# Correlation Analysis

Correlation is a measure of the relationship between two variables, or sets of variables. Do the variables increase and decrease together (positive correlation)? Does one variable increase as the other decreases (inverse correlation)? Or is there no relationship at all between the variables (no correlation)? The correlation coefficient is a measure of the strength of the correlation; it varies from -1 (perfect inverse correlation) through 0 (no correlation) to +1 (perfect positive correlation). The computations for correlation are similar to those for the regression of independent and dependent variables, but for correlation there is no assumption of causation (i.e. while the variables may change together in some way, one variable is not necessarily causing the other to change). statistiXL provides an extensive module for parametric correlation analyses, with options for bivariate, multivariate, partial, multiple and canonical correlation. Nonparametric correlation procedures are also available. Bivariate (simple) correlation is the measure of interrelationship between one variable and another. Multivariate correlation is a simple extension of bivariate correlation to more than two variables, exploring the simple bivariate correlation for all pair-wise combinations of the variables. Partial correlation is the correlation between two variables when taking into account one or more additional variables (e.g. correlating the times it took participants to complete each of 2 obstacle courses while taking into account measures of their fitness and IQ). Multiple correlation is the interrelationship between multiple variables examined collectively. Canonical correlation is a multivariate statistical method which determines the linear relationship between two sets of multivariate variables (e.g. the relationship between measures of environmental type and the species of plants found in different environments). The format of Results varies somewhat with the different forms of correlation. In general, summary descriptive statistics are provided as an option. The correlation matrix of r values for all combinations of the selected variables is presented, along with a corresponding matrix of P values for each of the r values. A graphical scatterplot (or scatterplots) is also provided as an option (except for partial and multiple correlations). The help file included with statistiXL provides an introduction to correlation, discusses input and output options, and provides an example for each of the types of correlation, simple bivariate (for 2 and for 5 variables), partial correlation, multiple correlation, and canonical correlation.