P values, Confidence Intervals, and Power: a guide to misinterpretations

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

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, the article provides definitions and a discussion of basic statistics that are more general and critical than typically found in traditional introductory expositions.

The 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.

The essay concludes with guidelines for improving statistical interpretation and reporting.

Question:

What are the common misinterpretations of P values comparisons and predictions?

And what are the common misinterpretations of confidence intervals and power?

Try to list at least two misinterpretations of each question, and share your answers and thoughts below!