Lesson 7: Inferences Regarding Multivariate Population Mean

Overview Section

This lesson deals with inference for a multivariate population mean. Similar to a univariate population, inference problems may arise in three different scenarios:

  • Case I: Inference problems regarding a single multivariate population
  • Case II: Inference problems regarding two means from a paired population
  • Case III: Inference problems regarding two means from two independent populations

All three cases are dealt with briefly in this lesson. All three cases make use of Hotelling's T-square statistic.

This lesson plan is divided into two parts: Basic and Advanced. In the basic section, we will introduce standard methods for statistical inference on mean vectors. The advanced section will discuss topics such as adjusting for multiple comparisons, profile analysis, etc.


Upon completion of the lesson, you should be able to:

  • Carry out Hotelling's T-square test for testing a population mean vector that meets specifications;
  • Carry out Hotelling's T-square test for comparing two independent/paired population mean vectors;
  • Compute and interpret simultaneous and Bonferroni confidence intervals;
Note! The current version of Minitab does not support Hotelling's T-square procedures, except in a very limited setting.