A Multivariate Hypothesis Testing Task is a hypothesis testing task that involves more than one outcome variable.

## References

### 2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/multivariate_analysis Retrieved:2014-11-13.
• Multivariate analysis (MVA) is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical outcome variable at a time. In design and analysis, the technique is used to perform trade studies across multiple dimensions while taking into account the effects of all variables on the responses of interest.

Uses for multivariate analysis include:

• Design for capability (also known as capability-based design)
• Inverse design, where any variable can be treated as an independent variable
• Analysis of Alternatives (AoA), the selection of concepts to fulfill a customer need
• Analysis of concepts with respect to changing scenarios
• Identification of critical design drivers and correlations across hierarchical levels.
• Multivariate analysis can be complicated by the desire to include physics-based analysis to calculate the effects of variables for a hierarchical "system-of-systems." Often, studies that wish to use multivariate analysis are stalled by the dimensionality of the problem. These concerns are often eased through the use of surrogate models, highly accurate approximations of the physics-based code. Since surrogate models take the form of an equation, they can be evaluated very quickly. This becomes an enabler for large-scale MVA studies: while a Monte Carlo simulation across the design space is difficult with physics-based codes, it becomes trivial when evaluating surrogate models, which often take the form of response surface equations.

### 2013

• http://en.wikipedia.org/wiki/Multivariate_statistics
• Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. The application of multivariate statistics is multivariate analysis.

Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical implementation of multivariate statistics to a particular problem may involve several types of univariate and multivariate analysis in order to understand the relationships between variables and their relevance to the actual problem being studied.

In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both: :*how these can be used to represent the distributions of observed data; :*how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis.

Certain types of problem involving multivariate data, for example simple linear regression and multiple regression, are NOT usually considered as special cases of multivariate statistics because the analysis is dealt with by considering the (univariate) conditional distribution of a single outcome variable given the other variables.