How Not To Sort By Average Rating

gistfile1.rb

# How Not To Sort By Average Rating
# url: http://www.evanmiller.org/how-not-to-sort-by-average-rating.html
# lib: http://blade.nagaokaut.ac.jp/~sinara/ruby/math/statistics2/ (need compile)

# statistics2 disabled
#require 'statistics2'

def ci_lower_bound(pos, n, power)
    if n == 0
        return 0
    end
    # statistics2 disabled / z hardcoded
    #z = Statistics2.pnormaldist(1-power/2)
    #z = Statistics2.pnormaldist(1-0.05/2) = 1.95996397158435
    z = 1.95996397158435
    phat = 1.0*pos/n
    (phat + z*z/(2*n) - z * Math.sqrt((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n)
end

puts ci_lower_bound(234, 600, 0.05) # 0.351790426361396
puts ci_lower_bound(2, 5, 0.05) # 0.11762077514747
puts ci_lower_bound(398, 400, 0.05) # 0.981955081697407
puts ci_lower_bound(19999, 20000, 0.05) # 0.999716809432394