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Primary Submission Category: general causality

In Search of the Third Number

Authors: guido imbens,

Presenting Author: guido imbens*

Consider a situation where a decision maker tasks a statistician with analyzing a data set to
inform a decision. The decision is whether or not to implement an intervention on all members a population of units. The decision maker has given the statistician the task to analyze the available data and report the results of his analysis to inform this decision. It is common in such settings for the statistician to report a point estimate of the average effect of the intervention and a measure of the uncertainty of that estimate, say, in the form of a standard error. However, suppose the decision maker has the sophistication to absorb more information. What else should the statistician report to the decision maker? Specifically, what should the third (and fourth and fifth) numbers be that the statistician reports to the decision maker? Compared to the apparent consensus that a point estimate and standard error are the two most relevant numbers, there is much less agreement on the additional information that would be important for the decision maker to take into account. In this paper we explore some measures that have been suggested in the literature, and discuss why there is so little agreement on what else is important to take into account for decision makers.