How Mean is the Mean?

Abstract

In this paper we voice concerns about the uncritical manner in which the mean is often used as a summary statistic in psychological research. We identify a number of implicit assumptions underlying the use of the mean and argue that the fragility of these assumptions should be more carefully considered. We examine some of the ways in which the potential violation of these assumptions can lead us into significant theoretical and methodological error. Illustrations of alternative models of research already extant within Psychology are used to explore methods of research less mean-dependent and suggest that a critical assessment of the assumptions underlying its use in research play a more explicit role in the process of study design and review.

Answering research questions without calculating the mean

“…This anecdote nicely dovetails with Speelman and McGann's (2013) assertion that psychological researchers tend to use procedures that involve calculating means in an uncritical manner. The goal of this article is to emphasize that there are procedures that do not involve calculating means, which are perfectly sound to answer research questions.…”

“…As indicated by Speelman and McGann (2013), calculating a mean of some dependent variable as a first step of other statistical procedures is only one of a range of procedures available for the psychological researcher. There are two main reasons why psychological researchers tend to overlook the type of analyses presented above.…”

“…This article builds upon Speelman and McGann's (2013) call for critical use of statistical procedures, and illustrates four sound procedures to answer research questions, which do not involve calculating the mean. It is to be hoped that this article contributes toward the development of formal theories and ingenious procedures to answer research questions, as opposed to fitting research questions to the requirements of extant popular statistical procedures.…”

“…In an important theoretical article Speelman and McGann (2013) indicated that psychological researchers tend to use statistical procedures that involve calculating the mean of a variable in an uncritical manner. A typical procedure in psychological research consists of calculating the mean of some dependent variable in two or more samples and to present those means as summaries of the samples.…”

BOLD and EEG Signal Variability at Rest Differently Relate to Aging in the Human Brain

“…Functional neuroimaging methods such as fMRI, PET, fNIRS, EEG, or MEG have allowed the non-invasive assessment of functional changes in the aging human brain (Cabeza, 2001;Cabeza et al, 2018). Most previous functional neuroimaging studies on aging have employed a task-based design (Grady, 2012) and in their data analysis the central tendency has typically been assumed to be the most representative value in a distribution (e.g., mean) (Speelman and McGann, 2013) or the "signal" within distributional "noise". In recent years, also the variability of brain activation in task-dependent and task-independent measurements (as spontaneous variations of background activity) has been shown to provide relevant information about the brain's functional state (Garrett et al, 2013b;Grady and Garrett, 2018;Nomi et al, 2017).…”