Login

One-way MANOVA in SPSS Statistics

Introduction

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 realize 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.

SPSS Statistics

Assumptions

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 on our Features: Overview page, or more specifically, learn how we help with testing assumptions on our Features: Assumptions page.

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.

Testimonials
TAKE THE TOUR


SPSS Statistics

Example

The pupils at a high school come from three different primary schools. The head teacher 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".

SPSS Statistics

Setup in SPSS Statistics

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 on our Features: Data Setup. Alternately, see our generic, "quick start" guide: Entering Data in SPSS Statistics.

SPSS Statistics

Test Procedure in SPSS Statistics

The General Linear Model > Multivariate... procedure 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.

Since some of the options in the General Linear Model > Multivariate... procedure changed in SPSS Statistics version 25, we show how to carry out a one-way MANOVA in SPSS Statistics version 25 and above (which includes the subscription version of SPSS Statistics) and version 24 and earlier. At the end of these steps, we show you how to interpret the results from this test.

Note: If you are unsure which version of SPSS Statistics you are using, see our guide: Identifying your version of SPSS Statistics.

SPSS Statistics version 25 and above
(which includes the subscription version of SPSS Statistics)
  1. Click Analyze > General Linear Model > Multivariate... on the top menu as shown below:
    Menu for the one-way MANOVA in SPSS Statistics

    Published with written permission from SPSS Statistics, IBM Corporation.


    You will be presented with the following Multivariate dialogue box:
    'Multivariate' dialogue box for the one-way MANOVA in SPSS. Variables 'School', 'English_Score' & 'Maths_Score' on the left

    Published with written permission from SPSS Statistics, IBM Corporation.

  2. 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 Right arrow button. For older versions of SPSS Statistics, you will need to use the latter method. The result is shown below:
    'Multivariate' dialogue box for the one-way MANOVA in SPSS. 'School', 'English_Score' & 'Maths_Score' transferred

    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.

  3. Click on the Plots button. You will be presented with the Multivariate: Profile Plots dialogue box:
    'Multivariate: Profile Plots' dialogue box for the one-way MANOVA in SPSS Statistics. 'School' in 'Factors' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  4. Transfer the independent variable, School, into the Horizontal Axis: box, as shown below:
    'Multivariate: Profile Plots' dialogue box for the one-way MANOVA in SPSS. 'School' transferred into 'Horizontal Axis' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  5. Click on the Add button. You will see that "School" has been added to the Plots: box, as shown below:
    'Multivariate: Profile Plots' dialogue box for the one-way MANOVA in SPSS. 'School' added to 'Plots' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  6. Click on the Continue button and you will be returned to the Multivariate dialogue box.
  7. Click on the Post hoc button. You will be presented with the Multivariate: Post Hoc Multiple Comparisons for Observed Means dialogue box, as shown below:
    'Multivariate: Post Hoc Multiple Comparisons for Observed' dialogue box. One-way MANOVA in SPSS. 'School' in 'Factor(s)' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  8. 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:
    'Multivariate: Post Hoc Multiple Comparisons for Observed' dialogue box in SPSS. 'School' transferred. 'Tukey' selected

    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.

  9. Click on the Continue button and you will be returned to the Multivariate dialogue box.
  10. Click on the EM Means button. You will be presented with the Multivariate: Estimated Marginal Means dialogue box, as shown below:
    'Multivariate: Estimated Marginal Means' dialogue box. One-way MANOVA SPSS. 'School' in 'Factor(s) & Factor Interactions' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  11. Transfer the independent variable, "School", from the Factor(s) and Factor Interactions: box into the Display Means for: box. You will be presented with the following screen:
    'Multivariate: Estimated Marginal Means' dialogue box for the one-way MANOVA in SPSS. 'School' transferred & options selected

    Published with written permission from SPSS Statistics, IBM Corporation.

  12. Click on the Continue button and you will be returned to the Multivariate dialogue box.
  13. Click on the Options button. You will be presented with the Multivariate: Options dialogue box, as shown below:
    'Multivariate: Options' dialogue box for the one-way MANOVA in SPSS. 'School' in 'Factor(s) and Factor Interactions' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  14. Select the Descriptive statistics and Estimates of effect size checkboxes in the –Display– area. You will be presented with the following screen:
    'Multivariate: Options' dialogue box for the one-way MANOVA in SPSS. 'School' transferred & options selected

    Published with written permission from SPSS Statistics, IBM Corporation.

  15. Click on the Continue button and you will be returned to the Multivariate dialogue box.
  16. Click on the OK button to generate the output.

Go to the next page for the SPSS Statistics output and explanation of the output. You can ignore the section below, which shows you how to carry out a one-way MANOVA if you have SPSS Statistics version 24 or earlier.

Join the 10,000s of students, academics and professionals who rely on Laerd Statistics.TAKE THE TOUR
SPSS Statistics version 24 and earlier
  1. Click Analyze > General Linear Model > Multivariate... on the top menu as shown below:
    Menu for the one-way MANOVA in SPSS Statistics

    Published with written permission from SPSS Statistics, IBM Corporation.


    You will be presented with the following Multivariate dialogue box:
    'Multivariate' dialogue box for the one-way MANOVA in SPSS. Variables 'School', 'English_Score' & 'Maths_Score' on the left

    Published with written permission from SPSS Statistics, IBM Corporation.

  2. 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 Right arrow button. For older versions of SPSS Statistics, you will need to use the latter method. The result is shown below:
    'Multivariate' dialogue box for the one-way MANOVA in SPSS. 'School', 'English_Score' & 'Maths_Score' transferred

    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.

  3. Click on the Plots button. You will be presented with the Multivariate: Profile Plots dialogue box:
    'Multivariate: Profile Plots' dialogue box for the one-way MANOVA in SPSS Statistics. 'School' in 'Factors' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  4. Transfer the independent variable, School, into the Horizontal Axis: box, as shown below:
    'Multivariate: Profile Plots' dialogue box for the one-way MANOVA in SPSS. 'School' transferred into 'Horizontal Axis' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  5. Click on the Add button. You will see that "School" has been added to the Plots: box, as shown below:
    'Multivariate: Profile Plots' dialogue box for the one-way MANOVA in SPSS. 'School' added to 'Plots' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  6. Click on the Continue button and you will be returned to the Multivariate dialogue box.
  7. Click on the Post hoc button. You will be presented with the Multivariate: Post Hoc Multiple Comparisons for Observed Means dialogue box, as shown below:
    'Multivariate: Post Hoc Multiple Comparisons for Observed' dialogue box. One-way MANOVA in SPSS. 'School' in 'Factor(s)' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  8. 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:
    'Multivariate: Post Hoc Multiple Comparisons for Observed' dialogue box in SPSS. 'School' transferred. 'Tukey' selected

    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.

  9. Click on the Continue button and you will be returned to the Multivariate dialogue box.
  10. Click on the Options button. You will be presented with the Multivariate: Options dialogue box, as shown below:
    'Multivariate: Options' dialogue box for the one-way MANOVA in SPSS. 'School' in 'Factor(s) and Factor Interactions' box

    Published with written permission from SPSS Statistics, IBM Corporation.

  11. Transfer the independent variable, "School", from the Factor(s) and Factor Interactions: box into the Display Means for: box. Select the Descriptive statistics and Estimates of effect size checkboxes in the –Display– area. You will be presented with the following screen:
    'Multivariate: Options' dialogue box for the one-way MANOVA in SPSS. 'School' transferred & options selected

    Published with written permission from SPSS Statistics, IBM Corporation.

  12. Click on the Continue button and you will returned to the Multivariate dialogue box.
  13. Click on the OK button to generate the output.

Go to the next page for the SPSS Statistics output and explanation of the output.

Join the 10,000s of students, academics and professionals who rely on Laerd Statistics.TAKE THE TOUR
next »