Ruby script to calculate a Spearman's Rank Correlation Coefficient.

calc_rcc_spearman.rb

#! /usr/local/bin/ruby

class Array
  def rcc_spearman(y)
    # 以下の場合は例外スロー
    # - 引数の配列が Array クラスでない
    # - 自身配列が空
    # - 配列サイズが異なる
    # - 数値以外のデータが存在する
    raise "Argument is not a Array class!"  unless y.class == Array
    raise "Self array is nil!"              if self.size == 0
    raise "Argument array size is invalid!" unless self.size == y.size
    (self + y).each do |v|
      raise "Items except numerical values exist!" unless v.to_s =~ /[\d\.]+/
    end

    # ランク付け
    rank_x = self.map { |v| self.count { |a| a > v } + 1 }
    rank_y = y.map { |v| y.count { |a| a > v } + 1 }
    # 同順位を中央（平均）順位(mid-rank)に
    rank_x = rank_x.map do |v|
      c = rank_x.count(v)
      (v...(v + c)).sum / c.to_f
    end
    rank_y = rank_y.map do |v|
      c = rank_y.count(v)
      (v...(v + c)).sum / c.to_f
    end
    # 同順位の数
    tai_x = rank_x.group_by { |a| a }.map { |k, v| [k, v.size] }.to_h
    tai_y = rank_y.group_by { |a| a }.map { |k, v| [k, v.size] }.to_h
    # Tx, Ty の sum 部分
    s_x = tai_x.select { |k, v| v > 1 }.map do |a|
      a[1] * a[1] * a[1] - a[1]
    end.sum
    s_y = tai_y.select { |k, v| v > 1 }.map do |a|
      a[1] * a[1] * a[1] - a[1]
    end.sum
    # 相関係数
    n = self.size
    n3 = n * n * n - n
    t_x = (n3 - s_x) / 12.0
    t_y = (n3 - s_y) / 12.0
    s = rank_x.zip(rank_y).inject(0) { |s, a| s + (a[0] - a[1]) * (a[0] - a[1]) }
    return (t_x + t_y - s) / (2 * Math.sqrt(t_x * t_y))
  end
end

# タイ（同順位）が存在しない例
#X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
#Y = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
# タイ（同順位）が存在する例
X = [1, 2, 3, 4, 5, 5, 7, 8, 9, 10]
Y = [1, 3, 5, 6, 9, 2, 4, 6, 8, 10]
# サイズが異なる例
#X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
#Y = [1, 3, 5, 7, 9, 2, 4, 6, 8]
# X のサイズがゼロの例
#X = []
#Y = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
# 数値以外のものが存在する例
#X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
#Y = [1, 3, 5, 7, 9, "ABC", 4, 6, 8, 10]

puts "  X = #{X}"
puts "  Y = #{Y}"
puts "  Spearman's RCC = #{X.rcc_spearman(Y)}"