Power of a One-Sided z-Test

Problem

Return the power 1 - Phi(z_alpha - delta*sqrt(n)/sigma) for a one-sided z-test with effect size delta, using the normal CDF. Return 0.0 when n <= 0 or sigma <= 0, and clamp the result to [0, 1].

Hint

The term delta*sqrt(n)/sigma is the noncentrality shift.

Test cases

case 1

in: [0.5,25,1,1.645]

expected: 0.8037244261254556

case 2

in: [0,100,2,1.96]

expected: 0.024997895148220428

case 3

in: [1,16,2,1.645]

expected: 0.6387052043836872

case 4

in: [2,9,1,1.28]

expected: 0.9999988207767835

case 5

in: [0.1,4,1,1]

expected: 0.21185539858339664

Starter codePython

import math
def power_one_sided_z(delta, n, sigma, z_alpha):
    # Your code here
    pass

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