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# frozen_string_literal: true
module Split
class Zscore
include Math
def self.calculate(p1, n1, p2, n2)
# p_1 = Pa = proportion of users who converted within the experiment split (conversion rate)
# p_2 = Pc = proportion of users who converted within the control split (conversion rate)
# n_1 = Na = the number of impressions within the experiment split
# n_2 = Nc = the number of impressions within the control split
# s_1 = SEa = standard error of p_1, the estiamte of the mean
# s_2 = SEc = standard error of p_2, the estimate of the control
# s_p = SEp = standard error of p_1 - p_2, assuming a pooled variance
# s_unp = SEunp = standard error of p_1 - p_2, assuming unpooled variance
p_1 = p1.to_f
p_2 = p2.to_f
n_1 = n1.to_f
n_2 = n2.to_f
# Perform checks on data to make sure we can validly run our confidence tests
if n_1 < 30 || n_2 < 30
error = "Needs 30+ participants."
return error
elsif p_1 * n_1 < 5 || p_2 * n_2 < 5
error = "Needs 5+ conversions."
return error
end
# Formula for standard error: root(pq/n) = root(p(1-p)/n)
s_1 = Math.sqrt((p_1)*(1-p_1)/(n_1))
s_2 = Math.sqrt((p_2)*(1-p_2)/(n_2))
# Formula for pooled error of the difference of the means: root(π*(1-π)*(1/na+1/nc)
# π = (xa + xc) / (na + nc)
pi = (p_1*n_1 + p_2*n_2)/(n_1 + n_2)
s_p = Math.sqrt(pi*(1-pi)*(1/n_1 + 1/n_2))
# Formula for unpooled error of the difference of the means: root(sa**2/na + sc**2/nc)
s_unp = Math.sqrt(s_1**2 + s_2**2)
# Boolean variable decides whether we can pool our variances
pooled = s_1/s_2 < 2 && s_2/s_1 < 2
# Assign standard error either the pooled or unpooled variance
se = pooled ? s_p : s_unp
# Calculate z-score
z_score = (p_1 - p_2)/(se)
return z_score
end
end
end
Version data entries
12 entries across 12 versions & 2 rubygems