# An aid to Multivariate Statistics

### Multivariate Analysis

Multivariate analysis (MVA) deals with multivariate statistics which is the study that takes into account more than one statistical variable at a time. To consider effect of all the variables ,analysis is performed by using multiple dimensions

Multivariate statistics: is that statistics that considers and analyse more than one statistical variable.

### Types of Analysis

1. Multivariate analysis of variance (MANOVA) : It is an extension of ANOVA. MANOVA is performed when we require analysis in the presence of more than one dependent variable.

2. Multivariate regression analysis : It determines a formula which tells us that how elements in vector of variables respond simultaneously to changes occurring in others . We take into consideration general linear model when we require regression analyses based on linear relations.

3. Principal components analysis (PCA) With the help of PCA a new set of orthogonal variables is created containing the same information as that of original set. This is done by rotating the axes of variation and the main reason for doing this is to summarize decreasing proportions of variation.

4. Factor analysis : It is an improvement over PCA. In Factor Analysis a number of synthetic variable is extracted which are fewer than the original set , and the unexplained variation are ignored by considering errors. Such extracted variables are termed as latent variables or factors. Each and every latent variable are accounted for covariation.

5. Canonical correlation analysis : In this analysis we are required to find linear relationships between two sets of variables. It is considered as a generalization of bivariate correlation.

6. Redundancy analysis : Same as canonical correlation analysis but different in the sense that it derives a specified and particular number of synthetic variables from one set of independent variables explaining the possible variance in another independent set.

7. Correspondence analysis (CA) also termed as reciprocal averaging, similar to PCA allows a set of synthetic variables summarizing the original set. The model under consideration is chi-squared dissimilarities among cases. Like canonical correlation analysis there is also canonical correspondence analysis (CCA) to summarize the variation in two sets of variables.

8. Multidimensional scaling : It is a collection of algorithms that determines a set of synthetic variables which is the best representation of the pair wise distances between cases. In originality the method is principal coordinate's analysis.

9. Discriminant analysis also known as canonical variate analysis is the analysis where we see whether we can consider a set of variables to distinguish between two or more groups.

10. Linear discriminant analysis (LDA) : To classify new observations LDA calculates a linear predictor from two sets of data which are normally distributed.

11. Clustering systems: Clusters are groups which assigns objects such that the object belonging to the same cluster are more similar compared to the objects belonging to dissimilar clusters.

##### Purpose of Using

We will discuss the three main situations where multivariate statistics is used. They are as follows:

First of all we may be interested in multiple individual variables. So in such cases we will use multiple statistics.

Secondly to examine a set containing a set of variables we require multiple statistics.There arise situations where the variables in the set are being measured on two groups. In such cases if we may want to know the patterns of differences between the two groups for the set of variables. We will be interested to know the variable or rather the group of variables which is different for two groups when we observe differences between the groups for the set of variables. Sometimes combination of variables in the set is distinguishable between two groups and not the variables individually.

Thirdly in multivariate analysis it may be required to use the combination or a subset of raw variables rather than the raw variables themselves.

### Analysis through Computer Programming and Interpretations

Analysis with the help of Spss and sas are as follows:

Multivariate analysis of variance (MANOVA) Exploratory and confirmatory factor analysis

Multivariate regression analysis

Principal components analysis

Canonical correlation

Discriminant function analyses

Structural equation modeling

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### A Helping Hand

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