# One-Way ANOVA in SPSS

T-tests are used to identify the mean difference between two groups.  But what do you do if you want to compare the mean difference of more than two groups?  Well, as you’ve probably guessed, you can perform an ANOVA.  Because ANOVA is a commonly-used statistical tool, I created the page below to provide a step-by-step guide to calculating an ANOVA in SPSS.  This page is for a one-way ANOVA, which is when you have a single grouping variable and a continuous outcome.  As always, if you have any questions, please email me a MHoward@SouthAlabama.edu!

As mentioned, an ANOVA is used to identify the mean difference between more than two groups, and a one-way ANOVA is used to identify the mean difference between more than two groups when you have a single grouping variable and a continuous outcome.  So, a one-way ANOVA is used to answer questions that are similar to the following:

• What is the mean difference of test grades between Dr. Howard’s class, Dr. Smith’s class, and Dr. Kim’s class?
• What is the mean difference in total output of five different factories?
• What is the mean difference in performance of four different training groups?

Now that we know what an one-way ANOVA is used for, we can now calculate an one-way ANOVA in SPSS.  To begin, open your data in SPSS.  If you don’t have a dataset, download the example dataset here. In the example dataset, we are simply comparing the means of three different groups on a single continuous outcome. You can imagine that the groups and the outcome are anything that you want. If you data doesn’t look like this, you should probably reformat it to appear similarly. Calculating an ANOVA in SPSS may be a little difficult with different data formats.

Like most analyses in SPSS, we are going to start by clicking the Analyze tab at the top, then Compare Means, and then One-Way ANOVA. If it worked, the following window should have appeared.  You’ll first want to put your outcome in the Dependent List.  So, click on Outcome, and then click on the highlighted arrow. Now, we want to put our grouping variable as the Factor.  So, click on Groups, and then click on the button highlighted below: Next, you’ll want to click on the Post Hoc button. You’ll have a lot of options here.  You can choose whichever post hoc tests that you want, but I prefer to select LSD, Bonferroni, and Tukey.  So, let’s click on the checkboxes for those three tests. Once we have our post hoc tests selected, click on Continue. Click on OK. We should get results.  Nice!

First, we should look at the effect size, which is the F-value. This is 117.391. When reporting our results, we would probably include this value, but it is difficult to interpret by itself… …For this reason, we’ll also want to look at the p-value. In this example, it is extremely small (p < .0001), which indicates that our result is statistically significant. In the context of ANOVA, this means that there is a significant difference among the means of our groups. We would report this p-value as well as our interpretation of the result. While we know that there is a significant difference among the groups, our F-value or p-value does not tell us the nature of these differences – only that some difference exists.

The best method to understand the nature of these differences would be to look at our post hoc tests. As seen from our results, below, each of the group comparisons were statistically significant (p < .001).  So, there was a significant difference between Group 1 and Group 2, Group 1 and Group 3, as well as Group 2 and Group 3.  So, in other words, each of the groups were significantly different from the others. That’s all for performing an ANOVA in Excel.  As always, if you have any questions or comments, please email me at MHoward@SouthAlabama.edu.