Graziano and Raulin (8th ed)Graziano & Raulin
Research Methods (8th edition)

Factorial ANOVA

Factorial studies are becoming increasingly more common in psychology as the interactive nature of independent variables becomes more obvious. SPSS for Windows is capable of analyzing many different factorial designs. We will cover the most common designs in this unit.

Opening the Data File

In Chapter 12, we introduced a hypothetical study of children's dark fears. [The data for this hypothetical study was in Table 12.3, and we have entered  those data into a file on the website, which you can download to your computer.] Open the file by clicking on the File Menu and the Open Submenu and navigating to the appropriate subdirectory as shown in this screen. Opening file Table_12-3.sav will give you this screen showing the data. Note that we have three variables in this file. The variables lightlvl and imagetyp (short for light level and image type) are necessary for defining the group membership of each participant. The variable h_rate (short for heart rate) is the dependent variable.

Checking on the Characteristics of the Variables

This is a rather simple file, but many data sets can be quite complex, and it can be hard to remember the details of each variable and the coding for the variable. This is one reason why it is critical to label the variables as clearly as possible and to use names for the variables that are reasonably descriptive. Of course, eight characters (the limit for the variable name) is often not enough to spell out the variable, so be sure that you give a more complete description when defining the variable. 

If you set up a data set earlier, or someone else sets it up as in this example, you may want to quickly check what each variable is and how each is coded by looking at the variables view. The quickest way to access this option is to hit cntl+T (hold the control key down while hitting the letter T), which will open the variables view.  An alternative way to do the same thing is to click the View menu and select Variables from the bottom of the list. Note that in the Label column, each of the variables are given a more complete name than the eight character definition of the variable. 

To see the codes for either the lightlvl or imagetyp variables, click in the values column and a gray box with three dots will appear as in this screen. Clicking on the gray box will open this screen. Now the labels that were given when the variable was first defined are available for your inspection. As you can see, the code of 1 refers to the lighted condition and the code of 2 refers to the dark condition. You can use this procedure anytime to refresh your memory about the details of a variable and the codes used for that variable.

Setting up the ANOVA

To set up the ANOVA for this hypothetical study, we select the Analyze menu, the General Linear Model submenu, and the Univariate option. This screen looks complicated, but it is relatively easy to set up the two-way ANOVA in our example. First we must move the h_rate variable to the box labeled dependent variables. We do this by clicking on the h_rate variable to highlight it and then clicking on the arrow next to the dependent variables box to move it. We must also move the independent variables. In the type of factorial studies that you are likely to run, the independent variables are fixed factors, so you should move both of them in our example to the fixed factors box. These actions will produce this screen.

Clicking on OK at this point will run your factorial ANOVA, but we recommend that you routinely arrange to have some additional computations done as part of the analysis. It is important to have descriptive statistics for the subgroups computed so that you can see how the groups differ. The ANOVA results will only tell you if the groups are statistically different. The table of means will let you see how the groups differ. 

To obtain such additional computations, click on the options button, which will give you the options window. Click the additional statistics you want run. We recommend descriptive statistics, estimates of effect size, and observed power. Then click on the continue button to close the options box and click OK to run the analysis. This screen shows the results of the analysis. 

Since the output is large, not all of the material will fit on this one screen. The frame at the left gives you the table of contents for the analysis. Clicking on any item in that table of contents will immediately bring that portion of the analysis to the screen. The first box shows the labels for the conditions and the number of participants in each condition. It is a good idea to check these numbers, because if you set up the analysis incorrectly, you will likely get numbers that make no sense. 

By scrolling down the screen, we can see the descriptive statistics for the groups and the results of the ANOVA. Note that you have the means for graphing the results available. The ANOVA summary table for SPSS for Windows is more complicated than it needs to be, but it is relatively easy to read. The important lines are the ones that define the main effects for the two variables, the interaction of the variables, and the error term. The main effects and interaction are labeled by the variable names, and the error term is labeled "error." The "corrected model," "intercept," and "corrected total" lines can be ignored. 

Note that both main effects are significant, as is the interaction. Remember, that when you have both significant main effects and significant interactions, you should always interpret the main effects in terms of the interactions. The effect size for each of the tests is listed in the column labeled "Partial Eta Squared," and the power for each of the three effects is listed in the last column. See Chapter 12 for more discussion of the interpretation of these results.

Other Factorial Designs

We just walked you through a two-way ANOVA, in which both factors were between-subjects factors. If you had a more complex between-subjects factorial (i.e., all factors between-subjects factors), you would set it up in the same way as shown above, except that you would move all of your independent variables to the fixed factors box. 

Factorial designs can also be repeated-measures factorials, in which all factors are within-subjects factors, or mixed designs, in which some factors are between-subjects factors and other factors are within-subjects factors. Repeated measures factorials and mixed factorials ARE NOT analyzed in the same manner as the between-subjects factorial illustrated in this unit. Unfortunately, the version of SPSS for Windows Student Edition will not handle these more advanced designs, although more sophisticated versions of SPSS for Windows will analyze all types of factorial designs. If you have to analyze a more complex factorial design, we recommend that you find out what statistical analysis software is available for you use at your university. Almost certainly, software to conduct the analysis of a complex factorial design is available there for you use.

Animations

We have prepared a series of animations that will walk you through these procedure. To run an animation, simply click on the title of the animation in the table below. 

Note that we do not recommend that you try to run the animations if you have a slow connection, such as a dial-up connection. You will find that the animations take forever to load with a slow connection.

Checking on the Variable Characteristics
Running a Basic Factorial Analysis