One-Way Between Subjects ANOVA

In situations where there are more than two groups, Analysis of Variance rather than the t test is the statistic of choice.  The following experiment involves the use of different participants in each experiment condition or group, hence it is a between subjects design.   Expeirments in which more than one measure is taken from participants are called within subjects designs and are described in another section.

A social psychologist interested in self-fulfilling prophecies conducted an experiment in which college students were asked to interview a female student in her Freshman year on the general topic of how she was adjusting to college life. (In each pair, the persons were in a different room and communicated by telephone). One third of the students were told that a previously administered personality test indicated that the young woman they would interview was a quite anxious and depressed person. One third were told that the test indicated that she was happy and self-confident. The remaining third of the students were given no information. (In actuality, all the women scored in the middle range on the personality test). After the experiment, raters who were blind to the experimental conditions listened to tape recordings of the women's responses and made a judgement about how confident and well adjusted each woman was. On the rating scale low scores indicated better adjustment. The investigator hypothesized that the interviewer's expectations about the women they interviewed would influence how they interviewed her in a way that would produce the kind of behavior they expected.

The data for this experiment are as follows:

Control Group             Happy Group             Depressed Group

    8.18                                 4.81                             13.22
    7.37                                 6.39                             11.71
    7.80                                 6.27                             16.32
    6.51                                 8.08                             15.30
    9.63                                 2.18                             17.19
 

To enter the data, begin by launching SPSS. Although the data set is small, it is a good idea to keep track of each individual (or as SPSS calls them, cases) with an ID. So the person who rated the confidence as 8.18 would be ID 1 while the person who rated the confidence 7.37 would be ID 2.

The data for a one-way between subjects ANOVA is entered much the same as that for the between-subjects t test. That is, a column indicates the group (in this case 1, 2, or 3) and one column contains the dependent variable. And, of course, we are going to add a third column with the ID number.

Create three variables with the following specifications:

    - first variable:
        - Variable Name: id
        - Type: Numeric 2.0
        - Variable Label: ID #

    - second variable:
        - Variable Name: group
        - Type: Numeric1.0
        - Variable Label: Experimental Groups
        - Value Labels:
            - 1 Control
            - 2 Happy
            - 3 Depressed

To add Value Labels enter a Value (1, for example) then the Value Label (Control) and press the Add button. Repeat for the other values. When you are finished with the second variable, the Define Labels panel should look like this.

    - third variable:
         - Variable Name: rating
        - Type: Numeric8.2 (default)
        - Variable Label: Rating Scale

Now enter the data. Your Data Editor should look like this. Notice that the columns have been widened to allow the variable labels to be read.

Once all of the data has been entered, double check to make sure that it has been entered correctly.

To begin the analysis, select Analyze/Compare Means/One-Way ANOVA from the main menu The first panel you see will look like this.

We need to indicate which variable is the independent variable (called Factor here) and which variable is the dependent variable. In our example group is the independent variable and rating is the dependent. Select those variables and use the arrow keys to move them to the appropriate boxes. Your screen should now look like this.

Notice that the column for ID Number is not included in the analysis. It is used to identify the data only.

Before we do the computations we need to specify some details for the analysis.

First click Options to get this panel:

We want to specify Descriptive Statistics and Homogeneity of Variance.

Press Continue to return to the One-Way ANOVA panel. Our final set of parameters is revealed when you click PostHoc (see below). On this panel select the Tukey option to produce the Tukey HSD statistic. Again, press Continue to return to the main panel. Now press OK on the One-Way ANOVA panel to do the analysis.

The results of this analysis are quite extensive. Let’s look at them one part at a time.

The first section of output provides us with the descriptive statistics for each group as well as confidence intervals.

The third output is the ANOVA summary table.

Recall that we selected to have the Tukey HSD results calculated. Examine the output carefully. All possible combinations are means are compared. For example, The Control group is compared with the Happy group, and then the Control group is compared with the Depressed group. In each case a mean difference, a standard error and a significance level is provided. If the difference is significant (alpha = .05) then that difference is stared. Although this output includes enough for us to make a conclusion about the results, a second set of output is provided to help us understand what is happening with the data.

The Homogeneous Subsets attempts to combine non-significant groups together. If you look carefully at the results from the Post Hoc Tests results you can see that Happy and Control are not different from each other but each is different from Depressed. It is this summary of results that are presented in the Homogeneous Subsets table.

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