Example
Example 1: A study was conducted to see the impact of social-economic class (rich, middle, poor) and gender (male, female) on kindness and optimism using a sample of 24 people based on the data in Figure 1.
Figure 1 – Two Factor MANOVA data
Data Analysis Tool
Real Statistics Data Analysis Tool: We conduct the analysis for Example 1 by pressing Ctrl-m and selecting MANOVA: Two factors from the Multivar tab. Next fill in the dialog box that appears as shown in Figure 2.
Figure 2 – Two Factor MANOVA dialog box
The output is as shown in Figures 3, 4, and 5.
Figure 3 – Main MANOVA output
We see from Figure 3 that the interaction between the two factors is significant (although the tests on the individual factors are not significant).
The various SSCP and covariance matrices are shown in Figure 4.
Figure 4 – SSCP and Covariance matrices
The Mahalanobis test for outliers is shown on the left side of Figure 5. Only the first 10 data elements are shown, although the full test shows that none of the data vectors is an outlier.
Figure 5 – Mahalanobis and Box tests
The Box test on the right side of Figure 5 shows that the assumption of equal covariance matrices holds.
See Two-way MANOVA Functions for information about how the values in Figures 3, 4, and 5 are calculated.
References
Penn State University (2022) Two-way MANOVA additive model and assumptions. Applied Multivariate Statistical Analysis
https://online.stat.psu.edu/stat505/lesson/8/8.10
Penn State University (2022) Forming a MANOVA table. Applied Multivariate Statistical Analysis
https://online.stat.psu.edu/stat505/lesson/8/8.11
Anderson, C. J. (2017) MANOVA: Part 2. Profile Analysis and 2-way MANOVA
https://education.illinois.edu/docs/default-source/carolyn-anderson/edpsy584/lectures/manova_part2_beamer-online.pdf