Editing Interaction (statistics) (section)

{{Short description|Causal or moderating relationship between statistical variables}}
[[File:GSS sealevel interaction.png|thumb|Interaction effect of education and ideology on concern about sea level rise]]

In [[statistics]], an '''interaction''' may arise when considering the relationship among three or more [[Variable (statistics)|variables]], and describes a situation in which the effect of one [[causal variable]] on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not [[additive map|additive]]).<ref name=Dodge>{{cite book | last=Dodge | first=Y. | year=2003 | title=''The Oxford Dictionary of Statistical Terms'' | publisher=Oxford University Press | isbn=978-0-19-920613-1 | url-access=registration | url=https://archive.org/details/oxforddictionary0000unse }}</ref><ref>{{cite journal | doi=10.2307/1403235 | last=Cox | first=D.R. | year=1984 | title=Interaction | journal=International Statistical Review | volume=52 | pages=1&ndash;25 | jstor=1403235 | issue=1 }}</ref> Although commonly thought of in terms of [[Causality|causal relationships]], the concept of an interaction can also describe non-causal associations (then also called [[Moderation (statistics)|''moderation'']] or ''effect modification''). Interactions are often considered in the context of [[regression analysis|regression analyses]] or [[factorial experiments]].

The presence of interactions can have important implications for the interpretation of [[statistical model]]s. If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable. In practice, this makes it more difficult to predict the consequences of changing the value of a variable, particularly if the variables it interacts with are hard to measure or difficult to control.

The notion of "interaction" is closely related to that of moderation that is common in social and health science research: the interaction between an explanatory variable and an environmental variable suggests that the effect of the explanatory variable has been moderated or modified by the environmental variable.<ref name=Dodge />