Sequential Alpha Spending

Problem

Return the O'Brien-Fleming alpha spending 2*(1 - Phi(z_crit / sqrt(t))) at information fraction t, where z_crit is the fixed-sample critical value. Return 0.0 when t is not in (0, 1].

Hint

Very little alpha is spent early when the boundary is conservative.

Test cases

case 1

in: [1.96,0.5]

expected: 0.005573724535172131

case 2

in: [1.96,1]

expected: 0.049995790296440745

case 3

in: [2.576,0.25]

expected: 2.577230360234495e-7

case 4

in: [1.96,0]

expected: 0

case 5

in: [1.645,0.5]

expected: 0.019998217783908867

Starter codePython

import math
def alpha_spending(z_crit, information_fraction):
    # Your code here
    pass

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