Naive pairwise comparisons power

wilson-interval.rb

#!/usr/bin/ruby -w

require 'statistics2'

class Numeric
  def to_percent
    "#{(self * 100).round}%"
  end
end

def puts_interval(wins, n, certainty)
  z = Statistics2.pnormaldist(certainty)
  phat = 1.0 * wins / n.to_f
  denominator = 1 + z*z / n.to_f
  estimate = (phat + z*z / (2.0 * n)) / denominator
  plusminus = z * Math.sqrt( (phat * (1-phat) + (z*z) / (4.0*n)) / n ) / denominator
  lower = estimate - plusminus
  higher = estimate + plusminus
  puts <<EOM
With #{wins} wins out of #{n} battles, you can be #{certainty.to_percent}
sure that the "true" value is between: #{lower.to_percent} and #{higher.to_percent}
EOM
end

puts_interval 75, 100, 0.95