# Biserial correlation

Biserial correlation measures the relationship between quantitative variables and binary variables. It is available in Excel using the XLSTAT software.

## What is biserial correlation

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

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).

## Biserial correlation in XLSTAT

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.

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