Hotelling’s T-square statistical analysis is an extension of the Student’s t-test to the multivariate domain. We show how to perform analyses with one sample, two independent samples, and paired samples.
Topics
- One sample hypothesis testing of the mean
- Paired sample hypothesis testing of the means
- Two sample hypothesis testing of the means with independent samples
- Two sample hypothesis testing of means with unequal covariance matrices
- Real Statistics capabilities
- Statistical power and sample size requirements
References
Penn State University (2013) Inferences regarding multivariate population mean. STAT 505: Applied multivariate statistical analysis (course notes)
https://online.stat.psu.edu/stat505/lesson/7
Rencher, A.C. (2002) Methods of multivariate analysis (2nd Ed). Wiley-Interscience, New York.
https://www.ipen.br/biblioteca/slr/cel/0241
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.
Dear Dr. Charles,
please, could you provide some key literature references on multivariate analysis and Hotelling’s T-Square statistical analysis that I might cite in my articles (in addition to your website, of course)?
Thank you very much
Best Regards
Piero
Piero,
There are a lot of books on multivariate statistical analysis that you can cite.
You can also cite Penn State’s excellent course notes at
https://online.stat.psu.edu/stat505/lesson/7
Charles
Charles,
is it correct to say that Hotelling’s T-square and ANOVA (MANOVA) are different representation of the same analysis
Hotelling’s T-square test plays the same role as the t test when there is more than one dependent variable. It is a special case of MANOVA, but not of ANOVA.
Charles
Good day sir
please sir, i want to know the importance or the justifications of hotelling’s t-square distribution
Hello,
It is like the t test except that now you can have multiple dependent variables. It takes the correlation between these variables into account.
See https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/one-sample-hotellings-t-square/
Charles
Hello,
Can the Hotelling T-square test be used to compare the dissolution profiles of two drugs. Sampling was done at 8 different time points.
Thanks.
Hanan,
Sorry, but I don’t know enough about the dissolution profiles of drugs to answer your question. If you can translate your question into one about statistics I may be able to answer your question. If you are trying to determine whether there is a significant difference in something measurable over 8 different time periods then perhaps you could use ANOVA with repeated measures (or alternatively some form of MANOVA).
Charles
hello Ihave two dependeds animalls with three variables(sex,weight and tall) can i used manova please reply
thanks
Mahmood,
MANOVA can be used when you have two dependent variables and three independent variables. Whether it is applicable in your situation depends on the details.
Charles
Dr.
This is nice stuff. I enjoyed during my statistics course.
nice