Bivariate and multivariate analyses are statistical methods to investigate relationships between data samples. Bivariate analysis looks at two paired data sets, studying whether a relationship exists between them. Multivariate analysis uses two or more variables and analyzes which, if any, are correlated with a specific outcome. The goal in the latter case is to determine which variables influence or cause the outcome.

## Bivariate Analysis

Bivariate analysis investigates the relationship between two data sets, with a pair of observations taken from a single sample or individual. However, each sample is independent. You analyze the data using tools such as t-tests and chi-squared tests, to see if the two groups of data correlate with each other. If the variables are quantitative, you usually graph them on a scatterplot. Bivariate analysis also examines the strength of any correlation.

## Bivariate Analysis Examples

One example of bivariate analysis is a research team recording the age of both husband and wife in a single marriage. This data is paired because both ages come from the same marriage, but independent because one person's age doesn't cause another person's age. You plot the data to showing a correlation: the older husbands have older wives. A second example is recording measurements of individuals' grip strength and arm strength. The data is paired because both measurements come from a single person, but independent because different muscles are used. You plot data from many individuals to show a correlation: people with higher grip strength have higher arm strength.

## Multivariate Analysis

Multivariate analysis examines several variables to see if one or more of them are predictive of a certain outcome. The predictive variables are independent variables and the outcome is the dependent variable. The variables can be continuous, meaning they can have a range of values, or they can be dichotomous, meaning they represent the answer to a yes or no question. Multiple regression analysis is the most common method used in multivariate analysis to find correlations between data sets. Others include logistic regression and multivariate analysis of variance.

## Multivariate Analysis Example

Multivariate analysis was used in by researchers in a 2009 Journal of Pediatrics study to investigate whether negative life events, family environment, family violence, media violence and depression are predictors of youth aggression and bullying. In this case, negative life events, family environment, family violence, media violence and depression were the independent predictor variables, and aggression and bullying were the dependent outcome variables. Over 600 subjects, with an average age of 12 years old, were given questionnaires to determine the predictor variables for each child. A survey also determined the outcome variables for each child. Multiple regression equations and structural equation modeling was used to study the data set. Negative life events and depression were found to be the strongest predictors of youth aggression.