Multivariate statistical analysis refers to multiple advanced techniques for examining relationships among multiple variables at the same time. Researchers use multivariate procedures in studies that involve more than one dependent variable (also known as the outcome or phenomenon of interest), more than one independent variable (also known as a predictor) or both. Upper-level undergraduate courses and graduate courses in statistics teach multivariate statistical analysis. This type of analysis is desirable because researchers often hypothesize that a given outcome of interest is effected or influenced by more than one thing.

## Types

There are many statistical techniques for conducting multivariate analysis, and the most appropriate technique for a given study varies with the type of study and the key research questions. Four of the most common multivariate techniques are multiple regression analysis, factor analysis, path analysis and multiple analysis of variance, or MANOVA.

## Multiple Regression

Multiple regression analysis, often referred to simply as regression analysis, examines the effects of multiple independent variables (predictors) on the value of a dependent variable, or outcome. Regression calculates a coefficient for each independent variable, as well as its statistical significance, to estimate the effect of each predictor on the dependent variable, with other predictors held constant. Researchers in economics and other social sciences often use regression analysis to study social and economic phenomena. An example of a regression study is to examine the effect of education, experience, gender, and ethnicity on income.

## Factor Analysis

Factor analysis is a data reduction technique in which a researcher reduces a large number of variables to a smaller, more manageable, number of factors. Factor analysis uncovers patterns among variables and then clusters highly interrelated variables into factors. Factor analysis has many applications, but a common use is in survey research, where researchers use the technique to see if lengthy series of questions can be grouped into shorter sets.

## Path Analysis

This is a graphical form of multivariate statistical analysis in which graphs known as path diagrams depict the correlations among variables, as well as the directions of those correlations and the "paths" along which these relationships travel. Statistical software programs calculate path coefficients, the values of which estimate the strength of relationships among the variables in a researcher's hypothesized model.

## MANOVA

Multiple Analysis of Variance, or MANOVA, is an advanced form of the more basic analysis of variance, or ANOVA. MANOVA extends the technique to studies with two or more related dependent variables while controlling for the correlations among them. An example of a study for which MANOVA would be an appropriate technique is a study of health among three groups of teens: those who exercise regularly, those who exercise on occasion, and those who never exercise. A MANOVA for this study would allow multiple health-related outcome measures such as weight, heart rate, and respiratory rates.

## Benefits

Multivariate statistical analysis is especially important in social science research because researchers in these fields are often unable to use randomized laboratory experiments that their counterparts in medicine and natural sciences often use. Instead, many social scientists must rely on quasi-experimental designs in which the experimental and control groups may have initial differences that could affect or bias the outcome of the study. Multivariate techniques try to statistically account for these differences and adjust outcome measures to control for the portion that can be attributed to the differences.

## Considerations

Statistical software programs such as SAS, Stata, and SPSS can perform multivariate statistical analyses. These programs are frequently used by university researchers and other research professionals. Spreadsheet programs can perform some multivariate analyses, but are intended for more general use and may have limited abilities than a specialized statistical software package.

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#### References

- Dictionary of Statistics and Methodology: A Nontechnical Guide for the Social Sciences, W. Paul Vogt, 1993
- Understanding Statistics: An Introduction for the Social Sciences, Dr. Daniel B. Wright, 1997