All previous ANOVA examples have demonstrated models which comply with the previously listed sentiments. However, there will occasions in which levels of the independent variables are not specifically chosen, but instead are drawn randomly from a larger population. If the experiment was repeated, the levels could potentially differ with the next sampling iteration. In such cases, the data can still be included to assist in the creation of a model which will be used to make inferences about a larger population.

A random effects model anticipates differing study size as it pertains to variables, and mean estimates of each variable grouping. In fixed effects models, narrower confidence intervals will occur due to the absence of this factor. In random effects models, larger confidence intervals will occur due to the model adjusting for such.

Therefore, fixed effect models are most appropriate when there is homogeneity. If this is indeed the case, the study will be more precise, and additionally the confidence interval will be narrower.

__Random Effects Analysis of Variance Example:__

Below is a modified data set from a previous example:

**“Satisfaction”**as the independent variable. Our dependent variables will be

**“School”**and

**“Study_Time”**. The

**“Random Factor(s)”**that we will select will be the

**“Race”**variable.

These options can be selected through the utilization of the following menu selections:

**“Post Hoc”**from the menu options, we will be presented with the following interface:

**“Tukey”**. The variables which we will specify for analysis are

**“School”**and

**“Study_Time”**.

Clicking

**“Continue”**, followed by

**“OK”,**will create the model and the necessary output.

Therefore, we will move on to the post hoc test, which, in tandem with the above model output, does not illustrate significant difference between variable values.

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