitive algebra as an empirical reality. The averaging model, in particular, makes possible the definition and estimation of weights and values as distinct psychological parameters. It can also solve the problem of common unit. Cognitive algebra thus provides a grounded theoretical foundation on which to develop self-estimation methodology, in which decision makers provide direct estimates of their values and weights. The logic is straightforward. Functional measurement can analyze global judgments to obtain validated psychological scales. These scales may then be used as validational criteria for the self-estimates. Procedures to eliminate biases in the self-estimates can thus be tested and refined in well-learned multiattribute tasks, such as judgments of meals, in which global judgments are trustworthy. Once developed, such self-estimation procedures may be used with some confidence for general multiattribute analysis. A number of studies from 20-odd years of work on the theory of information integration are summarized to show good, although not unmixed promise for self-estimation.     

Effectiveness of the GOFER course in decision making for high school students

The paper describes and evaluates the GOFER course in decision making for high school students (Mann, Harmoni and Power, 1988). The course was based on principles from the conflict theory of decision making (Janis and Mann, 1977) and was designed to provide adolescents with an understanding of factors that produce good and poor decision making as well as knowledge and practice of sound decision skills. Two evaluation studies were conducted to examine effectiveness of the course. Study 1 was conducted with young adolescents (12 year olds). It found a significant difference between students trained in the course and a control group on measures of self-esteem as a decision maker, self reported decision habits and knowledge of decision strategy. Study 2 was conducted with mid-adolescents (15 year olds). It, too, found a significant difference between students who took the course and a control group on measures of self esteem as a decision maker and self-reported decision habits. It is concluded that while the evaluation study fell short of an ideal test, the GOFER course met the criteria of improving student knowledge, raising confidence in decision making and changing self reported decision habits.     

ON MARTIN EGER'S "A TALE OF TWO CONTROVERSIES"

Abstract. Criticisms are presented against Eger's challenge to the demarcation between the natural sciences and ethics. Arguments are given both against his endorsement of the "new" philosophy of science and against his rejection of the fact-value dichotomy. However, his educational recommendations are reinforced rather than weakened by these criticisms     

The rhetorical foundation of philosophical argumentation

The rejection of rhetoric has been a constant theme in Western thought since Plato. The presupposition of such a debasement lies at the foundation of a certain view of Reason that I have called propositionalism, and which is analyzed in this article. The basic tenets of propositionalism are that truth is exclusive, i.e. it does not allow for any alternative, and that there is always only one proposition which must be true, the opposite one being false. Necessity and uniqueness are the ideals of propositionalism. But the question of the necessity of such a necessity is bound to arise. Foundationalism and propositionalism are intrinsically related. Since necessity excludes alternatives, rhetoric, which is based on the possibility of opposite standpoints, is unavoidably devalued as the crippled child of Reason, identical to sophistry or eristic. But propositionalism cannot justify itself and provide a justification for its own foundation without circle or contraditction. Since it responds to the problem of eradicating problems and alternatives through propositional entities, propositionalism is ultimately based on questioning to which it replies in the mode of denial. The unavowed foundation of Reason is therefore the question of questioning, even though this very question is suppressed as propositionalism. The trace of such a question is not only historical, but can also be seen, for instance, in the role played by the principle of contradiction in the constitution of propositional Reason (Artitotle): opposite propositions are not the expression of a problematic situation, they are either possible or successively unique propositions.We want to replace propositionalism by problematology which allows for the conceptualization of alternatives, thereby rendering a true rhetoric possible. Argumentation cannot then be equated with eristic any more, as propositionalism maintained.Rationality must be seen as having questioning as its true starting-point. Reason must be rhetorical if it is to survive the death of propositionalism which took place after the radical criticisms of Marx, Nietzsche and Freud. Even if it is still hard ffor philosophers and rhetoricians to think within another framework and even though they prefer endlessly to deconstauct the old one instead of changing it, problematology is bound to impose itself as the new voice for rationality, because Reason has always endeavored to solve problems. Propositionalism has been only one way of conceiving problems, based on the view that solutions could be but the suppression of questioning.     

Rhetoric and “doing philosophy”

By drawing new distinctions labelled appeal and response to replace traditional rhetorical modes of written discourse, the essay sketches a new perspective about what philosophers are doing rhetorically in doing philosophy. To think of philosophers as simply engaged in argument is an oversimplification and a distortion of what philosophers do. Crucial to doing philosophy are four activities: (1) definition and redefinition of problems and issues that form both the focus of the canonical historical literature of philosophy and what goes on in contemporary philosophy as a discipline, (2) the development and use of formal languages and technical vocabularies to abbreviate and label complexity and to disambiguate and precise distinctions necessary to deal with problems and issues, (3) the development and exploration of argumentative appeals for acceptance or refutation of answers to questions raised by the philosophical problematic, and (4) the development and exploration of explanatory responses to questions raised by the problematic. In so far as these four activities are driven and sanctioned by the current, self-defining philosophical problematic, contemporary philosophy as a body of knowledge is historical, cumulative, and marked by progress, and the doing of philosophy is fundamentally the making of written appeals and responses about its problematic.     

Choice with delayed and probabilistic reinforcers: effects of variability, time between trials, and conditioned reinforcers.

In a discrete-trials procedure with pigeons, a response on a green key led to a 4-s delay (during which green houselights were lit) and then a reinforcer might or might not be delivered. A response on a red key led to a delay of adjustable duration (during which red houselights were lit) and then a certain reinforcer. The delay was adjusted so as to estimate an indifference point--a duration for which the two alternatives were equally preferred. Once the green key was chosen, a subject had to continue to respond on the green key until a reinforcer was delivered. Each response on the green key, plus the 4-s delay that followed every response, was called one "link" of the green-key schedule. Subjects showed much greater preference for the green key when the number of links before reinforcement was variable (averaging four) than when it was fixed (always exactly four). These findings are consistent with the view that probabilistic reinforcers are analogous to reinforcers delivered after variable delays. When successive links were separated by 4-s or 8-s "interlink intervals" with white houselights, preference for the probabilistic alternative decreased somewhat for 2 subjects but was unaffected for the other 2 subjects. When the interlink intervals had the same green houselights that were present during the 4-s delays, preference for the green key decreased substantially for all subjects. These results provided mixed support for the view that preference for a probabilistic reinforcer is inversely related to the duration of conditioned reinforcers that precede the delivery of food.     

Fixed-ratio pausing: Joint effects of past reinforcer magnitude and stimuli correlated with upcoming magnitude

Pigeons responded on fixed-ratio schedules ending in small or large reinforcers (grain presentations of different duration) interspersed within each session. In mixed-schedule conditions, the response key was lit with a single color throughout the session, and pausing was directly related to the past reinforcer (longer pauses after large reinforcers than after small ones). In multiple-schedule conditions, different colors accompanied the ratios ending in small and large reinforcers, and pausing was affected by the upcoming reinforcer as well as the past one. Pauses were shorter before large reinforcers than before small ones, but they continued to be longer after large reinforcers than after small ones. The influence of the past reinforcer was modulated by the magnitude of the upcoming reinforcer; in the presence of the stimulus before the small reinforcer, the effect of the past reinforcer was enhanced relative to its effect in the stimulus before the large reinforcer. These results show that pausing between ratios is jointly determined by two competing factors: past conditions of reinforcement and stimuli correlated with upcoming conditions.