anova.rb

# Used to replace Abingo:Statistics
#
#  Background here: http://en.wikipedia.org/wiki/F-test
#  Has access to the following variables when included in an ABingo::Experiment
#
# TODO: Get a real stat guy to confirm my analysis
# Question: Does this work when there are varing observations per level
#
# alternatives (includes conversion_rate and participants)
# best_alternative
#
module Anova
  # Step 1) Calculate the mean within each group
  # Step 2) Calculate the overall mean
  # Step 3) Calculate the "between group" sum of squares
  # Step 4) Calculate the between group degrees of freedom
  # Step 4) Calculate the between group mean square value
  # Step 5) Calculate the "within-group" sum of squares
  # Step 6) Calculate F-ratio
  # Step 7) Is significant

    def fratio
      between_group_mean_square / within_group_mean_square
    end
    # Step 1) Calculate the mean within each group

    # Step 2) Calculate the overall mean
    def overall_mean
      @overall_mean ||= (alternatives.sum(:conversions) * 1.0) / alternatives.count
    end

    def between_group_sum
      @between_group_sum ||= alternatives.inject(0){|sum,n| sum + ((n.conversion_rate - overall_mean) ** 2)}
    end

    def between_group_degrees_of_freedom
      @between_group_degrees_of_freedom ||= alternatives.count - 1
    end

    def between_group_mean_square
      @between_group_mean_square ||= (between_group_sum * 1.0) / between_group_degrees_of_freedom
    end

    def within_group_degrees_of_freedom
      #@within_group_degrees_of_freedom ||= alternatives.count * alternatives.minimum(:participants)
      @within_group_degrees_of_freedom ||= alternatives.sum(:participants) - 1
    end

    def within_group_mean_square
      within_group_sum_of_squares = 0
      alternatives.each do |alt|
        number_of_ones = alt.conversions
        number_of_zeros = alt.participants - number_of_ones
        alternative_sum = (number_of_ones * ((1 - alt.conversion_rate) ** 2)) + (number_of_zeros * ((0 - alt.conversion_rate) ** 2))
        within_group_sum_of_squares = within_group_sum_of_squares + alternative_sum
      end

      (within_group_sum_of_squares * 1.0) / within_group_degrees_of_freedom
    end

    def f(p_value = 0.95)
      Distribution::F.p_value(p_value,between_group_degrees_of_freedom,within_group_degrees_of_freedom)
    end

    def significant?
      within_group_degrees_of_freedom > f
    end
    
#    def standard_error
#      
#    end
#
#    def tukey_test(larger_mean,smaller_mean)
#      (larger_mean - smaller_mean) / standard_error
#    end

    
end