Abstract
In many legal settings, a statistical sample can be an effective surrogate for a larger population when adjudicating questions of causation, liability, or damages. The current paper works through salient aspects of statistical sampling and sample size determination in legal proceedings. An economic model is developed to provide insight into the behavioral decision-making about sample size choice by a party that intends to offer statistical evidence to the court. The optimal sample size is defined to be the sample size that maximizes the expected payoff of the legal case to the party conducting the analysis. Assuming a probability model that describes a hypothetical court’s likelihood of accepting statistical evidence based on the sample size, the optimal sample size is reached at a point where the increase in the probability of the court accepting the sample from a unit increase in the chosen sample size, multiplied by the payoff from winning the case, is equal to the marginal cost of increasing the sample size.
Highlights
Introduction and BackgroundLegal and regulatory proceedings are often complex and can be troubled with large amounts of data or a large number of elements that require study
Assuming a probability model that describes a hypothetical court’s likelihood of accepting statistical evidence based on the sample size, the optimal sample size is reached at a point where the increase in the probability of the court accepting the sample from a unit increase in the chosen sample size, multiplied by the payoff from winning the case, is equal to the marginal cost of increasing the sample size
The analysis reveals that the optimal sample size chosen by the party presenting statistical evidence is reached where the increase in the probability of the court accepting the sample from a unit increase in the chosen sample size, multiplied by the payoff from winning the case, is equal to the marginal cost of increasing the sample size by a unit
Summary
Legal and regulatory proceedings are often complex and can be troubled with large amounts of data or a large number of elements that require study. Analyzing a sample can reduce the amount of evidence and contribute toward creating a reasonable trial length This was recognized early on in United States v. Courts and regulators should continue to appreciate that time and resources are finite, so it may be more effective to investigate a relatively small but reliable sample of subjects than to unreliably analyze all subjects in the population in question.. The analysis reveals that the optimal sample size chosen by the party presenting statistical evidence is reached where the increase in the probability of the court accepting the sample from a unit increase in the chosen sample size, multiplied by the payoff from winning the case, is equal to the marginal cost of increasing the sample size by a unit.
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