The Spearman Correlation Coefficient

• The original X and Y variables are ranks.
• The original X and Y variables are not ranks, but have been converted into ranks. It is especially useful when one of the variables is ordinal and the other is interval or ratio. Then both variables are changed into ranks.

To compute the Spearman Correlation Coefficient, you first convert your two variables into ranks, and then follow the procedure for Pearson correlation.

ViSta Applet: Transform variables into ranks by choosing the Transform menu's Ranks item. This produces a new dataset in which all ordinal or numeric variables have been converted into ranks. You now proceed as you would for the Pearson Correlation.

The commands to do this are:

(browse-data)
(ranks)
(browse-data)
(summarize-data :moments t :correlations t)
(correlations)
(browse-data)

The Point-Biserial Correlation Coefficient

To compute the Point-Biserial Correlation Coefficient, you first convert your binary variable into 1's and 0's, and then follow the procedure for Pearson correlation.

ViSta Applet: Code your binary variable with 1's and 0's. Once you have done this you proceed as you would for the Pearson Correlation.

The commands to do this (given that you already have a binary variable, and that you want to select it and some other, non-binary variables) are:

(list-variables)
(select-variables '("GPA" "MathSAT" "VerbSAT" "GenderN"))
(summarize-data :moments t :correlations t)
(correlations)
(browse-data)

The Phi Correlation Coefficient

To compute the Point-Biserial Correlation Coefficient, you first convert your two binary variable into 1's and 0's, and then follow the procedure for Pearson correlation.

ViSta Applet: Code both of your binary variables with 1's and 0's. Once you have done this you proceed as you would for the Pearson Correlation.

The commands to do this (given that you already have a datafile with at least two binary variables) are:

(browse-data)
(summarize-data :moments t :correlations t)
(correlations)
(browse-data)