Applied multivariate analysis refers to the application of any multivariate statistical technique (techniques for analyzing multiple variables at a time) to problems requiring statistical analysis. Business and industry analysts, market researchers, physicists, economists, education researchers and others use multivariate analysis techniques to analyze phenomena in their respective fields.
Many methods and techniques of multivariate analysis exist, and they can be applied in many settings. Some of the most analytical procedures include multiple analysis of variance (MANOVA), linear regression, logistic regression, factor analysis and path analysis.
MANOVA is a multivariate extension of the analysis of variance (ANOVA) procedure. ANOVA is a technique for determining if the mean scores on a variable of interest among two or more groups differ significantly. An example of a research question using ANOVA is whether there is a significant difference in average blood pressure among three groups of people.
MANOVA extends ANOVA by studying two or more related dependent variables while controlling for their similarities. If the multiple dependent variables are not related, there is no point in doing a MANOVA. An example of a MANOVA study would be to analyze the average blood pressure, heart rate and respiratory rate among three groups of people. These related variables make a MANOVA appropriate.
Often, a given dependent variable (income, for example) is affected by several independent variables. Regression analysis helps us analyze such situations by focusing on the change in a dependent variable associated with changes in two or more independent variables. For example, suppose you had a set of data on worker salaries and were interested in the extent to which age, education, experience, ethnicity and gender predict a person's income. Regression analysis is a useful tool for this type of research. The technique is popular among economists, political scientists and business analysts.
Also known as the Logit model, logistic regression is a type of regression analysis in which the dependent variable is a dichotomous variable, meaning that it has a value of either zero or 1. Logistic regression often is used for predicting whether something will happen. For example, a logistic regression model could help predict whether a person will graduate from high school.
Analysts use factor analysis when their research problem requires them to uncover patterns in relationships among multiple variables. Researchers often use factor analysis when they have between 10 and 100 variables. Factor analysis helps a researcher determine if the observed variables can be explained by a smaller number of unobserved variables, known as factors. A common use of factor analysis is in survey research.
Path analysis, based on regression, provides a visual representation of the relationships among variables by using graphs. These graphical displays, known as path diagrams, depict the strength of relationships among a set of variables. Path analysis assumes that the value of a dependent variable is caused by the values of independent variables.