The “numerical method ” in medicine goes back to Pierre Louis ’ study of pneumonia (1835), and John Snow’s book on the epidemiology of cholera (1855). Snow took advantage of natural experiments and used convergent lines of evidence to demonstrate that cholera is a waterborne infectious disease. More recently, investigators in the social and life sciences have used statistical models and significance tests to deduce cause-and-effect relationships from patterns of association; an early example is Yule’s study on the causes of poverty (1899). In my view, this modeling enterprise has not been successful. Investigators tend to neglect the difficulties in establishing causal relations, and the mathematical complexities obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work—a principle honored more often in the breach than the observance. Snow’s work on cholera will be contrasted with modern studies that depend on statistical models and tests of significance. The examples may help to clarify the limits of current statistical techniques for making causal inferences from patterns of association. 1.

For nearly a century, investigators in the social sciences have used regression models to deduce cause-and-effect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work-- a principle honored more often in the breach than the observance.

This paper (which is mainly expository) sets up graphical models for causation, having a bit less than the usual complement of hypothetical counterfactuals. Assuming the invariance of error distributions may be essential for causal inference, but the errors themselves need not be invariant. Graphs can be interpreted using conditional distributions, so that we can better address connections between the mathematical framework and causality in the world. The identification problem is posed in terms of conditionals. As will be seen, causal relationships cannot be inferred from a data set by running regressions unless there is substantial prior knowledge about the mechanisms that generated the data. There are few successful applications of graphical models, mainly because few causal pathways can be excluded on a priori grounds. The invariance conditions themselves remain to be assessed.

this article were defrayed in part by the that the behavioral relevance of a stimulus impacts on the payment of page charges. The article must therefore be hereby marked auditory system at the very earliest stages of processing. "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. The interactions between parallel auditory pathways also 3148 0022-3077/98 $5.00 Copyright q 1998 The American Physiological Society J236-8 / 9k2f$$de38 11-18-98 17:07:16 neupa LP-Neurophys FUNCTIONAL CONNECTIVITY IN AUDITORY LEARNING 3149 appear to change with learning. This was especially evident to explore the interactions in terms of covariance patterns between two or more brain regions. The second technique in the case where the behavioral relevance of an auditory stimulus depended on a visual stimulus (McIntosh and Gon- incorporates additional information, such as anatomic connections, to quantify explicitly the effect one brain region zalez-Lima 1995) . Two groups of rats received pairings of a tone (conditioned excitor: T / ) with a mild footshock. has on another. These two approaches are known as functional and effective connectivity, respectively. Both terms Group TL 0 was trained in a Pavlovian conditioned inhibition paradigm (T / /TL 0 ) where the tone-light compound sig- were introduced in the context of electrophysiological recordings from multiple cells (Aertsen et al. 1989; Gerstein naled the absence of footshock, making the light an inhibitor (L 0 ). Group TL 0 was trained with the tone as the excitor et al. 1978) . More recently, they have been used in reference to neuroimaging data (Friston 1994) . In most of our previ- and the light as a "neutral" stimulus in that it predicted the absence of footshock on only 50% of trials. During fluo...

Regression models are often used to infer causation from association. For instance, Yule [79] showed – or tried to show – that welfare was a cause of poverty. Path models and structural equation models are later

1997 Association for Child Psychology & Psychiatry.

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This paper is a brief overview and evaluation of current mathematical/statistical causal models, including the structural equation model (SEM), TETRAD, and the graphical model. The efficacy of these approaches will be discussed in the philosophical context of the Duhem-Quine thesis, realism, simplicity, identifiability (testability), empirical adequacy, and probabilistic causality. The emphasis of this paper is on the philosophical aspect, not the mathematical or computational aspect of SEM, nonetheless, readers are not required to have a philosophical background to follow the arguments.

Research over the past twenty-five years indicates that gender differences in math achievement favoring males are not typically found prior to high school. In high school, differences favoring males are common, particularly in the areas of problem solving and applications. The gender-related differences in math achievement have been attributed to a number of variables, most notably, differential coursetaking patterns and exposure to math, different learning styles, teacher behavior and learning environment, parental attitudes and expectations, and socioeconomic status as well as other background characteristics of students. One problem that is not addressed in this research is the inability to isolate the effects of gender socialization from observed biological sex when observational data is used. One method by which the effects of environment and socialization maybecontrolled for involves the use of a propensity score, as developed by Rosenbaum and Rubin, for gender. The gender propensit...

ive Theory, Bandura (1986) wrote that individuals possess beliefs that enable them to exercise a measure of control over their thoughts, feelings, and actions, that "what people think, believe, and feel affects how they behave" (p. 25). These beliefs comprise a self system with symbolizing, forethinking, vicarious, self-regulatory, and self-reflective capabilities, and human behavior is the result of the interplay between this personal system and external sources of influence. In all, Bandura painted a portrait of human behavior and motivation in which the beliefs that people have about themselves are key elements. Social Cognitive Theory and Self-efficacy Bandura (1986) argued that self-referent thought mediates between knowledge and action and that the capability to self-reflect is the most distinctively human characteristic, for it permits individuals to evaluate their own experiences and thought processes. Through reflection and selfevaluation, individuals can alter their