A common misapplication of statistical inference: nuisance control with null-hypothesis significance tests

TL;DR

This paper critiques the common misuse of null-hypothesis significance tests for controlling nuisance variables in experimental research, highlighting its conceptual flaws, high prevalence, and proposing regression as a better alternative.

Contribution

It exposes the widespread misapplication of significance tests for nuisance control, clarifies their conceptual issues, and advocates for regression methods as a more appropriate solution.

Findings

Significance tests are often misused for nuisance control in experiments.

Such tests have high error rates and are conceptually misguided.

Regression with nuisance variables is recommended as an alternative.

Abstract

Experimental research on behavior and cognition frequently rests on stimulus or subject selection where not all characteristics can be fully controlled, even when attempting strict matching. For example, when contrasting patients to controls, variables such as intelligence or socioeconomic status are often correlated with patient status. Similarly, when presenting word stimuli, variables such as word frequency are often correlated with primary variables of interest. One procedure very commonly employed to control for such nuisance effects is conducting inferential tests on confounding stimulus or subject characteristics. For example, if word length is not significantly different for two stimulus sets, they are considered as matched for word length. Such a test has high error rates and is conceptually misguided. It reflects a common misunderstanding of statistical tests: interpreting significance not to refer to inference about a particular population parameter, but about 1. the sample in question, 2. the practical relevance of a sample difference (so that a nonsignificant test is taken to indicate evidence for the absence of relevant differences). We show inferential testing for assessing nuisance effects to be inappropriate both pragmatically and philosophically, present a survey showing its high prevalence, and briefly discuss an alternative in the form of regression including nuisance variables.