gistfile1.txt

Combining Tony Wright's post on startup acquisition rate (http://is.gd/101m1)
and Evan Miller's post on statistical significance in percentage ratings
(http://bit.ly/19CJAd).

Results:

{"CA"=>[2739, 188, "5.98%"],
 "NY"=>[692, 34, "3.54%"],
 "MA"=>[386, 20, "3.38%"],
 "TX"=>[323, 19, "3.80%"],
 "WA"=>[317, 26, "5.66%"],
 "FL"=>[254, 3, "0.40%"],
 "NJ"=>[227, 8, "1.80%"],
 "IL"=>[180, 9, "2.65%"],
 "VA"=>[164, 7, "2.08%"],
 "CO"=>[133, 7, "2.57%"],
 "PA"=>[131, 2, "0.42%"],
 "GA"=>[117, 2, "0.47%"],
 "MD"=>[94, 4, "1.67%"],
 "NC"=>[80, 1, "0.22%"],
 "AZ"=>[77, 1, "0.23%"]}


Script to calculate these results:

NB: script requires statistics2 gem, which can be found at
    http://github.com/abscondment/statistics2 and installed like so:

    $ gem sources -a http://gems.github.com (you only have to do this once)
    $ sudo gem install abscondment-statistics2


#!/usr/bin/ruby
require 'pp'
require 'statistics2'

def ci_lower_bound(pos, n, power=0.05)
    if n == 0
        return 0
    end
    z = Statistics2.pnormaldist(1-power/2)
    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

results = %{
CA 	2739 	41.2% 	188 	53.3% 	6.9%
NY 	692 	10.4% 	34 	9.6% 	4.9%
MA 	386 	5.8% 	20 	5.7% 	5.2%
TX 	323 	4.9% 	19 	5.4% 	5.9%
WA 	317 	4.8% 	26 	7.4% 	8.2%
FL 	254 	3.8% 	3 	0.8% 	1.2%
NJ 	227 	1.8% 	8 	2.3% 	6.6%
IL 	180 	2.7% 	9 	2.5% 	5.0%
VA 	164 	2.5% 	7 	2.0% 	4.3%
CO 	133 	2.0% 	7 	2.0% 	5.3%
PA 	131 	2.0% 	2 	0.6% 	1.5%
GA 	117 	1.8% 	2 	0.6% 	1.7%
MD 	94 	1.4% 	4 	1.1% 	4.3%
NC 	80 	1.2% 	1 	0.3% 	1.2%
AZ 	77 	1.2% 	1 	.3% 	1.3%
}.split(/\n/).reject!{|l| l.gsub(/[\s]+/,'').empty?}
results = results.inject({}) {
  |h,l|
  l = l.split
  h[l[0]] = [l[1].to_i, l[3].to_i, sprintf("%.2f%%", 100.0 * ci_lower_bound(l[3].to_f, l[1].to_f))]
  h
}
pp results