On a recent argument for the impossibility of a statistical explanation of single events, and a defence of a modified form of Hempel''s theory of statistical explanation

An argument has been recently proposed by Watkins, whose objective is to show the impossibility of a statistical explanation of single events. This present paper is an attempt to show that Watkins's argument is unsuccessful, and goes on to argue for an account of statistical explanation which has much in common with Hempel's classic treatment.I am very grateful to Peter Clark for many helpful discussions of these issues.     

Covariational influences on goal-based explanation: an integrative model

Covariational and goal-based approaches to social attribution have been treated as competitive or incommensurable. This article integrates key aspects of each approach. Four studies examined preferences for motivating factors (or goals) and enabling factors (or preconditions) as explanations of intentional actions. The studies manipulated (Studies 1-3) and measured (Study 4) the perceived covariation of these goal-based causes with target actions. Causes that covaried with actions were preferred explanations, in contrast with the goal-based view that motivating factors are generally preferred to enabling factors. Combining goal-based beliefs and covariational reasoning resolves problems faced by each individual approach and generates a novel explanatory typology that combines strengths of goal-based and covariational typologies.     

The covering law model of historical explanation

It is often argued (as by Hempel and Nagel) that genuine historical explanations — if these are to be had — must exhibit a connection between events to be explained and universal or probabilistic laws (or ‘hypotheses'). This connection may take either a ‘strong’ or ‘weak’ form. The historian may show that a statement of the event to be explained is a logical consequence of statements of reasonably well‐confirmed universal laws and occurrences linked by the laws to the event to be explained. Or the historian may show that a statement of the event to be explained has high inductive probability conferred upon it given statements of reasonably well‐confirmed probabilistic laws and occurrences so linked by the laws to the type of event to be explained that one finds the occurrence of the particular event likely. This essay focuses on ‘strong’ explanations which meet a ‘deducibility’ requirement (for reasons given in the body of the article). It is argued that explanations in history (at least where it is plausible to construe them as ‘non‐rational') may meet a ‘deducibility’ requirement and count as genuine historical explanations although they do not meet a ‘covering law’ requirement (i. e. none of the premises of these explanations state universal or probabilistic hypotheses). It is required, however, that at least one premise in such explanations assert a reasonably well‐confirmed condition (e. g., a co‐variation) which can be taken as a sign or indication of the presence of laws. Rather than appealing to laws, the historian may appeal to the well‐founded possibility of laws.     

Self-monitoring and sex as moderator variables in the statistical explanation of self-reported marijuana and alcohol use

Self-monitoring and sex are examined as likely moderators of some of the known effective predictors of self-reported use of marijuana and alcohol. The theory of self-monitoring implies that in comparisons between low and high self-monitors, dispositional predictors account for more of the variance in reported use among low self-monitors and environmental predictors account for more of the variance among high self-monitors. With the two classes of predictors established via principal-components analysis and with subgroups defined by scores on Snyder's Self-Monitoring Scale, data from 807 college students showed that self-monitoring does not affect the action of either dispositional or environmental predictors. Thus, the self-monitoring construct promises explanatory leverage that in these tests, the scale is not able to deliver. When subgroups are defined by sex, analyses of reported alcohol use yield small but significant moderator effects: Women's use is more predictable from environmental variables, whereas men's use is more predictable from dispositional variables. These effects are consistent with the conclusions of recent meta-analyses of results from studies of sex differences in conformity to group pressures.     

Functional explanation and the function of explanation

Teleological explanations (TEs) account for the existence or properties of an entity in terms of a function: we have hearts because they pump blood, and telephones for communication. While many teleological explanations seem appropriate, others are clearly not warranted--for example, that rain exists for plants to grow. Five experiments explore the theoretical commitments that underlie teleological explanations. With the analysis of [Wright, L. (1976). Teleological Explanations. Berkeley, CA: University of California Press] from philosophy as a point of departure, we examine in Experiment 1 whether teleological explanations are interpreted causally, and confirm that TEs are only accepted when the function invoked in the explanation played a causal role in bringing about what is being explained. However, we also find that playing a causal role is not sufficient for all participants to accept TEs. Experiment 2 shows that this is not because participants fail to appreciate the causal structure of the scenarios used as stimuli. In Experiments 3-5 we show that the additional requirement for TE acceptance is that the process by which the function played a causal role must be general in the sense of conforming to a predictable pattern. These findings motivate a proposal, Explanation for Export, which suggests that a psychological function of explanation is to highlight information likely to subserve future prediction and intervention. We relate our proposal to normative accounts of explanation from philosophy of science, as well as to claims from psychology and artificial intelligence.     

An experimentally confirmed statistical model on arm movement

The purpose of this research work was to develop a methodology to model arm movement in normal subjects and neurologically impaired individuals through the application of a statistical modelling method. Thirteen subjects with Parkinson's disease and 29 normal controls were recruited to participate in an arm motor task. An infrared optoelectronic kinematic movement analysis system was employed to record arm movement at 50 times per second. This study identified the modified extended Freundlich model as one that could be used to describe this task. Results showed that this model fit the data well and that it has a good correspondence between the observed and the predicted data. However, verification of the model showed that the residuals contained a sizeable autocorrelation factor. The Cochrane and Orcutt method was applied to remove this factor, which improved the fit of the model. Results showed that Parkinson's disease subjects had a higher autocorrelation coefficient than the normal subjects for this task. A positive correlation (r(s) = 0.72, p < 0.001) was found between the Langton-Hewer stage and the autocorrelation coefficient of PD subjects. This finding suggests that if autocorrelation is positively correlated with disease progression, clinicians in their clinical practice might use the autocorrelation value as a useful indicator to quantify the progression of a subjects' disease. Significant differences in model parameters were seen between normal and Parkinson's disease subjects. The use of such a model to represent and quantify movement patterns provides an important base for future study.     

A statistical model of facial attractiveness

Previous research has identified facial averageness and sexual dimorphism as important factors in facial attractiveness. The averageness and sexual dimorphism accounts provide important first steps in understanding what makes faces attractive, and should be valued for their parsimony. However, we show that they explain relatively little of the variance in facial attractiveness, particularly for male faces. As an alternative to these accounts, we built a regression model that defines attractiveness as a function of a face's position in a multidimensional face space. The model provides much more predictive power than the averageness and sexual dimorphism accounts and reveals previously unreported components of attractiveness. The model shows that averageness is attractive in some dimensions but not in others and resolves previous contradictory reports about the effects of sexual dimorphism on the attractiveness of male faces.     

A statistical model of binocular disparity

Binocular disparity provides important information about the three-dimensional structure of the environment. The current study sought to complement our geometrical understanding of binocular vision by considering the distributions of horizontal and vertical disparities that might be expected in images of the natural environment, using a simple environmental model. It was observed that the distribution of disparities depends critically on fixation, and varies greatly from one image location to another. The results were considered in relation to computational models of binocular stereopsis, and compared to two known properties of the visual system—the small disparity preference in disparity matching, and the influence of eccentricity on Panum's fusional limit. Overall, the study characterizes the binocular disparities that are likely to be encountered in the real world scenes, and discusses the implications of these for our understanding of binocular visual systems.     

Concern for appropriateness as a moderator variable in the statistical explanation of self-reported use of alcohol and marijuana

Two studies examine the Concern for Appropriateness Scale (Lennox & Wolfe, 1984) as a likely moderator of dispositional and environmental variables associated with self-reported use of alcohol and marijuana by college and precollege students. In Study 1, data from 408 upper division students show that concern score interacts significantly with religiosity in analyses of use of both drugs, but not with any of 11 other dispositional variables nor with drug-specific environment predictors in analyses of use of either drug. In Study 2, data from 242 recent high school graduates show that concern score interacts significantly with religiosity and drug-specific environment in the explanation of alcohol use but not in the explanation of marijuana use. All of the significant interactions are in the predicted direction. Results therefore suggest that the concern scale is valid for some of its intended purposes.     

Lack of pervasiveness of the underconfidence-with-practice effect: boundary conditions and an explanation via anchoring

The authors investigated whether underconfidence in judgments of learning (JOLs) is pervasive across multiple study-test trials as suggested by A. Koriat, L. Sheffer, and H. Ma'ayan (2002) or whether underconfidence with practice (UWP) might be a kind of anchoring-and-adjustment effect, such that the occurrence or nonoccurrence of the UWP effect depends on whether recall is above a psychological anchor. Participants studied normatively difficult items or normatively easy items and made immediate JOLs or delayed JOLs. The UWP effect occurred for easy items, but for difficult items an overconfidence-with-practice (OWP) effect occurred for delayed JOLs and no bias occurred for immediate JOLs. The systematic occurrence of all 3 outcomes establishes boundary conditions for the UWP effect and confirms the hypothesis that underconfidence (or the lack thereof) may arise at least in part from an anchoring-and-adjustment mechanism.     

Methods for the quantification and statistical testing of ERP differences across conditions

Several standard methods, as well as a new method for the quantification of event-related potential (ERP) differences across conditions, are described. The standard methods are (1) peak analysis, (2) the calculation of mean values, and (3) the calculation of difference waveshapes. The new method, calledwindow analysis, was designed to quantify and statistically test in a very simple way any shape differences between two ERP curves in certain time intervals (windows) when clear peaks are lacking in one or all conditions. The window analysis is based on a conventional analysis of variance with sample time as an additional within-subjects factor. The significance of a shape difference between the curves for a factor of interest can then be determined with anF test for the interaction of this factor with the factor time. The usefulness of the window analysis is demonstrated in an example with real data.     

A statistical model for binocular rivalry

A probabilistic model is presented for the phase durations in binocular rivalry experiments. The hypothetical construct of inhibition or reaction inhibition is used to account for the length of the successive phases of left‐eye dominance and right‐eye dominance. In accordance with Hull's Postulate X.B. it is assumed that the inhibition increases linearly at rate a₁ during periods of left‐eye dominance and decreases linearly at rate a₀ during periods of right‐eye dominance. Two different versions of the proposed model are presented: the beta and the Bessel inhibition models. Inhibition fluctuates between the boundaries 0 and 1 in the beta inhibition model and between ?∞ and +∞ in the Bessel inhibition model. The transition rates λ₁(t) for switches from a state of left‐eye dominance to a state of right‐eye dominance, and λ₀(t) for switches from a state of right‐eye dominance to a state of left‐eye dominance depend on inhibition: , , where l₁ is a non‐decreasing function and l₀ is a non‐increasing function. In the beta inhibition model and . In the Bessel inhibition model and . Special attention is given to the derivation of the expectation of the stationary phase durations.     

A statistical model for relational analysis

The diadic relationships existing in a group can be defined in terms of the members' choices, rejections, and their perceptions of being chosen and rejected. The number of possible distinct diads is 45. Formulas are given for computing the expected frequency and variance of the different diadic forms expected, when certain random factors are taken into account. These values must be known if the operation of factors other than the specified random ones is to be studied. Values obtained from two models with different assumptions are compared with empirical values. A simplified treatment is possible for groups with ten or more members.The present problem emerged from research undertaken as part of a project in interpersonal perception being carried out at the Laboratory of Social Relations at Harvard with the financial aid of the Office of Naval Research (Task Order N5ori-07646).