Analysis of Variance (ANOVA)

Different Types of ANOVA

ANOVA can be applied to a variety of research designs and takes specific names that reflect the design to which it has been applied. The computational details of the analysis become more complex with the design, but the essence of the test remains the same. The first distinction that is made is in the number of independent variables in the research design. If there is simply one independent variable, then the ANOVA is called a one-way ANOVA. If two independent variables have been manipulated in the research, then a two-way ANOVA can be used to analyze the data; likewise if three independent variables[Page 33] have been manipulated, a three-way ANOVA is appropriate. The logic of the test extends to any number of independent variables; however, for ease of interpretation, researchers rarely go beyond a three-way ANOVA.

The second distinction that needs to be made is whether data in different conditions are independent or related. If data representing different levels of an independent variable are independent (i.e., collected from different entities), then an independent ANOVA can be used (also known as a between-groups ANOVA). If two independent variables have been used and all levels of all variables contain data from different entities, then a two-way independent ANOVA could be employed, and so on. When data are related—for example, when different entities have provided data for all levels of an independent variable or all levels of several independent variables—then a repeated measures ANOVA (also known as within subjects ANOVA) can be employed. As with independent designs, it is possible to have one-way, two-way, three-way, n-way repeated measures ANOVAs. A final type of ANOVA is used when a mixture of independent and related data have been collected. These mixed designs require at least two independent variables, one of which has been manipulated using different entities (and so data are independent) and the other of which has been manipulated using the same entities (data are related). In these situations, a mixed ANOVA is used. It is possible to combine different numbers of independent variables measured using different entities or the same entities to come up with three-way, four-way, or n-way mixed ANOVAs. ANOVAs involving more than one independent variable are known as factorial ANOVAs.

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