conversion_rate_test.go

package main

import (
	"fmt"
	"math"
)

// Cumulative distribution function for the standard normal distribution
// Percentage of data that lies within the standard distribution
func cdfNorm(x float64) float64 {
	return (1.0 + math.Erf(x/math.Sqrt(2.0))) / 2.0
}

func convRate(visitors, conversions float64) float64 {
	return visitors / conversions
}

func stdErr(convRate, visitors float64) float64 {
	return math.Sqrt((convRate * (1 - convRate) / visitors))
}

func zScore(control_p, variation_p, control_se, variation_se float64) float64 {
	return (control_p - variation_p) / math.Sqrt(math.Pow(control_se, 2)+math.Pow(variation_se, 2))
}

type lim struct {
	from float64
	to   float64
}

func limit(p, se float64) lim {
	var from, to float64

	if p-1.65*se < 0 {
		from = 0
	} else {
		from = p - 1.65*se
	}

	if p+1.65*se > 1 {
		to = 1
	} else {
		to = p + 1.65*se
	}

	return lim{from: from, to: to}
}

func main() {
	// input variables:
	var controlVisitors = 8368.
	var controlConversions = 116.

	var variationVisitors = 7956.
	var variationConversions = 133.

	// ------- computations
	controlp := convRate(controlConversions, controlVisitors)
	fmt.Println("Conversion rate control", controlp*100, "%")

	variationp := convRate(variationConversions, variationVisitors)
	fmt.Println("Conversion rate variation", variationp*100, "%")

	controlse := stdErr(controlp, controlVisitors)
	fmt.Println("Control standard error", controlse*100, "%")

	variationse := stdErr(variationp, variationVisitors)
	fmt.Println("Control standard error", variationse*100, "%")

	score := zScore(controlp, variationp, controlse, variationse)
	fmt.Println("z-score", score*100, "%")

	pval := cdfNorm(score)
	fmt.Println("P-value:", pval)

	if pval < 0.1 || pval > 0.9 {
		fmt.Println("Significance: YES")
	} else {
		fmt.Println("Significance: NO")
	}

	fmt.Println("Control 90% Conversion Rate Limits", limit(controlp, controlse))
	fmt.Println("Variation 90% Conversion Rate Limits", limit(variationp, variationse))
}