Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations

TLDR

Misinterpretation and abuse of statistical tests, confidence intervals, and power remain rampant because no simple, foolproof interpretation exists, leading scientists to adopt shortcut definitions that often produce wrong conclusions. The authors aim to supply clear, general definitions and a critical discussion of basic statistics to serve as a resource for instructors, researchers, and consumers with limited statistical knowledge, helping them avoid and detect misinterpretations. They highlight how violating unstated analysis protocols—such as selecting analyses based on P‑values—can produce misleading small or large P‑values, and present an explanatory list of 25 common misinterpretations. The paper concludes with practical guidelines for improving statistical interpretation and reporting.

Abstract

Misinterpretation and abuse of statistical tests, confidence intervals, and statistical power have been decried for decades, yet remain rampant. A key problem is that there are no interpretations of these concepts that are at once simple, intuitive, correct, and foolproof. Instead, correct use and interpretation of these statistics requires an attention to detail which seems to tax the patience of working scientists. This high cognitive demand has led to an epidemic of shortcut definitions and interpretations that are simply wrong, sometimes disastrously so—and yet these misinterpretations dominate much of the scientific literature. In light of this problem, we provide definitions and a discussion of basic statistics that are more general and critical than typically found in traditional introductory expositions. Our goal is to provide a resource for instructors, researchers, and consumers of statistics whose knowledge of statistical theory and technique may be limited but who wish to avoid and spot misinterpretations. We emphasize how violation of often unstated analysis protocols (such as selecting analyses for presentation based on the P values they produce) can lead to small P values even if the declared test hypothesis is correct, and can lead to large P values even if that hypothesis is incorrect. We then provide an explanatory list of 25 misinterpretations of P values, confidence intervals, and power. We conclude with guidelines for improving statistical interpretation and reporting.