How to quantify support for and against the null hypothesis: A flexible WinBUGS implementation of a default Bayesian t test

We propose a sampling-based Bayesian t test that allows researchers to quantify the statistical evidence in favor of the null hypothesis. This Savage—Dickey (SD) t test is inspired by the Jeffreys—Zellner—Siow (JZS) t test recently proposed by Rouder, Speckman, Sun, Morey, and Iverson (2009). The SD test retains the key concepts of the JZS test but is applicable to a wider range of statistical problems. The SD test allows researchers to test order restrictions and applies to two-sample situations in which the different groups do not share the same variance.     

A test of the reward-value hypothesis

Rats retain source memory (memory for the origin of information) over a retention interval of at least 1 week, whereas their spatial working memory (radial maze locations) decays within approximately 1 day. We have argued that different forgetting functions dissociate memory systems. However, the two tasks, in our previous work, used different reward values. The source memory task used multiple pellets of a preferred food flavor (chocolate), whereas the spatial working memory task provided access to a single pellet of standard chow-flavored food at each location. Thus, according to the reward-value hypothesis, enhanced performance in the source memory task stems from enhanced encoding/memory of a preferred reward. We tested the reward-value hypothesis by using a standard 8-arm radial maze task to compare spatial working memory accuracy of rats rewarded with either multiple chocolate or chow pellets at each location using a between-subjects design. The reward-value hypothesis predicts superior accuracy for high-valued rewards. We documented equivalent spatial memory accuracy for high- and low-value rewards. Importantly, a 24-h retention interval produced equivalent spatial working memory accuracy for both flavors. These data are inconsistent with the reward-value hypothesis and suggest that reward value does not explain our earlier findings that source memory survives unusually long retention intervals.     

Hierarchical Bayesian estimation and hypothesis testing for delay discounting tasks

A state-of-the-art data analysis procedure is presented to conduct hierarchical Bayesian inference and hypothesis testing on delay discounting data. The delay discounting task is a key experimental paradigm used across a wide range of disciplines from economics, cognitive science, and neuroscience, all of which seek to understand how humans or animals trade off the immediacy verses the magnitude of a reward. Bayesian estimation allows rich inferences to be drawn, along with measures of confidence, based upon limited and noisy behavioural data. Hierarchical modelling allows more precise inferences to be made, thus using sometimes expensive or difficult to obtain data in the most efficient way. The proposed probabilistic generative model describes how participants compare the present subjective value of reward choices on a trial-to-trial basis, estimates participant- and group-level parameters. We infer discount rate as a function of reward size, allowing the magnitude effect to be measured. Demonstrations are provided to show how this analysis approach can aid hypothesis testing. The analysis is demonstrated on data from the popular 27-item monetary choice questionnaire (Kirby, Psychonomic Bulletin & Review, 16(3), 457–462 2009), but will accept data from a range of protocols, including adaptive procedures. The software is made freely available to researchers.     

Bayesian t tests for accepting and rejecting the null hypothesis

Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.     

Within-category feature correlations and Bayesian adjustment strategies

To the extent that categories inform judgments about items, the accuracy with which categories capture the statistical structure of experience should affect judgment accuracy. The authors argue that representations of feature correlations can serve as Bayesian priors, increasing the accuracy of stimulus estimates by decreasing variability. Participants viewed a series of objects that varied on two dimensions that were either uncorrelated or correlated. They estimated each item by manipulating a response object to make it match the presented stimulus. Subsequent classification and featureinference tasks indicated that the correlation was detected. The pattern of variability in recollections of stimuli suggested that the feature correlation informed estimates as predicted by a Bayesian model of category effects on memory. This work was supported by NIMH Grant 1 F31 MH12072-01A1 to the first author.     

A negative test of the drive-reduction hypothesis

A major deduction of the drive-reduction hypothesis of reinforcement was tested. A light which follows the termination of a shock coincides with a condition of drive or need reduction. If drive reduction is a sufficient condition for reinforcement, then the light should become a secondary reinforcing agent by virtue of its association with the drive-reduction event. If it becomes a secondary reinforcing agent, it should be able to reinforce an instrumental act.

This sequence of deductions was tested by placing rats in a stock, giving them a brief shock upon the termination of which a light was flashed for one second. After sixty such pairings, subjects were then placed in a Skinner box under operant test conditions; when they pressed the bar a light flashed on.

Animals subjected to this training programme were compared for rate of bar pressing with animals subjected to a variety of control conditions. No significant differences were found among the groups, and it was concluded that in so far as the deductions from drive-reduction theory were correct, the theory was not substantiated. The paper concludes with a discussion of various problems which might limit the interpretation of the experimental results.     

A strong test of the dual-mode hypothesis

One account of facial cognition, the dual-mode hypothesis, maintains that there are two sources of information in a human face, featural and configural, and that these sources are processed simultaneously and independently of one another. According to the hypothesis, the processing and identification of upright faces relies primarily on configural information, and this information is disrupted to such an extent upon inversion as to result in a reliance on featural information for identifying inverted faces (e.g., Searcy & Bartlett, 1996). When considered in terms of the general characteristics of human information processing, the foundational assumptions of the dual-mode hypothesis are as follows: Facial information processing is accomplished by a parallel self-terminating architecture with unlimited capacity to supercapacity and a preservation of independence between the rates of processing of featural and configural information. Although a number of studies have provided evidence consistent with the dual-mode hypothesis, until now there have been no direct tests of the foundational assumptions of the hypothesis. The present study provides that direct test, providing strong support for three of the assumptions (parallel self-terminating processing with unlimited capacity to supercapacity) while contradicting a fourth (independence in rates).     

A Bayesian predictive analysis of test scores

In the classical test theory, a high-reliability test always leads to a precise measurement. However, when it comes to the prediction of test scores, it is not necessarily so. Based on a Bayesian statistical approach, we predicted the distributions of test scores for a new subject, a new test, and a new subject taking a new test. Under some reasonable conditions, the predicted means, variances, and covariances of predicted scores were obtained and investigated. We found that high test reliability did not necessarily lead to small variances or covariances. For a new subject, higher test reliability led to larger predicted variances and covariances, because high test reliability enabled a more accurate prediction of test score variances. Regarding a new subject taking a new test, in this study, higher test reliability led to a large variance when the sample size was smaller than half the number of tests. The classical test theory is reanalyzed from the viewpoint of predictions and some suggestions are made.     

A laboratory test of the constant risk hypothesis

It has been repeatedly suggested that subjects aim at maintaining a constant error probability in many variants of self-paced performance and that they adjust their behaviour so as to keep their risks relatively constant. This constant risk hypothesis is investigated in a simple computer-controlled addition task it which subjects manipulated exercise difficulty as a function of their own calculation proficiency and the allotted solution time. Error probability proved to be unrelated to level of skill and to amount of allotted computation time, but to depend onuncertainty with respect to exercise difficulty.     

Unidimensional factor models imply weaker partial correlations than zero-order correlations

In this paper we present a new implication of the unidimensional factor model. We prove that the partial correlation between two observed variables that load on one factor given any subset of other observed variables that load on this factor lies between zero and the zero-order correlation between these two observed variables. We implement this result in an empirical bootstrap test that rejects the unidimensional factor model when partial correlations are identified that are either stronger than the zero-order correlation or have a different sign than the zero-order correlation. We demonstrate the use of the test in an empirical data example with data consisting of fourteen items that measure extraversion.     

Alcohol and aggression: A test of the affect-arousal hypothesis

Forty-eight male social drinkers participated in a study designed to test the interaction between prevailing mood and alcohol on aggressive behavior in a 2 × 3 factorial design. Half of the subjects underwent a positive mood-induction procedure, while the other half underwent a negative mood-induction procedure. Within each of these conditions, one-third of the subjects received 1.32 ml/kg of 95% ethanol, one-third received placebo drinks, and the rest remained sober. Aggression was measured using a modified version of the Buss aggression machine. Results indicated that subjects receiving alcohol were significantly more aggressive than placebo or sober subjects. The mood-induction procedure, while significantly altering affect, did not affect aggressive responding. These findings are discussed with respect to levels of blood-alcohol and alcohol-aggression theories.     

A base logic for default reasoning

Based on a close study of benchmark examples in default reasoning, such as Nixon Diamond, Penguin Principle, etc., this paper provides an in depth analysis of the basic features of default reasoning. We formalize default inferences based on Modus Ponens for Default Implication, and mark the distinction between “local inferences” (to infer a conclusion from a subset of given premises) and “global inferences” (to infer a conclusion from the entire set of given premises). These conceptual analyses are captured by a formal semantics that is built upon the set-selection function technique. A minimal logic system M of default reasoning that accommodates Modus Ponens for Default Implication and suitable for local inferences is proposed, and its soundness is proved. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Studies), 2003 (special issue) by Ye Feng     

A cross-cultural test of the personality integration hypothesis1

This study attempted to validate the psychological integration hypothesis by comparing the levels of psychological functioning of individuals from four cultural groups on three dimensions of personality. The personality attributes investigated were field-dependence/independence cognitive style, tolerance of ambiguity (an affective style variable) and machiavellianism (an index of stylistic orientation in interpersonal relationships). Subjects were 218 first-level supervisors from five industrial plants in Auckland, New Zealand. Comparisons of mean group scores on each personality variable showed that a similar rank order among the groups held for each personality variable. It was also found that, for the sample as a whole, there were positive intercorrelations between the personality variables. The symmetrical rank ordering of the groups on the personality variables was considered to indicate that members of each group had attained relatively similar levels of psychological development on each personality attribute. The relatively low levels of intercorrelations between the personality variables were held to indicate that they were measuring separate areas of psychological functioning.