Minimum Detectable Effect

Problem

Return the minimum detectable effect for a two-sided test: (z(1 - alpha/2) + z(power)) * sqrt(2 * variance / n), where z is the standard normal quantile obtained by bisecting the normal CDF. Return 0.0 when n <= 0, variance <= 0, or alpha or power lie outside (0, 1).

Hint

Bisect the normal CDF, which is 0.5 * (1 + erf(x / sqrt(2))).

Test cases

case 1

in: [100,0.25,0.05,0.8]

expected: 0.19810199057996716

case 2

in: [400,1,0.05,0.9]

expected: 0.22920976267865004

case 3

in: [0,1,0.05,0.8]

expected: 0

case 4

in: [100,0,0.05,0.8]

expected: 0

Starter codePython

import math
def minimum_detectable_effect(n, variance, alpha, power):
    # Your code here
    pass

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