Join with a free account for more service, or become a member for full access to exclusives and extra support of WorldSupporter >>
Week 5: MANOVA and Descriptive DA
The goal of MANOVA and of Descriptive DA is the optimal prediction of differences between group means on several interval variables.
Why? Often very natural to compare groups on more than one variable, for example:
• quality and quantity of task performance;
• different stress reaction (e.g. emotions, physiological measures).
Compared to ANOVA:
ANOVA: one dependent variable -->(univariate)
MANOVA: two or more dependent variables -->(multivariate)
Check the assumption of equality of the covariance matrices and discuss robustness ofthe MANOVA against violations of the assumption of multivariate normality.
To check for the equality of covariance matrices, in the table: Test of Equality of Covariance Matrices, look at Box’s M. If higher than 0.05 then not significant.
To check for robustness of non-normality: number of participants per group has to be ≥20:
The design is balanced when robust to unequal covariance matrices.
Consider the mean values in the descriptive statistics. Which groups differ a lot on characteristic x (e.g. physical complaints)? Which groups differ only a little?
Look at descriptive statistics table and the appropriate box, in this case: physical complaints. Compare the values under Mean.
Given your crude assessment in the previous question, is it plausible to expect a multivariate effect?
If there are differences under sample group means, then yes, a multivariate effect is expected.
Example: Is there a significant effect of occupation on physical complaints, experience of hostility, and/or dissatisfaction?
We look at the multivariate tests table, in the Occupation box. Then, we report F statistic, df, and p value. If the tests are higher than p≤.05, there is a significant effect.
For which variables is the univariate effect significant?
We look at the Tests of Between-Subjects Effects table. Then, you report the tests were the p<0.05.
What is the answer to the previous question be if we apply a Bonferroni correction for multiple testing?
For Bonferroni, we divide the Alpha by number of categories (dependent variables). For example, if there are three categories (e.g.: hostility, physical complaint, dissatisfaction). The alpha then becomes smaller and we have to check if the p values are still smaller. Often, they aren’t or only few remain significant. Example:
Before Bonferroni:
Physical complaints F(2,177) = 3.196,p=.043 -->significant
Hostility F(2,177) = 3.405,p=.035 ---> significant
Dissatisfaction F(2,177) = 4.511,p=.013 --> significant
After Bonferroni, Withα=.05/3 =.0167:
Only Dissatisfaction F(2,177) = 4.511,p=.013 -->significant.
Interpret the significant effect(s) (after Bonferroni correction) using the table with multiple comparisons. Why is the Tukey HSD correction applied?
The Tukey test is invoked when you need to determine if the interaction among three or more variables is mutually statistically significant. We look at the multiple comparisons table with Tukey HSD applied and look at the category with significant effect. Example:
Dissatisfaction: catering different from management, (Mdif f= 2.767,p=.009)
What is theoretically the maximum number of discriminant functions?
imax= min(k−1,p) = min(2,3) = 2
How many discriminant functions are significant?
We look at the Wilk’s Lamda box. Then, under chi square. We count how many p scores are below 0.05, and that’s the number of significant discriminant functions. Report wilk’s lamda and p value.
Use the Structure matrix to interpret the significant functions.
Example: All variables high correlations with F1→general (workplace stress) function
Which group has the highest mean value on the first discriminant function?
We look at the table Functions at Group Centroids. Then, under F1 look for the highest number to get the mean value score.
How good is the overall classification? For which group does the classification work best?
Under the classification table it says: x%( e.g.: 40.6 %) of original grouped cases correctly classified. Within the classification table, check which group whichever number is highest belongs to, and that’s the group where the classification works best.
Multivariate data analysis (MVDA) bundle
Bunndle for the course Multivariate Data Analysis (2019)
- Lees verder over Multivariate data analysis (MVDA) bundle
- 1929 keer gelezen
JoHo can really use your help! Check out the various student jobs here that match your studies, improve your competencies, strengthen your CV and contribute to a more tolerant world
Online access to all summaries, study notes en practice exams
- Check out: Register with JoHo WorldSupporter: starting page (EN)
- Check out: Aanmelden bij JoHo WorldSupporter - startpagina (NL)
How and why would you use WorldSupporter.org for your summaries and study assistance?
- For free use of many of the summaries and study aids provided or collected by your fellow students.
- For free use of many of the lecture and study group notes, exam questions and practice questions.
- For use of all exclusive summaries and study assistance for those who are member with JoHo WorldSupporter with online access
- For compiling your own materials and contributions with relevant study help
- For sharing and finding relevant and interesting summaries, documents, notes, blogs, tips, videos, discussions, activities, recipes, side jobs and more.
Using and finding summaries, study notes en practice exams on JoHo WorldSupporter
There are several ways to navigate the large amount of summaries, study notes en practice exams on JoHo WorldSupporter.
- Use the menu above every page to go to one of the main starting pages
- Starting pages: for some fields of study and some university curricula editors have created (start) magazines where customised selections of summaries are put together to smoothen navigation. When you have found a magazine of your likings, add that page to your favorites so you can easily go to that starting point directly from your profile during future visits. Below you will find some start magazines per field of study
- Use the topics and taxonomy terms
- The topics and taxonomy of the study and working fields gives you insight in the amount of summaries that are tagged by authors on specific subjects. This type of navigation can help find summaries that you could have missed when just using the search tools. Tags are organised per field of study and per study institution. Note: not all content is tagged thoroughly, so when this approach doesn't give the results you were looking for, please check the search tool as back up
- Check or follow your (study) organizations:
- by checking or using your study organizations you are likely to discover all relevant study materials.
- this option is only available trough partner organizations
- Check or follow authors or other WorldSupporters
- by following individual users, authors you are likely to discover more relevant study materials.
- Use the Search tools
- 'Quick & Easy'- not very elegant but the fastest way to find a specific summary of a book or study assistance with a specific course or subject.
- The search tool is also available at the bottom of most pages
Do you want to share your summaries with JoHo WorldSupporter and its visitors?
- Check out: Why and how to add a WorldSupporter contributions
- JoHo members: JoHo WorldSupporter members can share content directly and have access to all content: Join JoHo and become a JoHo member
- Non-members: When you are not a member you do not have full access, but if you want to share your own content with others you can fill out the contact form
Quicklinks to fields of study for summaries and study assistance
Field of study
- All studies for summaries, study assistance and working fields
- Communication & Media sciences
- Corporate & Organizational Sciences
- Cultural Studies & Humanities
- Economy & Economical sciences
- Education & Pedagogic Sciences
- Health & Medical Sciences
- IT & Exact sciences
- Law & Justice
- Nature & Environmental Sciences
- Psychology & Behavioral Sciences
- Public Administration & Social Sciences
- Science & Research
- Technical Sciences
Add new contribution