We extend the univariate normal distribution (as described in Normal Distribution) to the multivariate domain.
Topics
- Basic Concepts
- Real Statistics Support for Multivariate Normal Distributions
- Confidence Hyper-ellipse and Eigenvalues
- Confidence Ellipse
- Real Statistics Confidence Ellipse Analysis Tool
- More Properties
- Multivariate Central Limit Theorem
- Generating Random Vectors
- Friedman-Rafsky Test (Runs test for multivariate samples)
- Testing for Multivariate Normality (Mardia)
- Testing for Multivariate Normality (FRSJ)
References
Penn State University (2013) Multivariate normal distribution. STAT 505: Applied multivariate statistical analysis (course notes)
https://online.stat.psu.edu/stat505/lesson/4
Rencher, A.C. (2002) Methods of multivariate analysis (2nd Ed). Wiley-Interscience, New York.
http://ndl.ethernet.edu.et/bitstream/123456789/27185/1/Alvin%20C.%20Rencher_2012.pdf
Johnson, R. A. and Wichern, D. W. (2007) Applied multivariate statistical analysis. 6th Ed. Pearson.
https://www.webpages.uidaho.edu/~stevel/519/Applied%20Multivariate%20Statistical%20Analysis%20by%20Johnson%20and%20Wichern.pdf
Pituch, K. A. and Stevens, J. P. (2016) Applied multivariate statistical analysis for the social sciences. Routledge.
Estimado Dr. excuseme, si la matriz de datos no tienen distribución normal multivariante, podemos utilizar la caja de Cox Transformación?
Y si esta transformación no tienen distribución normal multivariante, ¿cómo podría ser el trabajo con estos datos ?.
Dear Dr. excuseme, if data matrix do not have Multivariate Distribution Normal, we can use Box Cox Transformation?
And if this transformation do not have Multivariate Distribution Normal, how could be work with this data?.
Gerardo,
The Box-Cox transformation can be used to transform one sample at a time (univariate normality). This doesn’t guarantee that the combined sample will be multivariate normal, but it might be. See Box-Cox Transformation.
You can use Mardia’s test to check for multivariate normality. See the webèpage https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normality-testing/
Most multivariate tests are quite robust for violations of multivariate normality, and so it is likely that the test will work even if the data is not multivariate normal. I would think that if univariate normality is achieved you are probably ok (although there is no guarantee).
Charles
Thank you, Sir
If I am running bivariate parametric tests do both the interpendent and dependent variable need to be normally distributed or just the dependent variable?
Lola,
Which test are you running?
Charles
Chi-square, Kruskals Tau.
Possibly t-test/anova
Correlations
Lola,
For these types of tests, you are checking the normality of the dependent variables. The independent variables are categorical (and so won’t be normal). I suggest that you look at the assumptions for each test separately.
Charles
Charles,
Thank you for your work. It is a great help in my research work.
You have the talent to build a bridge between professional statistician and common users.
Have you ever considered publishing your work in a printed book? I would be happy to see that on my shelf.
Tom
Tamas,
Thank you for your kind remarks. I try my best to make statistics accessible to everyone.
I am planning to release an ebook shortly.
Charles
Charles,
Can you show us how to solve A generalization of Shapiro-Wilk for Multivariate Normality.. I recently conducting this study for my undergraduate thesis. my adviser wants me to solve this manually using excel. hope you can help me this one.
Thank you.
Romil,
I haven’t implemented a test for multivariate normality yet.
In any case, here is a paper that describes the state of the art today.
https://www.stat.ubc.ca/~matias/mvn-scs5.pdf
I was planning on implementing the the approaches described in references [10] and [19].
Charles