Multivariate Analysis Overview
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Use Minitab's multivariate analysis procedures to analyze your data when you have made multiple measurements on items or subjects. You can choose to:

·    Analyze the data covariance structure to understand it or to reduce the data dimension

·    Assign observations to groups

·    Explore relationships among categorical variables

Because Minitab does not compare tests of significance for multivariate procedures, interpreting the results is somewhat subjective. However, you can make informed conclusions if you are familiar with your data.

Analysis of the data structure

Minitab offers two procedures for analyzing the data covariance structure:

·    Principal Components helps you to understand the covariance structure in the original variables and/or to create a smaller number of variables using this structure.

·    Factor Analysis, like principal components, summarizes the data covariance structure in a smaller number of dimensions. The emphasis in factor analysis is the identification of underlying "factors" that might explain the dimensions associated with large data variability.

Internal Consistency

·    Item Analysis assesses how reliably multiple items in a survey or test measure the same construct.

Grouping observations

Minitab offers three cluster analysis methods and discriminant analysis for grouping observations:

·    Cluster Observations groups or clusters observations that are "close" to each other when the groups are initially unknown. This method is a good choice when no outside information about grouping exists. The choice of final grouping is usually made according to what makes sense for your data after viewing clustering statistics.

·    Cluster Variables groups or clusters variables that are "close" to each other when the groups are initially unknown. The procedure is similar to clustering of observations. You may want to cluster variables to reduce their number.

·    Cluster K-Means, like clustering of observations, groups observations that are "close" to each other. K-means clustering works best when sufficient information is available to make good starting cluster designations.

·    Discriminant Analysis classifies observations into two or more groups if you have a sample with known groups. You can use discriminant analysis to investigate how the predictors contribute to the groupings.

Correspondence Analysis

Minitab offers two methods of correspondence analysis to explore the relationships among categorical variables:

·    Simple Correspondence Analysis explores relationships in a 2-way classification. You can use this procedure with 3-way and 4-way tables because Minitab can collapse them into 2-way tables. Simple correspondence analysis decomposes a contingency table similar to how principal components analysis decomposes multivariate continuous data. Simple correspondence analysis performs an eigen analysis of data, breaks down variability into underlying dimensions, and associates variability with rows and/or columns.

·    Multiple Correspondence Analysis extends simple correspondence analysis to the case of 3 or more categorical variables. Multiple correspondence analysis performs a simple correspondence analysis on an indicator variables matrix in which each column  corresponds to a level of a categorical variable. Rather than a 2-way table, the multi-way table is collapsed into 1 dimension.