Example 2: A 2 x 3 Between-Groups ANOVA Design

Suppose that we have conducted an experiment to address the nature vs. nurture question; specifically, we test the performance of different rats in the "T-maze." The T-maze is a simple maze, and the rats' task is to learn to run straight to the food placed in a particular location, without errors. Three strains of rats whose general ability to solve the T-maze can be described as bright, mixed, and dull, were used. From each of these strains, we rear 4 animals in a free (stimulating) environment, and 4 animals in a restricted environment. The dependent measure is the number of errors made by each rat while running the T-maze problem.

Ribbon bar. Select the Home tab. In the File group, click the Open arrow and from the menu, select Open Examples. The Open a STATISTICA Data File dialog box is displayed. Rats.sta is located in the Datasets folder.

Classic menus. From the File menu, select Open Examples to display the Open a STATISTICA Data File dialog box; Rats.sta is located in the Datasets folder.

A portion of this file is shown below.

The General ANOVA/MANOVA Startup Panel will be displayed, in which we can enter the specifications for the design.

In the data file Rats.sta, the codes 1-free and 2-restricted were used in the categorical predictor variable Envirnmt to denote whether the rat belongs to the group of rats that were raised in the free or restricted environment, respectively. The codes used for the second independent variables (Strain) are 1-bright, 2-mixed, and 3-dull. The dependent variable in an experiment is the one that depends on or is affected by the independent variables; in this study this would be the variable Errors, which contains the number of errors made by the rats running the maze.

Click the Variables button to display a standard variable selection dialog box. Select Errors on the Dependent variable list and Envirnmt and Strain on the Categorical predictors (factors) list, and then click the OK button.

Next, specify the codes that were used to uniquely identify the groups; click the Factor codes button and either enter each of the codes for each variable or click the All button for each variable to enter all of the codes for that variable. Finally, click the OK button. The ANOVA/MANOVA Factorial ANOVA dialog box will now look as follows:

Click the All effects/Graphs button to display the table of all effects.

The default graph for all spreadsheets with marginal means is the means plot. In this case, the plot is rather simple. To produce this plot of the two means for the free and restricted environment, return to the Table of All Effects dialog box (by clicking the All effects/Graphs button on the Quick tab), change the Display option to Graph, and again click the OK button.

It appears that rats raised in the more restricted environment made more errors than rats raised in the free environment.

As you can see, we have full control over the order in which the factors in the interaction will be plotted. For this example, select STRAIN under x-axis, upper and ENVIRNMT under Line pattern (see above). Click the OK button, and the graph of means is displayed.

The graph, shown below, below nicely summarizes the results of this study, that is, the two main effects pattern. The rats raised in the restricted environment (dashed line) made more errors than those raised in the free environment (solid line). At the same time, the dull rats made the most errors, followed by the mixed rats, and the bright rats made the fewest number of errors.

In this table, the means are sorted from smallest to largest, and the means that are not significantly different from each other have four "stars" (*) in the same column (i.e., they form a homogenous group of means); all means that do not share stars in the same column are significantly different from each other. Thus, and as discussed in Winer, Brown, and Michels (1991, p. 528), the only means that are significantly different from each other are the means group 1 (bright) and group 3 (dull). Thus, we would conclude that the dull strain of rats made significantly more errors than the bright strain of rats, while the mixed strain of rats is not significantly different from either.

For this example, click the OK button to accept the default selection of All Groups, and a histogram of the distribution will be produced.

It appears as if the distribution across groups is multi-modal, that is to say, it has more than one "peak." We could have anticipated that, given the fact that strong main effects were found. If you want to test the homogeneity assumption more thoroughly, you could look at the distributions within individual groups.

For this example, a potentially more serious violation of the ANOVA assumptions will be tested.

Now, look at the correlation between the 6 means and standard deviations in this design. We can elect to plot the means vs. either the standard deviations or the variances by clicking the appropriate button (Plot means vs. std. deviations or Variances, respectively) on the Assumptions tab. For this example, click the Plot means vs. std. deviations button.