Three indices of correlation are used to investigate nonlinear
relationships. The Spearman index is used for two ordinal
variables. The Point-Biserial index is used when
one variable is numeric and the other is binary. The Phi
coefficient is used when both variables are binary.
The Spearman Correlation Coefficient
The Spearman Correlation Coefficient is designed to measure
the degree of relation for two ordinal variables.
It is designed to be used when:
- 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
The Point-Biserial Correlation Coefficient is designed to
measure the degree of relation for two variables when one
variable is quantitative (interval or ratio) and the other
variable is binary (has only two values --- also called
dichotomous).
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
The Phi Correlation Coefficient is designed to measure the
degree of relation for two variables which are binary (each
has only two values --- also called dichotomous).
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)
