Module: Abongo::Statistics

Defined in:
lib/abongo/statistics.rb

Constant Summary collapse

HANDY_Z_SCORE_CHEATSHEET = 
[[0.10, 1.29], [0.05, 1.65], [0.01, 2.33], [0.001, 3.08]]
PERCENTAGES = 
{0.10 => '90%', 0.05 => '95%', 0.01 => '99%', 0.001 => '99.9%'}
DESCRIPTION_IN_WORDS = 
{0.10 => 'fairly confident', 0.05 => 'confident',
0.01 => 'very confident', 0.001 => 'extremely confident'}

Class Method Summary collapse

Class Method Details

.conversion_rate(exp) ⇒ Object 



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# File 'lib/abongo/statistics.rb', line 50

def self.conversion_rate(exp)
  1.0 * exp['conversions'] / exp['participants']
end

.describe_result_in_words(experiment, alternatives) ⇒ Object 



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# File 'lib/abongo/statistics.rb', line 58

def self.describe_result_in_words(experiment, alternatives)
  begin
    z = zscore(alternatives)
  rescue
    return "Could not execute the significance test because one or more of the alternatives has not been seen yet."
  end
  p = p_value(alternatives)

  words = ""
  if (alternatives[0]['participants'] < 10) || (alternatives[1]['participants'] < 10)
    words += "Take these results with a grain of salt since your samples are so small: "
  end

  best_alternative = alternatives.max{|a, b| conversion_rate(a) <=> conversion_rate(b)}
  alts = alternatives - [best_alternative]
  worst_alternative = alts.first

  words += "The best alternative you have is: [#{best_alternative['content']}], which had "
  words += "#{best_alternative['conversions']} conversions from #{best_alternative['participants']} participants "
  words += "(#{pretty_conversion_rate(best_alternative)}).  The other alternative was [#{worst_alternative['content']}], "
  words += "which had #{worst_alternative['conversions']} conversions from #{worst_alternative['participants']} participants "
  words += "(#{pretty_conversion_rate(worst_alternative)}).  "

  if (p.nil?)
    words += "However, this difference is not statistically significant."
  else
    words += "This difference is #{PERCENTAGES[p]} likely to be statistically significant, which means you can be "
    words += "#{DESCRIPTION_IN_WORDS[p]} that it is the result of your alternatives actually mattering, rather than "
    words += "being due to random chance.  However, this statistical test can't measure how likely the currently "
    words += "observed magnitude of the difference is to be accurate or not.  It only says \"better\", not \"better "
    words += "by so much\"."
  end
  words
end

.is_statistically_significant?(p = 0.05) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/abongo/statistics.rb', line 46

def self.is_statistically_significant?(p = 0.05)
  p_value <= p
end

.p_value(alternatives) ⇒ Object 



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# File 'lib/abongo/statistics.rb', line 32

def self.p_value(alternatives)
  index = 0
  z = zscore(alternatives)
  z = z.abs
  found_p = nil
  while index < HANDY_Z_SCORE_CHEATSHEET.size do
    if (z > HANDY_Z_SCORE_CHEATSHEET[index][1])
      found_p = HANDY_Z_SCORE_CHEATSHEET[index][0]
    end
    index += 1
  end
  found_p
end

.pretty_conversion_rate(exp) ⇒ Object 



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# File 'lib/abongo/statistics.rb', line 54

def self.pretty_conversion_rate(exp)
  sprintf("%4.2f%%", conversion_rate(exp) * 100)
end

.zscore(alternatives) ⇒ Object 



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# File 'lib/abongo/statistics.rb', line 10

def self.zscore(alternatives)
  if alternatives.size != 2
    raise "Sorry, can't currently automatically calculate statistics for A/B tests with > 2 alternatives."
  end

  if (alternatives[0]['participants'] == 0) || (alternatives[1]['participants'] == 0)
    raise "Can't calculate the z score if either of the alternatives lacks participants."
  end

  cr1 = conversion_rate(alternatives[0])
  cr2 = conversion_rate(alternatives[1])

  n1 = alternatives[0]['participants']
  n2 = alternatives[1]['participants']

  numerator = cr1 - cr2
  frac1 = cr1 * (1 - cr1) / n1
  frac2 = cr2 * (1 - cr2) / n2

  numerator / ((frac1 + frac2) ** 0.5)
end