Biserial Correlation

Problem

Return the biserial correlation between continuous scores and a 0/1 group indicator: (mean_1 - mean_0)/s * (p*q)/phi(z_cut), where p is the proportion coded 1, s is the population standard deviation of scores, and phi(z_cut) is the standard normal density at the supplied z_cut. Return 0.0 when a group is missing, lengths differ, or the scores are constant.

Hint

The biserial correlation assumes an underlying continuous, normal variable.

Test cases

case 1

in: [[1,2,3,4],[0,0,1,1],0]

expected: 1.1209982432795857

case 2

in: [[5,4,3,2],[1,0,1,0],0]

expected: 0.5604991216397929

case 3

in: [[1,1,2,2],[1,1,0,0],0]

expected: -1.2533141373155001

case 4

in: [[1,2],[1,1],0]

expected: 0

case 5

in: [[2,2,2],[1,1,0],0]

expected: 0

Starter codePython

import math
def biserial_correlation(scores, groups, z_cut):
    # Your code here
    pass

5 test cases · run your code against them in the editor