Optimal Pre-Analysis Plans: Statistical Decisions Subject to Implementability

TL;DR

This paper models the strategic interaction between data analysts and decision-makers, demonstrating that optimal pre-analysis plans enhance decision rule implementability and can be derived via linear programming, improving hypothesis testing validity.

Contribution

It introduces a formal model of agent-principal interactions emphasizing the importance of pre-analysis plans and characterizes optimal mechanisms for statistical decision-making.

Findings

Pre-analysis plans expand implementable decision rules.

Optimal tests pre-register valid procedures and account for unreported data.

Linear programming can identify optimal hypothesis tests.

Abstract

What is the purpose of pre-analysis plans, and how should they be designed? We model the interaction between an agent who analyzes data and a principal who makes a decision based on agent reports. The agent could be the manufacturer of a new drug, and the principal a regulator deciding whether the drug is approved. Or the agent could be a researcher submitting a research paper, and the principal an editor deciding whether it is published. The agent decides which statistics to report to the principal. The principal cannot verify whether the analyst reported selectively. Absent a pre-analysis message, if there are conflicts of interest, then many desirable decision rules cannot be implemented. Allowing the agent to send a message before seeing the data increases the set of decision rules that can be implemented, and allows the principal to leverage agent expertise. The optimal mechanisms that we characterize require pre-analysis plans. Applying these results to hypothesis testing, we show that optimal rejection rules pre-register a valid test, and make worst-case assumptions about unreported statistics. Optimal tests can be found as a solution to a linear-programming problem.