What is MANOVA and how can you use it in SPSS?

1 MANOVA Basics

MANOVA is an extension of ANOVA, or analysis of variance, which compares the means of one or more groups on a single dependent variable. MANOVA, on the other hand, can handle multiple dependent variables at once, and examine how they vary together across groups. For example, if you want to compare the academic performance of students from different majors on math, science, and language tests, you can use MANOVA to see if there are any significant differences among the majors on all three tests simultaneously, and how the test scores are related to each other.

3 MANOVA Procedure

To perform a MANOVA in SPSS, you will need to open your data file and navigate to Analyze > General Linear Model > Multivariate. Here, you should select the dependent variables you want to include in the analysis and move them to the Dependent Variables box. Additionally, select the independent variable that defines the groups and move it to the Fixed Factor(s) box. If there are any covariates, or variables that might affect the dependent variables but are not of interest, move them to the Covariate(s) box. Then, click on Options and check the boxes for Descriptive statistics, Effect size, and Homogeneity tests. You may also choose other options depending on your research question and hypothesis. Finally, click on Continue and then on OK to run the analysis.

4 MANOVA Output

Once you run the analysis, SPSS will generate several tables in the output window. The most crucial of these are the Descriptive Statistics table, which displays the mean, standard deviation, and sample size of each dependent variable for each group; the Box's Test of Equality of Covariance Matrices table that tests if the variances of the dependent variables are equal across groups; the Multivariate Tests table that displays the results of the MANOVA for the main effect of the independent variable and any interaction effect with the covariates; and the Between-Subjects Effects table that shows the results of ANOVA for each dependent variable separately. Additionally, you should look at the Parameter Estimates table to see how covariates affect dependent variables and how they vary across groups. All in all, these tables can help you identify if an effect is significant at your chosen alpha level (usually 0.05) and allow you to use post-hoc tests (such as Tukey's HSD) to compare means pairwise.

5 MANOVA Interpretation

Interpreting the results of a MANOVA requires answering several questions, such as whether there is a significant difference among the groups on the combination of dependent variables, which dependent variables contribute to the difference, and which groups differ from each other and on which dependent variables. For example, if a MANOVA was conducted to compare the math, science, and language test scores of students from three majors - engineering, humanities, and social sciences - and it was found that the MANOVA was significant using the Wilks' Lambda criterion with a p-value of 0.001, it can be concluded that there is a significant difference among the majors on the combination of test scores. Furthermore, looking at the Between-Subjects Effects table showed that all three test scores were significant with p-values of 0.000, 0.002, and 0.004 respectively. Additionally, running a post-hoc test revealed that engineering students scored higher than humanities and social sciences students on math and science tests but lower than humanities students on language test; humanities students scored higher than social sciences students on language test but lower than them on math and science tests; and social sciences students scored lower than engineering and humanities students on language test but higher than humanities students on math and science tests. In summary, the MANOVA showed that the majors had a significant effect on the math, science, and language test scores of the students with engineering students excelling in math and science but struggling in language; humanities students performing well in language but poorly in math and science; and social sciences students having a balanced performance across the three tests.

6 Here’s what else to consider

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