# The Various Forms of ANOVA

Quantitative Results
Statistical Analysis

An analysis of variance (ANOVA) is an appropriate statistical analysis when assessing for differences between groups on a continuous measurement (Tabachnick & Fidell, 2013). Depending on the goal of the research, there are several types of ANOVAs that can be utilized.

Between-Subjects ANOVA: One of the most common forms of an ANOVA is a between-subjects ANOVA. This type of analysis is applied when examining for differences between independent groups on a continuous level variable. Within this “branch” of ANOVA, there are one-way ANOVAs and factorial ANOVAs.

A one-way ANOVA is used when assessing for differences in one continuous variable between ONE grouping variable. For example, a one-way ANOVA would be appropriate if the goal of research is to assess for differences in job satisfaction levels between ethnicities. In this example, there is only one dependent variable (job satisfaction) and ONE independent variable (ethnicity).

A factorial ANOVA is a general term applied when examining multiple independent variables. For example, a factorial ANOVA would be appropriate if the goal of a study was to examine for differences in job satisfaction levels by ethnicity and education level. In this example, there is only one dependent variable (job satisfaction) and TWO independent variables (ethnicity and education level). A factorial ANOVA can be applied when there are two or more independent variables.

Within-Subjects ANOVA: A within-subjects ANOVA is appropriate when examining for differences in a continuous level variable over time. A within-subjects ANOVA is also called a repeated measures ANOVA. This type of test is frequently used when using a pretest and posttest design, but is not limited to only two time periods. The repeated measures ANOVA can be used when examining for differences over two or more time periods. For example, this analysis would be appropriate if the researcher seeks to explore for differences in job satisfaction levels, measured at three points in time (pretest, posttest, 2-month follow up).

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Mixed-Model ANOVA: A mixed model ANOVA, sometimes called a within-between ANOVA, is appropriate when examining for differences in a continuous level variable by group and time. This type of ANOVA is frequently applied when using a quasi-experimental or true experimental design. This analysis would be applicable if the purpose of the research is to examine for potential differences in a continuous level variable between a treatment and control group, and over time (pretest and posttest).

ANCOVA: An analysis of covariance (ANCOVA) is appropriate when examining for differences in a continuous dependent variable between groups, while controlling for the effect of additional variables. The “C” in ANCOVA denotes that a covariate is being inputted into the model, and this covariate examination can be applied to a between-subjects design, a within-subjects design, or a mixed-model design. ANCOVAs are frequently used in experimental studies when the researcher wants to account for the effects of an antecedent (control) variable.

MANOVA: Finally, a multivariate analysis of variance (MANOVA) is an extension on the ANOVA, and is appropriate when examining for differences in multiple continuous level variables between groups. For example, a MANOVA would be applicable if assessing for differences between ethnicities in job satisfaction AND intrinsic motivation levels of participants. In this example, job satisfaction and intrinsic motivation are the continuous level dependent variables. The MANOVA can be conducted with multiple independent variables, and can also include covariates (i.e., MANCOVA).

References
Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics, 6th ed. Boston: Allyn and Bacon.

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