Moderation (statistics)
Encyclopedia
In statistics
, moderation occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable or simply the moderator . The effect of a moderating variable is characterized statistically as an interaction
; that is, a qualitative
(e.g., sex, race, class) or quantitative
(e.g., level of reward) variable
that affects the direction and/or strength of the relation between dependent and independent variables
. Specifically within a correlation
al analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables. In analysis of variance
(ANOVA) terms, a basic moderator effect can be represented as an interaction
between a focal independent
variable and a factor that specifies the appropriate conditions for its operation (Baron and Kenny, 1986: p. 1174).
Moderation analysis in the behavioral sciences involves the use of linear multiple regression analysis
or causal modelling. To quantify the effect of a moderating variable in multiple regression analyses, regressing random variable
s Y on X, an additional term is added to the model. This term is the interaction between X and the proposed moderating variable .
Thus, for a response Y and two variables x1 and moderating variable x2,:
In this case, the role of x2 as a moderating variable is accomplished by evaluating b3, the parameter estimate for the interaction term. See linear regression
for discussion of statistical evaluation of parameter estimates in regression analyses.
Moderation should not be confused with mediation
.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, moderation occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable or simply the moderator . The effect of a moderating variable is characterized statistically as an interaction
Interaction (statistics)
In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive...
; that is, a qualitative
Qualitative research
Qualitative research is a method of inquiry employed in many different academic disciplines, traditionally in the social sciences, but also in market research and further contexts. Qualitative researchers aim to gather an in-depth understanding of human behavior and the reasons that govern such...
(e.g., sex, race, class) or quantitative
Quantitative research
In the social sciences, quantitative research refers to the systematic empirical investigation of social phenomena via statistical, mathematical or computational techniques. The objective of quantitative research is to develop and employ mathematical models, theories and/or hypotheses pertaining to...
(e.g., level of reward) variable
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
that affects the direction and/or strength of the relation between dependent and independent variables
Dependent and independent variables
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
. Specifically within a correlation
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
al analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables. In analysis of variance
Analysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
(ANOVA) terms, a basic moderator effect can be represented as an interaction
Interaction (statistics)
In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive...
between a focal independent
Statistical independence
In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...
variable and a factor that specifies the appropriate conditions for its operation (Baron and Kenny, 1986: p. 1174).
Moderation analysis in the behavioral sciences involves the use of linear multiple regression analysis
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
or causal modelling. To quantify the effect of a moderating variable in multiple regression analyses, regressing random variable
Random variable
In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...
s Y on X, an additional term is added to the model. This term is the interaction between X and the proposed moderating variable .
Thus, for a response Y and two variables x1 and moderating variable x2,:
In this case, the role of x2 as a moderating variable is accomplished by evaluating b3, the parameter estimate for the interaction term. See linear regression
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
for discussion of statistical evaluation of parameter estimates in regression analyses.
Moderation should not be confused with mediation
Mediation (Statistics)
In statistics, a mediation model is one that seeks to identify and explicate the mechanism that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third explanatory variable, known as a mediator variable...
.