Module: Laboratory::Calculations::ZScore

Includes:
Math
Defined in:
lib/laboratory/calculations/z_score.rb

Class Method Summary collapse

Class Method Details

.calculate(n1:, p1:, n2:, p2:) ⇒ Object

n: Total population p: conversion percentage



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# File 'lib/laboratory/calculations/z_score.rb', line 9

def self.calculate(n1:, p1:, n2:, p2:) # rubocop:disable Metrics/AbcSize, Naming/MethodParameterName, Metrics/MethodLength
  p1_float = p1.to_f
  p2_float = p2.to_f

  n1_float = n1.to_f
  n2_float = n2.to_f

  # Formula for standard error: root(pq/n) = root(p(1-p)/n)
  s1_float = Math.sqrt(p1_float * (1 - p1_float) / n1_float)
  s2_float = Math.sqrt(p2_float * (1 - p2_float) / n2_float)

  # Formula for pooled error of the difference of the means:
  # root(pi*(1-pi)*(1/na+1/nc)
  # pi = (xa + xc) / (na + nc)
  pi = (p2_float * n2_float + p1_float * n1_float) / (n2_float + n1_float)
  s_p = Math.sqrt(pi * (1 - pi) * (1 / n2_float + 1 / n1_float))

  # Formula for unpooled error of the difference of the means:
  # root(sa**2/pi*a + sc**2/nc)
  s_unp = Math.sqrt(s2_float**2 + s1_float**2)

  # Boolean variable decides whether we can pool our variances
  pooled = s2_float / s1_float < 2 && s1_float / s2_float < 2

  # Assign standard error either the pooled or unpooled variance
  se = pooled ? s_p : s_unp

  # Calculate z-score
  z_score = (p2_float - p1_float) / se

  z_score.round(4)
end