One-way ANOVA using SPSS

Objectives

The one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. This guide will provide a brief introduction to the one-way ANOVA including the assumptions of the test and when you should use interpret the output. This guide will then go through the procedure for running this test in SPSS using an appropriate example, which options to choose and how to interpret the output. Should you wish to learn more about this test before doing the procedure in SPSS, please click here.

What does this test do?

The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are significantly different from each other. Specifically, it tests the null hypothesis:

where µ = group mean and k = number of groups. If, however, the one-way ANOVA returns a significant result then we accept the alternative hypothesis (H_A), which is that there are at least 2 group means that are significantly different from each other.

At this point, it is important to realise that the one-way ANOVA is an omnibus test statistic and cannot tell you which specific groups were significantly different from each other, only that at least two groups were. To determine which specific groups differed from each other you need to use a post-hoc test. Post-hoc tests are described later in this guide.

Assumptions

Independent variable consists of two or more categorical independent groups.
Dependent variable is either interval or ratio (continuous) (see our guide on Types of Variable).
Dependent variable is approximately normally distributed for each category of the independent variable (see our guide on Testing for Normality).
Equality of variances between the independent groups (homogeneity of variances).
Independence of cases.

Example

A manager wants to raise the productivity at his company by increasing the speed at which his employees can use a particular spreadsheet program. As he does not have the skills in-house, he employs an external agency which provides training in this spreadsheet program. They offer 3 packages - a beginner, intermediate and advanced course. He is unsure which course is needed for the type of work they do at his company so he sends 10 employees on the beginner course, 10 on the intermediate and 10 on the advanced course. When they all return from the training he gives them a problem to solve using the spreadsheet program and times how long it takes them to complete the problem. He wishes to then compare the three courses (beginner, intermediate, advanced) to see if there are any differences in the average time it took to complete the problem.

Setup in SPSS

In SPSS we separated the groups for analysis by creating a grouping variable called "Course" and gave the beginners course a value of "1", the intermediate course a value of "2" and the advanced course a value of "3". Time to complete the set problem was entered under the variable name "Time". To know how to correctly enter your data into SPSS in order to run a repeated measures ANOVA please read our Entering Data in SPSS tutorial.

Testing assumptions

See how to test the normality assumption for this test in our Testing for Normality guide.

Test Procedure in SPSS

Click Analyze > Compare Means > One-Way ANOVA... on the top menu as shown below.

Published with written permission from SPSS Inc, an IBM Company.
You will be presented with the following screen:

Published with written permission from SPSS Inc, an IBM Company.
Drag-and-drop (or use the buttons) to transfer the dependent variable () into the Dependent List: box and the independent variable (Course) into the Factor: box as indicted in the diagram below:

Published with written permission from SPSS Inc, an IBM Company.
Click the button. Tick the "Tukey" checkbox as shown below:

Published with written permission from SPSS Inc, an IBM Company.

Click the button.
Click the button. Tick the "Descriptive", "Homogeneity of variance test", "Brown-Forsythe", and "Welch" checkboxes in the Statistics area as shown below:

Published with written permission from SPSS Inc, an IBM Company.

Click the button.
Click the button.