Power from Effect Size

Problem

For a one-sided z-test, the power is Phi(delta * sqrt(n) - z_alpha) where delta is the standardized effect size. Use the normal CDF implementation Phi(x) = 0.5 (1 + erf(x / sqrt(2))).

Given delta, n, and the critical z_alpha, return [power, beta] where beta = 1 - power.

Hint

Shift the critical value by the noncentrality delta * sqrt(n).

Test cases

case 1

in: [0.5,25,1.645]

expected: [0.8037244261254556,0.19627557387454442]

case 2

in: [0.2,100,1.96]

expected: [0.5159534368528308,0.4840465631471692]

case 3

in: [0,30,1.645]

expected: [0.04998490553912138,0.9500150944608786]

Starter codePython

def power_from_effect_size(delta, n, z_alpha):
    # Your code here
    pass

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