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Two-Way Between Subjects ANOVA


If you have two independent variables and both are between subject variables, then this is the statistical routine that you need.

To illustrate the procedures involved in this type of experiment, let's imagine that six groups of male students in a business administration program were presented with one of six descriptions of a 28-year-old mid-level manager containing both personal and job relevant information. The students were told that next year, salary increases for persons at this level would be 5 to 15 percent, with an average of 10 percent. They were asked to recommend a raise for the manager. In three descriptions the manager was a man and in the other three the manager was a women. Within each sex, one version described the person as single, in another the person was married but childless, and in the third they were married with two children. The score obtained for each participant was the percent raise recommended by the student.

Begin by creating three variables, one for the variable gender (will have values 1 for male or 2 for female), one for the variable status (will have three values 1 single; 2 married but childless; and 3 married with children), and one for the percent of raise given.  You can get a idea of how the data would be entered by looking at the SPSS spread sheet below.  Each row in the sheet represents the data for one participant.  The initial group is the data from all the male subjects (gender = 1) who got a report where the manager was single (status = 1) followed by those male (gender = 1) particpants who are married but childless (status = 2).  The remaining data would be entered in the same fashion. 

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To begin the anlaysis:

    Select Analyze/General Linear Model/GLM-General Factorial to see the following window:

   Highlight each independent variable in the window on the left and click the arrow button beside the "Fixed Factor(s)" window. Then highlight the dependent variable in the left window and click the arrow beside the "Dependent Variable" window.

    Select Post Hoc from the GLM-General Factorial window and highlight each variable in the left window that you would like to do a post hoc analysis and then click the arrow beside "Post Hoc Test for" (status). Then select Tukey which is the type of post hoc test you would like to conduct. When you have completed making your selections, press Continue.

    Select Options from the GLM-General Factorial window. Highlight each variable and interaction in the left window and move to the right window by clicking on the arrow button Select the following options to obtain descriptive statistics, effect size, homogeneity of variance, and select Continue.

Select Plots from the GLM-General Factorial window. To obtain a line graph of the interaction, highlight gender and click the arrow beside "Separate Lines" and highlight status and click the arrow beside "Horizontal Axis" then press Add. Press Continue in order to return to the GLM-General Factorial window.

    The completed GLM-General Factorial window should look like the following window. If it does, click OK to run the requested analyses.

As with other procedures, the output is quite extensive. The left window shows the outputs that we requested.

The first window, "Between-Subjects Factors" shows the coding for each categorical variable and the corresponding values label and well as the n.

The next section contains the descriptive statistics for each condition.

The homogeneity of variance test is next. (In this example, the variances are not equal.)

The next output is the ANOVA summary table. In addition to the usual ANOVA information, this table also includes Eta Squared as the measure of effect size.

The estimated marginal means are in the next section. This contains the mean, standard error, and confidence interval for each factor and the interaction (the interaction is not shown below but will be visible on the output).

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The next section contains the post hoc test and it is followed by the homogeneous subsets.

The last section consists of a graph of the interaction to help you interpret it. Remember that this is not how to formally graph an interaction.

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