# Biserial correlation

The biserial correlation between on one hand, one or more quantitative variables, and on the other hand one or more binary variables can be calculated with XLSTAT. The biserial correlation was introduced by Pearson (1909).

As for the Pearson correlation, the biserial correlation coefficient varies between -1 and 1. 0 corresponds to no association (the means of the quantitative variable for the two categories of the qualitative variable are identical).

XLSTAT allows testing if the value of the biserial correlation r that has been obtained is different from 0 or not.

For the two-tailed test, the null H0 and alternative Ha hypotheses are as follows:

• H0 : r = 0
• Ha : r ≠ 0

In the left one-tailed test, the following hypotheses are used:

• H0 : r = 0
• Ha : r < 0

In the right one-tailed test, the following hypotheses are used:

• H0 : r = 0
• Ha : r > 0

Two methods to compute the p-value are proposed by XLSTAT. The user can choose between a p-value computed using on a large sample approximation, and a p-value computed using Monte Carlo resamplings. The second method is recommended.

Note: the XLSTAT_Biserial spreadsheet function can be used to compute the biserial correlation between a quantitative variable and a binary variable.

This analysis is available in the XLStat-Basic addin for Microsoft Excel

Kovach Computing Services (KCS) was founded in 1993 by Dr. Warren Kovach. The company specializes in the development and marketing of inexpensive and easy-to-use statistical software for scientists, as well as in data analysis consulting.