SPSS Tutorial

One-Way Analysis of Variance (ANOVA)

A one-way analysis of variance (ANOVA) is used to test the difference between two or more means when there is one factor of interest. SPSS can perform the calculations for this as well as some of the post hoc test needed if it is found that there is a statistically significant difference. The example from the Visual Learner media piece on one-way ANOVA will be used to illustrate this.

A professor at a local University believes there is a relationship between head size and the major of the students in her biostatistics classes. She takes a random sample of 20 students from each of three classes and records their major and head circumference. The data are shown in the following table.

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The data entry into SPSS is not straight from the table. You will need to classify the data into two variables, major and head circumference. The head circumferences can be entered in directly but each major will need to be given a numerical value as follows:

1: Pre Med2: Pre PT3: Nursing4: Health Care Admin

02

Once the data is entered, the analysis can begin by click-ing on Analyze – Compare Means – One-Way ANOVA…

When the One-Way ANOVA box opens, move the Head Circumference to the Dependent List and Major to the Factor.

Now you are ready to select the Post Hoc test, which allows you to determine which factors have significantly different means when a difference has been detected with the ANOVA test. Click on the Post Hoc button to see the options. There are several options available, one common choice is Tukey, put a check mark by Tukey and click Continue and then OK.

03

The output window will have three different output boxes of information to be interpreted.

The first box is the ANOVA table which displays the results of the one-way ANOVA test. The first column tells the source of variation, the second is the sums of squares, followed by the degrees of freedom, mean squares, test statistics, and finally the p-value.

The second box shows the results of the post hoc test you selected. This box will be different depending on which test you are using. One important column to identify is the p-value, which is labeled as Sig. in SPSS.

The last output box is additional information for the post hoc test.

With these results, you can conclude there is not sufficient evidence to indicate a statistically significant difference between the mean head size of different majors in the biostatistics classes of this professor at a level of significance of 0.05.

Since the one-way ANOVA test did not show significance, then the post hoc test was not needed here but it is important to understand how to get those results when they are needed.

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Means for groups in homogeneous subsets are displayed.a. Uses Harmonic Mean Sample Size = 15.992.b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.