XLSTAT: Biserial Correlation Coefficients

A biserial correlation coefficient is useful to evaluate the degree of association between a binary (or dichotomous) variable and a continuous variable.

Dataset for Example

The data used in this example corresponds to concentrations of a particular molecule measured in blood samples of 30 mice, split into two different groups depending on their species (see attached file).

We want to use the biserial correlation to check whether there is an association between the concentration and the species. The variance is assumed to be the same whatever the group to which an observation belongs.

The biserial correlation values range between -1 and 1.

0 corresponds to no association.

Setting Up

• Open XLSTAT.

• Click on the Describing data menu and select the Biserial correlation feature: 

In the General tab:

• Select the column B in the Quantitative variables
• Select the column C in the Binary variable
• Select the modality "a" in the Control category

In the Options tab:

• Choose to test whether the biserial correlation is different from 0.

• Select the Monte Carlo Method.

 

• Click on the OK button to launch the computations.
• The results are displayed on a new Excel sheet.

Interpreting the Results

The first table shows basic summary statistics for the various input variables. 

The second table shows the results including the biserial correlation and p-value of the test.

We can see here that the correlation is close to zero (0.19) and not significantly different from 0 as the p-value is greater than 0.05.

The biserial correlation can be calculated directly in EXCEL using the formula XLSTAT_Biserial.

See the example below, which uses the p-value based on the large sample approximation, different than the example above.

Use this Statistical Test Guide to find other calculation options.