Some exact conditional tests of independence forR ×C cross-classification tables

Exact conditional tests of independence in cross-classification tables are formulated based on the ² statistic and statistics with stronger operational interpretations, such as some nominal and ordinal measures of association. Guidelines for the table dimensions and sample sizes for which the tests are economically implemented on a computer are given. Some selected sample sizes and marginal distributions are used in a numerical comparison between the significance levels of the approximate and exact conditional tests based on the ² statistic.The authors are grateful for the suggestions of the referees and for computer funding provided by the Northeast Regional Data Center at the University of Florida.     

Testing a unidimensional,qualitative unfolding model for attitudinal or developmental data

Assuming that subject responses rank order stimuli by preference, statistical methods are presented for testing the hypothesis that responses conform to a unidimensional, qualitative unfolding model and to an a priori stimulus ordering. The model postulates that persons and stimulus variables are ordered along a single continuum and that subjects most prefer stimuli nearest their own position. The underlying continuum need not form an interval scale of the stimulus attribute. The general assumptions of the test for the unfolding model make it suitable for the analysis of structure in attitude responses, preference data, and developmental stage data.This research was supported by a grant from the U.S. Public Health Service (Grant No. 1-R01-MH27861-01) to the University of Minnesota. I wish to thank Sanford Weisberg for his helpful suggestions. I also wish to thank Karen Kitchener and Patricia King for letting me use their data.     

Exact conditional tests for cross-classifications: Approximation of attained significance levels

A procedure is proposed for approximating attained significance levels of exact conditional tests. The procedure utilizes a sampling from the null distribution of tables having the same marginal frequencies as the observed table. Application of the approximation through a computer subroutine yields precise approximations for practically any table dimensions and sample size.     

The functional independence of mands and tacts

This study demonstrates functional independence in the acquisition of mands and tacts. Some subjects first learned to mand the experimenter's placement of objects with the prepositional phrases “On the left” and “On the right.” They were regularly tested for collateral appearance of tacts with these same phrases. Other subjects learned to tact the location of objects with these prepositional phrases and were regularly tested for collateral appearance of mands. All subjects were next trained in the repertoire that had not been trained in the first condition (either tact or mand). After all subjects had learned both to mand and to tact correctly, another assessment of mand-tact independence was undertaken. Mands (tacts) were reversed and testing assessed collateral reversal of tacts (mands). The results demonstrated that tacts and mands, even when incorporating identical response forms, were functionally independent during acquisition. Subsequent modification of one repertoire (by reversal training) produced collateral reversal in three of nine subjects.     

Rasch models for item bundles

This paper discusses the application of a class of Rasch models to situations where test items are grouped into subsets and the common attributes of items within these subsets brings into question the usual assumption of conditional independence. The models are all expressed as particular cases of the random coefficients multinomial logit model developed by Adams and Wilson. This formulation allows a very flexible approach to the specification of alternative models, and makes model testing particularly straightforward. The use of the models is illustrated using item bundles constructed in the framework of the SOLO taxonomy of Biggs and Collis.The work of both authors was supported by fellowships from the National Academy of Education Spencer Fellowship.     

Covariation and quantifier polarity: what determines causal attribution in vignettes?

Tests of causal attribution often use verbal vignettes, with covariation information provided through statements quantified with natural language expressions. The effect of covariation information has typically been taken to show that set size information affects attribution. However, recent research shows that quantifiers provide information about discourse focus as well as covariation information. In the attribution literature, quantifiers are used to depict covariation, but they confound quantity and focus. In four experiments, we show that focus explains all (Experiment 1) or some (Experiment 2-4) of the impact of covariation information on the attributions made, confirming the importance of the confound. Attribution experiments using vignettes that present covariation information with natural language quantifiers may overestimate the impact of set size information, and ignore the impact of quantifier-induced focus.     

The perception of causality in chimpanzees (Pan spp.)

Chimpanzees (Pan spp.) were tested on a habituation/dishabituation paradigm that was originally developed to test for comprehension of causality in very young human infants. Three versions of the test were used: a food item being moved by a hand, a human pushing another human off a chair to obtain a food item, and a film clip of natural chimpanzee behaviour (capturing and eating a monkey). Chimpanzees exhibited similar results to those obtained with human infants, with significantly elevated levels of looking on the dishabituation trials. Since the level of response was significantly greater on natural/unnatural sequences than on unnatural/natural sequences, we conclude that the chimpanzees were not responding just to novelty but rather to events that infringed their sense of natural causation.     

Response-reinforcer independence and the economic continuum: A preliminary analysis

Three pigeons were exposed to 1-hr and 4-hr sessions during which they earned food under a fixed-ratio 50 schedule of reinforcement while obtaining additional food according to either a variable-interval or a variable-time schedule. Postsession food was provided after the 1-hr sessions. The frequency of the variable-interval and variable-time food presentations was varied under the two session durations. The various combinations of within-session earned and unearned food, as well as the postsession food, defined conditions on the open-to-closed economy continuum. Key pecks tended to increase as the frequency of either variable-interval or variable-time food decreased. An economic-continuum analysis based on an independence quotient as a measure of response-reinforcer independence is presented to account for the effects.     

Against the Vagueness Argument

In this paper I offer a counterexample to the so called vagueness argument against restricted composition. This will be done in the lines of a recent suggestion by Trenton Merricks, namely by challenging the claim that there cannot be a sharp cut-off point in a composition sequence. It will be suggested that causal powers which emerge when composition occurs can serve as an indicator of such sharp cut-off points. The main example will be the case of a heap. It seems that heaps might provide a very plausible counterexample to the vagueness argument if we accept the idea that four grains of sand is the least number required to compose a heap—the case has been supported by W. D. Hart. My purpose here is not to put forward a new theory of composition, I only wish to refute the vagueness argument and point out that we should be wary of arguments of its form.