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## Inferential Statistics

Last Updated: Jan 10, 2022
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# Multivariate Analysis

It is used to study more complex sets of data than univariate analysis can handle. Multivariate analysis is almost always performed with software, as working with even the smallest of data sets could be overwhelming by hand.

The multivariate analysis could reduce the likelihood of Type I errors. Sometimes, the univariate analysis method is preferred as multivariate techniques can be challenging to interpret the test results. Additionally, multivariate analysis is usually not suitable for small sets of data.

There are various ways to perform multivariate analysis. Choosing one depends upon the type of data and your goals. For instance, for a single set of data, you can have many choices:

• Principal component analysis (PCA) decomposes a data table with correlated measures into a new set of uncorrelated measures.
• Cluster analysis, multidimensional scaling, additive trees are appropriate when rows and columns in your data table represent the same units, and the measure is a similarity or a distance.
• Correspondence analysis is similar to PCA. However, it applies to contingency tables.

Multivariate analysis is based on the principles of multivariate statistics. Typically, it is used to address situations where multiple measurements are made on each experimental unit and the essential relations among these measurements and their structures. A modern, overlapping categorization of MVA includes:

• Normal and general multivariate models and distribution theory
• The study and measurement of relationships
• Probability computations of multidimensional regions
• The exploration of data structures and patterns

What is MANOVA (multivariate analysis of variance) ?:

It is a type of multivariate analysis method used to analyze a set of data that involves two or more dependent variables at a time. It allows us to test hypotheses regarding the effect of one or more independent variables on two or more dependent variables. MANOVA has both a one-way flavor and a two-way flavor. The number of factor variables involved separates the one-way MANOVA from a two-way MANOVA.

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Hypothesis Testing
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Central Limit Theorem
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Distribution Analysis: Multivariate
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Estimation and Sampling

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