RubyでSpearman's R （順位相関係数）を計算しよう
Rubyの配列(Arrayクラス)を拡張して和，分散，標準偏差，相関係数を計算する - Loud Minority や Ruby で Mann-Whitney U test をする - Loud Minority の続き．
Spearman(スピアマン)の順位相関係数を計算しよう．
http://d.hatena.ne.jp/sesejun/20070502/p1 を改良して，順位相関係数を計算できるようにしてみました．
使い方
x = [2.8,3.4,3.6,5.8,7.0,9.5,10.2,12.3,13.2,13.4]
y = [0.6,3.0,0.4,1.5,15.0,13.4,7.6,19.8,18.3,18.9]
puts x.corrcoef(y, :spearman)
#=> 0.854545454545454
ソース
class Array
def sum_with_number
s = 0.0
n = 0
self.each do |v|
next if v.nil?
s += v.to_f
n += 1
end
[s, n]
end
def sum
s, n = self.sum_with_number
s
end
def avg
s, n = self.sum_with_number
s / n
end
alias mean avg
def var
c = 0
while self[c].nil?
c += 1
end
mean = self[c].to_f
sum = 0.0
n = 1
(c+1).upto(self.size-1) do |i|
next if self[i].nil?
sweep = n.to_f / (n + 1.0)
delta = self[i].to_f - mean
sum += delta * delta * sweep
mean += delta / (n + 1.0)
n += 1
end
sum / n.to_f
end
def stddev
Math.sqrt(self.var)
end
def corrcoef(y, method = :pearson)
if method == :pearson
corrcoef_pearson(y)
elsif method == :spearman
corrcoef_spearman(y)
end
end
def corrcoef_pearson(y)
raise "Invalid Argument Array Size" unless self.size == y.size
sum_sq_x = 0.0
sum_sq_y = 0.0
sum_coproduct = 0.0
c = 0
while self[c].nil? || y[c].nil?
c += 1
end
mean_x = self[c].to_f
mean_y = y[c].to_f
n = 1
(c+1).upto(self.size-1) do |i|
next if self[i].nil? || y[i].nil?
sweep = n.to_f / (n + 1.0)
delta_x = self[i].to_f - mean_x
delta_y = y[i].to_f - mean_y
sum_sq_x += delta_x * delta_x * sweep
sum_sq_y += delta_y * delta_y * sweep
mean_x += delta_x / (n + 1.0)
mean_y += delta_y / (n + 1.0)
n += 1
end
pop_sd_x = Math.sqrt(sum_sq_x / n.to_f)
pop_sd_y = Math.sqrt(sum_sq_y / n.to_f)
cov_x_y = sum_coproduct / n.to_f
cov_x_y / (pop_sd_x * pop_sd_y)
end
def corrcoef_spearman(y)
xo = Array.new
yo = Array.new
self.size.times do |n|
xo << [n, self[n]]
yo << [n, y[n]]
end
xo = xo.sort{|a, b| a[1]<=>b[1]}
yo = yo.sort{|a, b| a[1]<=>b[1]}
self.size.times do |n|
xo[n][1] = n
yo[n][1] = n
end
xo = xo.sort{|a, b| a[0]<=>b[0]}
yo = yo.sort{|a, b| a[0]<=>b[0]}
xary = xo.map{|v| v[1]}
yary = yo.map{|v| v[1]}
xary.corrcoef_pearson(yary)
end
end
