Effect Size

Abstract

Simply put, effect size (ES) is the magnitude or strength of association between or among variables. Effect sizes (ESs) are commonly represented numerically (i.e., as parameters for population ESs and statistics for sample estimates of population ESs) but also may be communicated graphically. Although the word “effect” may imply that an ES quantifies the strength of a causal association (“cause and effect”), ESs are used more broadly to represent any empirical association between variables. Effect sizes serve three general purposes: research results reporting, power analysis, and meta-analysis. Even under the same research design, an ES that is appropriate for one of these purposes may not be ideal for another. Effect size can be conveyed graphically or numerically using either unstandardized metrics, which are interpreted relative to the original scales of the variables involved (e.g., the difference between two means or an unstandardized regression slope), or standardized metrics, which are interpreted in relative terms (e.g., Cohen’s d or multiple R2). Whereas unstandardized ESs and graphs illustrating ES are typically most effective for research reporting, that is, communicating the original findings of an empirical study, many standardized ES measures have been developed for use in power analysis and especially meta-analysis. Although the concept of ES is clearly fundamental to data analysis, ES reporting has been advocated as an essential complement to null hypothesis significance testing (NHST), or even as a replacement for NHST. A null hypothesis significance test involves making a dichotomous judgment about whether to reject a hypothesis that a true population effect equals zero. Even in the context of a traditional NHST paradigm, ES is a critical concept because of its central role in power analysis.