An objective theory of statistical testing

Theories of statistical testing may be seen as attempts to provide systematic means for evaluating scientific conjectures on the basis of incomplete or inaccurate observational data. The Neyman-Pearson Theory of Testing (NPT) has purported to provide an objective means for testing statistical hypotheses corresponding to scientific claims. Despite their widespread use in science, methods of NPT have themselves been accused of failing to be objective; and the purported objectivity of scientific claims based upon NPT has been called into question. The purpose of this paper is first to clarify this question by examining the conceptions of (I) the function served by NPT in science, and (II) the requirements of an objective theory of statistics upon which attacks on NPT's objectivity are based. Our grounds for rejecting these conceptions suggest altered conceptions of (I) and (II) that might avoid such attacks. Second, we propose a reformulation of NPT, denoted by NPT*, based on these altered conceptions, and argue that it provides an objective theory of statistics. The crux of our argument is that by being able to objectively control error frequencies NPT* is able to objectively evaluate what has or has not been learned from the result of a statistical test.     

Counterfactuals vs. conditional probabilities: A critical analysis of the counterfactual theory of information

Cohen and Meskin 2006 Cohen, Jonathan and Meskin, Aaron. 2006. An Objective Counterfactual Theory of Information. Australasian Journal of Philosophy, 84: 333–352. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar] recently offered a counterfactual theory of information to replace the standard probabilistic theory of information. They claim that the counterfactual theory fares better than the standard account on three grounds: first, it provides a better framework for explaining information flow properties; second, it requires a less expensive ontology; and third, because it does not refer to doxastic states of the information-receiving organism, it provides an objective basis. In this paper, I show that none of these is really an advantage. Moreover, the counterfactual theory fails to satisfy one of the basic properties of information flow, namely the Conjunction principle. Thus, I conclude, there is no reason to give up the standard probabilistic theory for the counterfactual theory of information.     

The functional theory of counterfactual thinking.

Counterfactuals are thoughts about alternatives to past events, that is, thoughts of what might have been. This article provides an updated account of the functional theory of counterfactual thinking, suggesting that such thoughts are best explained in terms of their role in behavior regulation and performance improvement. The article reviews a wide range of cognitive experiments indicating that counterfactual thoughts may influence behavior by either of two routes: a content-specific pathway (which involves specific informational effects on behavioral intentions, which then influence behavior) and a content-neutral pathway (which involves indirect effects via affect, mind-sets, or motivation). The functional theory is particularly useful in organizing recent findings regarding counterfactual thinking and mental health. The article concludes by considering the connections to other theoretical conceptions, especially recent advances in goal cognition.     

The importance of contextual variables when judging fairness: An examination of counterfactual thoughts and fairness theory

This research empirically examines the underlying mechanisms of fairness theory (  and ), namely counterfactual thought processes. Study 1 used a policy-capturing design to examine the relative importance of contextual variables in predicting counterfactual thoughts and fairness perceptions. Study 2 utilized a between-subjects design and asked participants to generate their own counterfactuals in response to an unfortunate event. Results of both studies showed that fairness perceptions are influenced by contextual variables (i.e., outcome severity, target knowledge and expertise, sin of commission vs. omission) and counterfactual thinking. Counterfactual thoughts partially mediated the effects of contextual variables and fairness perceptions in Study 1. Exploratory analyses from Study 3 revealed that the measurement of counterfactual thoughts (frequency vs. strength) may capture different underlying constructs. Implications are discussed.     

An information theory analysis of duration of lifeguards' scanning

Observers recorded the duration of scanning by six lifeguards in three indoor swimming pools. Duration of scanning was significantly predicted by the absolute numbers of child swimmers (< 17 years) in the pools and when numbers of child swimmers were represented in terms of bits of information. Duration of scanning increased as a linear function of both numbers of children and child bits of information. These results are interpreted in terms of the Hick-Hyman law of information theory. Lifeguards appear to simplify the task of information processing and decision-making by concentrating on children as a more at-risk group of swimmers. Duration of scanning was not significantly related to changes in number of adult swimmers.     

An information theory analysis of visual complexity and dissimilarity

The subjective complexity of a computer-generated bitmap image can be measured by magnitude estimation scaling, and its objective complexity can be measured by its compressed file size. There is a high correlation between these measures of subjective and objective complexity over a large set of marine electronic chart and radar images. The subjective dissimilarity of a pair of bitmap images can be predicted from subjective and objective measures of the complexity of each image, and from the subjective and objective complexity of the image produced by overlaying the two simple images. In addition, the subjective complexity of the image produced by overlaying two simple images can be predicted from the subjective complexity of the simple images and the subjective dissimilarity of the image pair. The results of the experiments that generated these complexity and dissimilarity judgments are consistent with a theory, outlined here, that treats objective and subjective measures of image complexity and dissimilarity as vectors in Euclidean space.     

Pre-emption cases may support,not undermine,the counterfactual theory of causation

Synthese - Pre-emption cases have been taken by almost everyone to imply the unviability of the simple counterfactual theory of causation. Yet there is ample motivation from scientific practice to...     

An investigation into the online processing of counterfactual and indicative conditionals

The ability to represent conditional information is central to human cognition. In two self-paced reading experiments we investigated how readers process counterfactual conditionals (e.g., If Darren had been athletic, he could probably have played on the rugby team) and indicative conditionals (e.g., If Darren is athletic, he probably plays on the rugby team). In Experiment 1 we focused on how readers process counterfactual conditional sentences. We found that processing of the antecedent of counterfactual conditionals was rapidly constrained by prior context (i.e., knowing whether Darren was or was not athletic). A reading-time penalty was observed for the critical region of text comprising the last word of the antecedent and the first word of the consequent when the information in the antecedent did not fit with prior context. In Experiment 2 we contrasted counterfactual conditionals with indicative conditionals. For counterfactual conditionals we found the same effect on the critical region as we found in Experiment 1. In contrast, however, we found no evidence that processing of the antecedent of indicative conditionals was constrained by prior context. For indicative conditionals (but not for counterfactual conditionals), the results we report are consistent with the suppositional account of conditionals. We propose that current theories of conditionals need to be able to account for online processing differences between indicative and counterfactual conditionals.     

Superexplanations for counterfactual knowledge

Philosophical Studies - I discuss several problems for Williamson’s counterfactual-theory of modal knowledge and argue that they have a common source, in that the theory neglects to elucidate...     

Judgment dissociation theory: an analysis of differences in causal,counterfactual, and covariational reasoning

Research suggests that causal judgment is influenced primarily by counterfactual or covariational reasoning. In contrast, the author of this article develops judgment dissociation theory (JDT), which predicts that these types of reasoning differ in function and can lead to divergent judgments. The actuality principle proposes that causal selections focus on antecedents that are sufficient to generate the actual outcome. The substitution principle proposes that ad hoc categorization plays a key role in counterfactual and covariational reasoning such that counterfactual selections focus on antecedents that would have been sufficient to prevent the outcome or something like it and covariational selections focus on antecedents that yield the largest increase in the probability of the outcome or something like it. The findings of 4 experiments support JDT but not the competing counterfactual and covariational accounts.