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Analysis of Variance (ANOVA)
In many social science disciplines such as communication and media studies, researchers wish to compare group averages on a dependent variable across different levels of an independent variable. Analysis of variance (ANOVA) is a collection of inferential statistical tests belonging to the general linear model (GLM) family that examine whether two or more levels (e.g., conditions) of a categorical independent variable have an influence on a dependent variable. As with most inferential tests, the purpose of ANOVA is to test the likelihood that the results observed are due to change differences between the groups.
This entry provides a general overview of ANOVA, including a discussion of the assumptions underlying the tests, comparison with t-tests, different forms of ANOVA, and provides two examples of ANOVA designs.
Assumptions Underlying ANOVA Tests
ANOVA belongs to the family of parametric inferential tests; therefore, a number of requirements related to the variables and the population of interest must be met or else assumptions underlying the mathematical properties will be violated. One requirement is that independent variables should be measured on a nominal scale, such that the variables’ conditions vary qualitatively (e.g., presence or absence of a variable) but not quantitatively. Another requirement is that the variance associated with the populations from which the independent variable was sampled should be equal (i.e., homogeneity of variance). Dependent variables should be quantifiable on at least an interval scale (e.g., extent of agreement with a statement; amount of satisfaction with a relationship) and should also be normally distributed. These assumptions also highlight ANOVA’s roots in experimental design, where researchers have a significant amount of control in the manipulation and measure of the variables of interests. However, it is possible to utilize ANOVA in quasi-experimental and some correlational designs where random assignment of participants to conditions is too costly or not possible (e.g., gender). Violation of these assumptions can affect the interpretation of the results from these tests; under these conditions nonparametric tests might better serve the researcher.
Comparison to t-Test
To better understand and appreciate the utility of ANOVA tests, it might be useful to compare it to t-test types of analyses. Both tests share similar assumptions and are applicable for designs where different levels of a condition can be independent (i.e., participants are exposed to only one level of the independent variable) or dependent (i.e., participants are exposed to all levels of the independent variable). And just like t-tests, ANOVA partitions out the variability attributed to the difference between the independent variable (i.e., difference between groups or treatment variance) and variability in the research context (e.g., naturally occurring variability or error variance). However, two important differences between t-tests and F tests derived from ANOVA are that ANOVA can accommodate research designs that utilize (a) more than two levels of an independent variable and (b) multiple independent variables.
Types of ANOVA Designs
One-Way ANOVA
To illustrate the different types of variables in a research context, consider the following example involving message source effects in persuasion—common variables of interest in communication research. Imagine that a researcher is interested in the effect of source credibility on the persuasiveness of a message advocating the reduction of greenhouse gases. In this case, credibility is the independent variable and persuasion is the dependent variable. The researcher hypothesizes that participants exposed to the message from the high-credibility source will be more persuaded than those who are exposed to the same message from either the low-credibility source or where no source information is mentioned. To test this, three conditions are created: a high-credibility condition, a low-credibility condition, and a control condition where credibility-related information is absent. Following exposure to the independent variable and the message, participants report their opinion toward the reduction of greenhouse gases.
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