# Class: Split::Zscore

Inherits:
Object
• Object
show all
Includes:
Math
Defined in:
lib/split/zscore.rb

## Class Method Details

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

 ``` 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54``` ```# File 'lib/split/zscore.rb', line 7 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) z_score end```