Assignment Task:

Task:

Problems involving causal inference have dogged at the heels of statistics since its earliest days. Correlation does not imply causation, and yet causal conclusions drawn from a carefully designed experiment are often valid. What can a statistical model say about causation? This question is ad- dressed by using a particular model for causal inference (Holland and Rubin 1983; Rubin 1974) to critique the discussions of other writers on causation and causal inference. These include selected philosophers, med- ical researchers, statisticians, econometricians, and proponents of causal modeling. KEY WORDS: Causal model; Philosophy; Association; Experiments; Mill's methods; Causal effect; Koch's postulates; Hill's nine factors; Gran- ger causality; Path diagrams; Probabilistic causality.

1. INTRODUCTION

The reaction of many statisticians when confronted with the possibility that their profession might contribute to a discussion of causation is immediately to deny that there is any such possibility. "That correlation is not causation is perhaps the first thing that must be said" (Barnard 1982, p. 387). Possibly this evasive action is in response to all of those needling little headlines that pop up in the most unexpected places, for example, "If the statistics cannot relate cause and effect, they can certainly add to the rhet- oric" (Smith 1980, p. 998). One need only recall that a well-designed randomized experiment can be a powerful aid in investigating causal relations to question the need for such a defensive posture by statisticians. Randomized experiments have trans- formed many branches of science, and the early proponents of such studies were the sanle statisticians who founded the modern era of our field. This article takes the view that statistics has a great deal to say about certain problems of causal inference and ought to play a more significant role in philosophical analyses of causation than it has heretofore. In addition, I will try to show why the statistical models used to draw causal infer- ences are distinctly different from those used to draw as- sociational inferences. The article is organized as follows. First, statistical models appropriate for associational and causal inferences will be discussed and compared. Then they will be applied to vari- ous ideas about causation that have been expressed by several writers on this subject. One difficulty that arises in talking about causation is the variety of questions that are subsumed under the heading. Some authors focus on the ultimate meaningfulness of the notion of causation. Others are concerned with deducing the causes of a given effect. Still others are interested in understanding the details of causal mechanisms

 

2. MODEL FOR ASSOCIATIONAL INFERENCE

The model appropriate for associational inference is sim- ply the standard statistical model that relates two vari- ables over a population. For clarity and for comparison with the model for causal inference described in the next section, however, I will briefly review association here. If I seem overly explicit in describing the model it is only because I wish to be absolutely clear on the fundamental elements of the theory presented here. The model begins with a population or universe U of "units." A unit in U will be denoted by u. Units are the basic objects of study in an investigation. Examples of units are human subjects, laboratory equipment, households, and plots of land. A variable is simply a real-valued func- tion -that is defined on every unit in U. The value of a variable for a given unit u is the number assigned by some measurement process to u. A population of units and vari- ables defined on these units are the basic elements of the models for both association and causation presented here. They correspond to the mathematical concepts of a set and real-valued functions defined on the elements of the set. They are the primitives of the theory and will not be further defined.

 


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  • Posted on : March 05th, 2019

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