Spearman’s rank correlation coefficient function

spearman.rb

# xs & ys are arrays of results in order of rank
def spearman(xs, ys)
  # remove items that aren't common to both result sets
  # these are mostly outliers anyway which we want to ignore
  xs_common = xs.select{|i| ys.include? i }
  ys_common = ys.select{|i| xs.include? i }

  # calculate the mean of each set of ranks (simple sum/length calculation)
  # as both are just the sum of ranks [1,2,3,4...] and have same length,
  # we can figure it out based on an arithmetic sum
  total = 0.5 * xs_common.length * (xs_common.length + 1)
  x_mean = y_mean = total / xs_common.length 

  # initialize totals that we'll need
  sum_mean_diff = 0
  sum_x_mean_diff_sq = 0
  sum_y_mean_diff_sq = 0

  # sum the differences of the items
  xs_common.each_with_index do |x, x_rank|
    x_rank = x_rank + 1 # ranking is 1-based, not 0-based
    # grab the corresponding item from the other set of ranked items
    y_rank = ys_common.index(x) + 1 

    # work out the error of each item from it's mean
    x_mean_diff = x_rank - x_mean
    y_mean_diff = y_rank - y_mean

    # aggregate totals for final calc
    sum_mean_diff += x_mean_diff * y_mean_diff
    sum_x_mean_diff_sq += x_mean_diff ** 2
    sum_y_mean_diff_sq += y_mean_diff ** 2
  end

  # final coefficient
  sum_mean_diff / Math.sqrt(sum_x_mean_diff_sq * sum_y_mean_diff_sq)
end

spearman_example.rb

require 'spearman'

ranks1 = [:a, :b, :c, :d, :e]
ranks2 = [:a, :b, :c, :d, :e]
puts spearman(ranks1, ranks2) # = 1.0 (in exactly the same order)

ranks1 = [:a, :b, :c, :d, :e]
ranks2 = [:e, :d, :c, :b, :a]
puts spearman(ranks1, ranks2) # = -1.0 (in exactly reverse order)

ranks1 = [:a, :b, :c, :d, :e]
ranks2 = [:b, :a, :c, :d, :e]
puts spearman(ranks1, ranks2) # = 0.9 (a & b are out of order)

ranks1 = [:a, :b, :c, :d, :e]
ranks2 = [:b, :d, :c, :a, :e]
puts spearman(ranks1, ranks2) # = 0.3 (stuff is all over the place)