Random Effects Analysis of Variance (SPSS)

In today’s article, we will again be discussing the ANOVA model. When building an ANOVA model, typically, as a researcher, you will prefer to have the same amount of categorical variables representing each category. Also, the experimental parameters should be pre-established in way in which the same levels can be re-utilized in future models.

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:

For this example, we will build a model which utilizes “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:

Below is an image which illustrates variable specification:

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

The post hoc test that we will select for subsequent analysis will be “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.

Similarly, in the manner in which we analyzed previous ANOVA examples, we will specifically be investigating significant values as they pertain to each value, or combination of values, as they appear in the leftmost column. In this particular example, there are no significant values which coincide with interactions or specific model variables.

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.

In the next article, we will review the concept of repeated measures ANOVA. We also will discuss how to create these models within SPSS.