Exact and resampling probability values for measures of categorical variation and consensus

When analyzing categorical data, it is often important to assess the magnitude of variation, or consensus, among observations in unordered categories. Utilizing the theory of partitions, exact solutions for five commonly used measures of categorical variation are presented. When the number of partitions is very large, resampling methods provide close approximations to exact probability values.     

Resampling probability values for weighted kappa with multiple raters

A new procedure to compute weighted kappa with multiple raters is described. A resampling procedure to compute approximate probability values for weighted kappa with multiple raters is presented. Applications of weighted kappa are illustrated with an example analysis of classifications by three independent raters.     

Contingency and its two indices within conditional probability analysis

FOUR THEORETICAL BASES FOR DETECTING A CONTINGENCY BETWEEN BEHAVIOR AND CONSEQUENT STIMULI ARE CONSIDERED: contiguity, correlation, conditional probability, and logical implication. It is argued that conditional probability analysis is statistically the most powerful of these options, in part due to its provision of two indices of contingency: a forward time probability that reinforcement follows behavior and a backward time probability that behavior precedes reinforcement. Evidence is cited that both indices appear to bear on the learning of a variety of animals, although they are unequally salient to human adults and to artificial neural networks designed to solve time-series functions. It is hypothesized that humans may acquire the capacity to detect contingency in the progressive sequence: contiguity, correlation, forward time conditional probability, backward time conditional probability, and ultimately logical implication.     

Rorschach indices for discriminating between two schizophrenic syndromes

Thinking disturbance and disorder of affects may be different in two subtypes of schizophrenia, the "florid" and the "withdrawal" syndromes. In Exner's approach to the Rorschach system, the diagnostic indicators of disordered thinking may point out large differences not only between schizophrenic and control subjects but also between different types of schizophrenics. The Rorschach protocols of 45 subjects (15 "florid" schizophrenics, 15 "withdrawn" schizophrenics, and 15 controls of the same age and education, matched by sex) were examined on several Exner indices. Compared with the control group, both schizophrenic types confirmed an impairment of perceptual accuracy and of reality testing as well as a reduced emotional control. Compared with the "withdrawn" group, the "florid" schizophrenic subjects showed significantly higher indices of poor perceptual functioning, of an inadequate organizational activity (more Whole and Z responses characterized by negative Form Quality) and greater disordered ideational production.     

Reinforcement probability and ordinal position of response in fixed-interval schedules

Four rats pressed levers and received food pellets under fixed-interval reinforcement schedules of 20, 60, and 180 seconds. The number of responses in each interval was recorded. From these data, the probability of reinforcement was determined as a function of response count. These functions were generally increasing. This finding is consistent with previous suggestions that increasing response rates within fixed intervals may be a function of response count in addition to or instead of elapsed or remaining time.     

Exact and resampling probability values for weighted kappa

Permutation procedures to compute exact and resampling probability values for weighted kappa are described. Comparisons with asymptotic probability values demonstrate that exact permutation procedures are advantageous for sparse data sets, whereas resampling permutation procedures are appropriate for both sparse and nonsparse data sets.     

Combining probability values from independent permutation tests: a discrete analog of Fisher's classical method

Permutation tests are based on all possible arrangements of observed data sets. Consequently, such tests yield exact probability values obtained from discrete probability distributions. An exact nondirectional method to combine independent probability values that obey discrete probability distributions is introduced. The exact method is the discrete analog to Fisher's classical method for combining probability values from independent continuous probability distributions. If the combination of probability values includes even one probability value that obeys a sparse discrete probability distribution, then Fisher's classical method may be grossly inadequate.     

Testing significance of differences between two chi-squares

This paper presents a way to test the difference between twoX ²'s. The test requires evaluating the difference with respect to theT _m (x) Bessel function. Included is a table of the 5 percent and 1 percent points for the Bessel function with degrees of freedom up to 100.This investigation was supported by National Science Foundation Grant Number GE 9846.     

Choice between sequences of fixed-ratio schedules: effects of ratio values and probability of food delivery.

Pigeons were exposed to schedules of food delivery that consisted of two sequential fixed ratios. When alternative sequences provided two food deliveries per 50 responses, the schedule with the shorter initial fixed-ratio value was consistently preferred. Progressively reducing from 1.0 to .25 the probability of food delivery following completion of the second fixed ratio of the sequence with the shorter initial fixed ratio did not reduce preference for this sequence. Moreover, the sequence with the shorter initial fixed ratio also was preferred when the probability of food delivery following completion of the initial ratio in that sequence was progressively reduced from 1.0 to .5, although preference shifted to the alternative when the probability was reduced to 0. These findings suggest that the length of the initial fixed ratio was a primary determinant of choice. Subsequent manipulations demonstrated, however, that when the initial fixed ratios of the two alternatives were equal, changes in the ratio value and probability of food delivery following completion of the second fixed ratio lawfully affected choice.     

Effect size indices for analyses of measurement equivalence: understanding the practical importance of differences between groups

Because of the practical, theoretical, and legal implications of differential item functioning (DIF) for organizational assessments, studies of measurement equivalence are a necessary first step before scores can be compared across individuals from different groups. However, commonly recommended criteria for evaluating results from these analyses have several important limitations. The present study proposes an effect size index for confirmatory factor analytic (CFA) studies of measurement equivalence to address 1 of these limitations. The application of this index is illustrated with personality data from American English, Greek, and Chinese samples. Results showed a range of nonequivalence across these samples, and these differences were linked to the observed effects of DIF on the outcomes of the assessment (i.e., group-level mean differences and adverse impact).     

Differences between probability and frequency judgments: The role of individual differences in working memory capacity

Most theories of probability judgment assume that judgments are made by comparing the strength of a focal hypothesis relative to the strength of alternative hypotheses. In contrast, research suggests that frequency judgments are assessed using a non-comparative process; the strength of the focal hypothesis is assessed without comparing it to the strength of alternative hypotheses. We tested this distinction between probability and frequency judgments using the alternative outcomes paradigm (Windschitl, Young, & Jenson, 2002). Assuming that judgments of probability (but not judgments of frequency) entail comparing the focal hypothesis with alternative hypotheses, we hypothesized that probability judgments would be sensitive to the distribution of the alternative hypotheses and would be negatively correlated with individual differences in working memory (WM) capacity. In contrast, frequency judgments should be unrelated to the distribution of the alternatives and uncorrelated with WM-capacity. Results supported the hypotheses.     

Syntax for calculation of discounting indices from the monetary choice questionnaire and probability discounting questionnaire

The 27‐item Monetary Choice Questionnaire (MCQ; Kirby, Petry, & Bickel, 1999) and 30‐item Probability Discounting Questionnaire (PDQ; Madden, Petry, & Johnson, 2009) are widely used, validated measures of preferences for immediate versus delayed rewards and guaranteed versus risky rewards, respectively. The MCQ measures delayed discounting by asking individuals to choose between rewards available immediately and larger rewards available after a delay. The PDQ measures probability discounting by asking individuals to choose between guaranteed rewards and a chance at winning larger rewards. Numerous studies have implicated these measures in addiction and other health behaviors. Unlike typical self‐report measures, the MCQ and PDQ generate inferred hyperbolic temporal and probability discounting functions by comparing choice preferences to arrays of functions to which the individual items are preconfigured. This article provides R and SPSS syntax for processing the MCQ and PDQ. Specifically, for the MCQ, the syntax generates k values, consistency of the inferred k, and immediate choice ratios; for the PDQ, the syntax generates h indices, consistency of the inferred h, and risky choice ratios. The syntax is intended to increase the accessibility of these measures, expedite the data processing, and reduce risk for error.     

Dissociating between cardinal and ordinal and between the value and size magnitudes of coins

In mathematics, the ordinal (relative) magnitude of a numerical object conveys a separate meaning from its cardinal (absolute) magnitude, whereas its physical size bears no inherent relationship to its magnitude. In numerical cognition, the ordinal-cardinal distinction has been scarcely addressed, whereas the size-magnitude distinction has been studied extensively, with the surprising demonstration of an interaction between semantic magnitude and physical size (Besner & Coltheart, 1979). The present work used coins to study the intricate relations between these meanings. In two experiments, Israeli observers (Experiment 1) and American observers (Experiment 2) performed numerical and physical comparative judgments of coins. Consensual markers of magnitude activation (e.g., the size congruity effect and the distance effect) were obtained. The results of the two experiments converged on the same conclusions. Comparisons of value were governed by ordinal magnitude. Magnitude interfered with comparisons of size, but size did not affect value. The results provided a set of clear dissociations between cardinal and ordinal magnitude and between value and size of coins. They highlight the important role played by ordinal information in magnitude processing.     

Aetiology of spider phobia: classificatory differences between two origins instruments

The origins of fear of spiders was investigated in 33 spider phobic Ss entering a treatment study. All Ss completed Menzies and Clarke's (1993a) Origins Questionnaire (OQ) (Behaviour Research and Therapy, 31, 355–365) and Öst and Hugdahl's (1981) Phobic Origins Questionnaire (POQ) (Behaviour Research and Therapy, 19, 439–447). The results for the individual questionnaires were similar to those reported in previous studies. However a comparison of assignments of origin category for the two questionnaires showed widely discrepant results. The POQ returned 17 positive responses for classical conditioning, the OQ only 2. By contrast the OQ returned 10 origins as ‘non-conditioning traumatic event’, 9 of which returned positive responses for classical conditioning on the POQ. A further 15 Ss on the OQ were categorised as ‘always been this way’, the preponderance of these being classified as vicarious or informational in origin on the POQ. The POQ does not have a specific question or category for non-associative acquisition of phobias. The results of the origins assignments are detailed and their relation to the structure and questions of the questionnaires is outlined. Past studies using the POQ have produced results supporting acquisition of a substantial proportion of phobias by classical conditioning. The findings of this study suggest that such results mainly reflect inherent bias in that instrument.