## Dialog box for computing a correlation matrix

### Description

Computes a correlation matrix and confidence intervals for the chosen variables. Possible computational methods are Pearson's r, Kendall's tau, and Spearman's rho.

### Details

Correlation coefficients measure the strength of the linear relationship between two variables. This module produces a correlation matrix, which presents the correlation coefficients for several variables, along with confidence intervals.

Correlation coefficients are unitless and range between -1 and 1. A positive correlation implies as one variable increases, the other increases. A negative correlation implies as one variable increases, the other decreases. The closer the correlation is to -1 or 1, the stronger the relationship. If the correlation is near 0, then the variables are not related linearly. In all cases, a scatterplot should be inspected to help determine if a linear model is appropriate for the variables.

Estimation

This module offers 3 methods for computing a correlation coefficient. One is parametric, Pearson's r, and two are nonparametric, Kendall's tau and Spearman's rho.

Pearson's r is equal to the covariance of the two variables divided by the square root of the product of the variances. Since Pearson's r is based upon variances and covariances, it is sensitive to outliers. The nonparametric methods are based upon data ranks rather than data values so they are not sensitive to outliers. Also, Spearman's rho may be a better indicator of a non-linear relationship.

Plots

The user may select to have a scatterplot matrix created. This is a matrix of scatterplots between all pairs of variables. These plots are useful in determining the type and strength of the relationship between two variables.

User Interface

To perform a correlation analysis, select Analysis Tools -> Correlation Analysis from the menu. A dialog box will appear that allows the user to enter analysis parameters:

Provide the variables (column names) of interest.

Click the Method radio button to indicate the desired method.

Click the Create Scatterplot Matrix check box to indicate whether a scatterplot matrix should be produced.

Click the Compute Confidence Intervals check box to indicate whether confidence intervals for the correlation between all variable pairs should be computed.

If confidence intervals are desired, then enter the confidence level into the Confidence Level text box. The confidence level must be between 0 and 1.