Ruby Z-Table lookup class. Given a z-score, return approximate percentile rank.

example.md

Data for the Z-Table comes from: http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm

How to use: http://www.measuringu.com/blog/interpret-responses.php

Example Usage:

Ztable.percentile(0.1388) => 0.5552

ztable.rb

class Ztable
  ZTABLE = <<-EOT
  Z       0       0.01    0.02    0.03    0.04    0.05    0.06    0.07    0.08    0.09
  0       0.5     0.504   0.508   0.512   0.516   0.5199  0.5239  0.5279  0.5319  0.5359
  0.1     0.5398  0.5438  0.5478  0.5517  0.5557  0.5596  0.5636  0.5675  0.5714  0.5753
  0.2     0.5793  0.5832  0.5871  0.591   0.5948  0.5987  0.6026  0.6064  0.6103  0.6141
  0.3     0.6179  0.6217  0.6255  0.6293  0.6331  0.6368  0.6406  0.6443  0.648   0.6517
  0.4     0.6554  0.6591  0.6628  0.6664  0.67    0.6736  0.6772  0.6808  0.6844  0.6879
  0.5     0.6915  0.695   0.6985  0.7019  0.7054  0.7088  0.7123  0.7157  0.719   0.7224
  0.6     0.7257  0.7291  0.7324  0.7357  0.7389  0.7422  0.7454  0.7486  0.7517  0.7549
  0.7     0.758   0.7611  0.7642  0.7673  0.7704  0.7734  0.7764  0.7794  0.7823  0.7852
  0.8     0.7881  0.791   0.7939  0.7967  0.7995  0.8023  0.8051  0.8078  0.8106  0.8133
  0.9     0.8159  0.8186  0.8212  0.8238  0.8264  0.8289  0.8315  0.834   0.8365  0.8389
  1       0.8413  0.8438  0.8461  0.8485  0.8508  0.8531  0.8554  0.8577  0.8599  0.8621
  1.1     0.8643  0.8665  0.8686  0.8708  0.8729  0.8749  0.877   0.879   0.881   0.883
  1.2     0.8849  0.8869  0.8888  0.8907  0.8925  0.8944  0.8962  0.898   0.8997  0.9015
  1.3     0.9032  0.9049  0.9066  0.9082  0.9099  0.9115  0.9131  0.9147  0.9162  0.9177
  1.4     0.9192  0.9207  0.9222  0.9236  0.9251  0.9265  0.9279  0.9292  0.9306  0.9319
  1.5     0.9332  0.9345  0.9357  0.937   0.9382  0.9394  0.9406  0.9418  0.9429  0.9441
  1.6     0.9452  0.9463  0.9474  0.9484  0.9495  0.9505  0.9515  0.9525  0.9535  0.9545
  1.7     0.9554  0.9564  0.9573  0.9582  0.9591  0.9599  0.9608  0.9616  0.9625  0.9633
  1.8     0.9641  0.9649  0.9656  0.9664  0.9671  0.9678  0.9686  0.9693  0.9699  0.9706
  1.9     0.9713  0.9719  0.9726  0.9732  0.9738  0.9744  0.975   0.9756  0.9761  0.9767
  2       0.9772  0.9778  0.9783  0.9788  0.9793  0.9798  0.9803  0.9808  0.9812  0.9817
  2.1     0.9821  0.9826  0.983   0.9834  0.9838  0.9842  0.9846  0.985   0.9854  0.9857
  2.2     0.9861  0.9864  0.9868  0.9871  0.9875  0.9878  0.9881  0.9884  0.9887  0.989
  2.3     0.9893  0.9896  0.9898  0.9901  0.9904  0.9906  0.9909  0.9911  0.9913  0.9916
  2.4     0.9918  0.992   0.9922  0.9925  0.9927  0.9929  0.9931  0.9932  0.9934  0.9936
  2.5     0.9938  0.994   0.9941  0.9943  0.9945  0.9946  0.9948  0.9949  0.9951  0.9952
  2.6     0.9953  0.9955  0.9956  0.9957  0.9959  0.996   0.9961  0.9962  0.9963  0.9964
  2.7     0.9965  0.9966  0.9967  0.9968  0.9969  0.997   0.9971  0.9972  0.9973  0.9974
  2.8     0.9974  0.9975  0.9976  0.9977  0.9977  0.9978  0.9979  0.9979  0.998   0.9981
  2.9     0.9981  0.9982  0.9982  0.9983  0.9984  0.9984  0.9985  0.9985  0.9986  0.9986
  3       0.9987  0.9987  0.9987  0.9988  0.9988  0.9989  0.9989  0.9989  0.999   0.999
  EOT

  def self.[](key)
    load_ztable unless @ztable
    @ztable[key]
  end

  def self.values
    load_ztable unless @ztable
    @ztable
  end

  def self.spit
    lines = ZTABLE.split("\n").map{|l| l.split(/[\t\s]+/)}
    lines.each do |line|
      puts line.map{|m| "%-8s" % m}.join
    end
  end

  def self.percentile(zscore)
    fl = (zscore.abs * 100).floor / 100.0
    cl = (zscore.abs * 100).ceil / 100.0
    low_value = self[fl]
    high_value = self[cl]

    return 0.0 if low_value.nil? || high_value.nil?

    weight = (zscore.abs - fl.abs) * 100.0
    value = (low_value + (high_value - low_value) * weight).round(4)
    zscore < 0.0 ? (1.0 - value) : value
  end

  def self.load_ztable
    lines = ZTABLE.split("\n").map{|l| l.split(/[\t\s]+/).slice(2, 10).map(&:to_f) }
    lines.shift
    @ztable = {}
    lines.each_with_index do |line, row|
      line.each_with_index do |value, col|
        @ztable[(row / 10.0 + col / 100.0).round(2)] = value
      end
    end
  end

end