Probability and Statistics > Multivariate Analysis

## What is Multivariate Analysis?

Multivariate analysis is used to study more complex sets of data than what univariate analysis methods can handle. This type of analysis is almost always performed with software (i.e. SPSS or SAS), as working with even the smallest of data sets can be overwhelming by hand.

Multivariate analysis can reduce the likelihood of Type I errors. Sometimes, univariate analysis is preferred as multivariate techniques can result in difficulty interpreting the results of the test. For example, group differences on a linear combination of dependent variables in MANOVA can be unclear. In addition, multivariate analysis is usually unsuitable for small sets of data.

There are more than 20 different ways to perform multivariate analysis. Which one you choose depends upon the type of data you have and what your goals are. For example, if you have a single data set you have several choices:

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

Although there are fairly clear boundaries with one data set (for example, if you have a single data set in a contingency table your options are limited to correspondence analysis), in most cases you’ll be able to choose from several methods.

Click on a topic to read about specific types of multivariate analysis:

- Additive Tree.
- Canonical Correlation Analysis.
- Cluster Analysis.
- Correspondence Analysis / Multiple Correspondence Analysis.
- Factor Analysis.
- Generalized Procrustean Analysis.
- Independent Component Analysis.
- MANOVA.
- Multidimensional Scaling.
- Multiple Regression Analysis.
- Partial Least Square Regression.
- Principal Component Analysis / Regression / PARAFAC.
- Redundancy Analysis.

Related:

## References

Beyer, W. H. CRC Standard Mathematical Tables, 31st ed. Boca Raton, FL: CRC Press, pp. 536 and 571, 2002.

Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.

Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.

Vogt, W.P. (2005). Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences. SAGE.

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**Stephanie Glen**. "Multivariate Analysis" From

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