The one-way multivariate analysis of variance (one-way MANOVA) is used to determine whether there are any differences between independent groups on more than one continuous dependent variable. In this regard, it differs from a one-way ANOVA, which only measures one dependent variable.
For example, you could use a one-way MANOVA to understand whether there were differences in the perceptions of attractiveness and intelligence of drug users in movies (i.e., the two dependent variables are "perceptions of attractiveness" and "perceptions of intelligence", whilst the independent variable is "drug users in movies", which has three independent groups: "non-user", "experimenter" and "regular user"). Alternatively, you could use a one-way MANOVA to understand whether there were differences in students' short-term and long-term recall of facts based on three different lengths of lecture (i.e., the two dependent variables are "short-term memory recall" and "long-term memory recall", whilst the independent variable is "lecture duration", which has four independent groups: "30 minutes", "60 minutes", "90 minutes" and "120 minutes").
Note: If you have two independent variables rather than one, you can run a two-way MANOVA instead. Alternatively, if you have one independent variable and a continuous covariate, you can run a one-way MANCOVA. In addition, if your independent variable consists of repeated measures, you can use the one-way repeated measures MANOVA.
It is important to realise that the one-way MANOVA is an omnibus test statistic and cannot tell you which specific groups were significantly different from each other; it only tells you that at least two groups were different. Since you may have three, four, five or more groups in your study design, determining which of these groups differ from each other is important. You can do this using a post-hoc test (N.B., we discuss post-hoc tests later in this guide).
In this "quick start" guide, we show you how to carry out a one-way MANOVA using SPSS Statistics, as well as interpret and report the results from this test. Since the one-way MANOVA is often followed up with post-hoc tests, we also show you how to carry these out using SPSS Statistics. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for a one-way MANOVA to give you a valid result. We discuss these assumptions next.
When you choose to analyse your data using a one-way MANOVA, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a one-way MANOVA. You need to do this because it is only appropriate to use a one-way MANOVA if your data "passes" nine assumptions that are required for a one-way MANOVA to give you a valid result. Do not be surprised if, when analysing your own data using SPSS Statistics, one or more of these assumptions is violated (i.e., is not met). This is not uncommon when working with real-world data. However, even when your data fails certain assumptions, there is often a solution to overcome this.
In practice, checking for these nine assumptions adds some more time to your analysis, requiring you to work through additional procedures in SPSS Statistics when performing your analysis, as well as thinking a little bit more about your data. These nine assumptions are presented below:
You can check assumptions #5, #6, #7, #8 and #9 using SPSS Statistics. Before doing this, you should make sure that your data meets assumptions #1, #2, #3 and #4, although you don't need SPSS Statistics to do this. Just remember that if you do not run the statistical tests on these assumptions correctly, the results you get when running a one-way MANOVA might not be valid. This is why we dedicate a number of sections of our enhanced one-way MANOVA guide to help you get this right. You can find out about our enhanced content as a whole here, or more specifically, learn how we help with testing assumptions here.
In the section, Procedure, we illustrate the SPSS Statistics procedure to perform a one-way MANOVA assuming that no assumptions have been violated. First, we set out the example we use to explain the one-way MANOVA procedure in SPSS Statistics.
The pupils at a high school come from three different primary schools. The headteacher wanted to know whether there were academic differences between the pupils from the three different primary schools. As such, she randomly selected 20 pupils from School A, 20 pupils from School B and 20 pupils from School C, and measured their academic performance as assessed by the marks they received for their end-of-year English and Maths exams. Therefore, the two dependent variables were "English score" and "Maths score", whilst the independent variable was "School", which consisted of three categories: "School A", "School B" and "School C".
In SPSS Statistics, we separated the groups for analysis by creating a grouping variable called School (i.e., the independent variable), and gave the three categories of the independent variable the labels "School A", "School B" and "School C". The two dependent variables were labelled English_Score and Maths_Score, respectively. We would also recommend that you create a fourth variable, subject_id, to act as a case number. This latter variable is required to test whether there are any multivariate outliers (i.e., part of Assumption #5 above). We do not include it in the test procedure in the next section because we do not show you how to test for the assumptions of the one-way MANOVA in this "quick start" guide. However, in our enhanced one-way MANOVA guide, we show you how to correctly enter data in SPSS Statistics to run a one-way MANOVA when you are also checking for assumptions. You can learn about our enhanced data setup content here. Alternately, we have a generic, "quick start" guide to show you how to enter data into SPSS Statistics, available here.
The 14 steps below show you how to analyse your data using a one-way MANOVA in SPSS Statistics when the nine assumptions in the previous section, Assumptions, have not been violated. At the end of these 14 steps, we show you how to interpret the results from this test.
Click Analyze > General Linear Model > Multivariate... on the top menu as shown below:
Published with written permission from SPSS Statistics, IBM Corporation.
You will be presented with the Multivariate dialogue box:
Published with written permission from SPSS Statistics, IBM Corporation.
Transfer the independent variable, School, into the Fixed Factor(s): box and transfer the dependent variables, English_Score and Maths_Score, into the Dependent Variables: box. You can do this by drag-and-dropping the variables into their respective boxes or by using the button. For older versions of SPSS Statistics, you will need to use the latter method. The result is shown below:
Published with written permission from SPSS Statistics, IBM Corporation.
Note: For this analysis, you will not need to use the Covariate(s): box (used for MANCOVA) or the WLS Weight: box.
Click on the button. You will be presented with the Multivariate: Profile Plots dialogue box:
Published with written permission from SPSS Statistics, IBM Corporation.
Transfer the independent variable, School, into the Horizontal Axis: box, as shown below:
Published with written permission from SPSS Statistics, IBM Corporation.
Click the button. You will see that "School" has been added to the Plots: box, as shown below:
Published with written permission from SPSS Statistics, IBM Corporation.
Click the button. This will return you to the Multivariate dialogue box.
Click the button. You will be presented with the Multivariate: Post Hoc Multiple Comparisons for Observed... dialogue box, as shown below:
Published with written permission from SPSS Statistics, IBM Corporation.
Transfer the independent variable, School, into the Post Hoc Tests for: box and select the Tukey checkbox in the -Equal Variances Assumed- area, as shown below:
Published with written permission from SPSS Statistics, IBM Corporation.
Note: You can select other post-hoc tests depending on your data and study design. If your independent variable only has two levels/categories, you do not need to complete this post-hoc section.
Click the button. This will return you to the Multivariate dialogue box.
Click the button. This will present you with the Multivariate: Options dialogue box, as shown below:
Published with written permission from SPSS Statistics, IBM Corporation.
Transfer the independent variable, "School", from the Factor(s) and Factor Interactions: box into the Display Means for: box. Select the Descriptive statistics, Estimates of effect size and Observed power checkboxes in the -Display- area. You will be presented with the following screen:
Published with written permission from SPSS Statistics, IBM Corporation.
Go to the next page for the SPSS Statistics output and explanation of the output.