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Diffstat (limited to 'lib/confidence_intervals.rb')
| -rw-r--r-- | lib/confidence_intervals.rb | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/lib/confidence_intervals.rb b/lib/confidence_intervals.rb new file mode 100644 index 000000000..9fe38045a --- /dev/null +++ b/lib/confidence_intervals.rb @@ -0,0 +1,31 @@ +# Calculate the confidence interval for a samples from a binonial +# distribution using Wilson's score interval. For more theoretical +# details, please see: +# +# http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson%20score%20interval +# +# This is a variant of the function suggested here: +# +# http://www.evanmiller.org/how-not-to-sort-by-average-rating.html +# +# total: the total number of observations +# successes: the subset of those observations that were "successes" +# power: for a 95% confidence interval, this should be 0.05 +# +# The naive proportion is (successes / total). This returns an array +# with the proportions that represent the lower and higher confidence +# intervals around that. + +require 'statistics2' + +def ci_bounds(successes, total, power) + if total == 0 + raise RuntimeError, "Can't calculate the CI for 0 observations" + end + z = Statistics2.pnormaldist(1 - power/2) + phat = successes.to_f/total + offset = z*Math.sqrt((phat*(1 - phat) + z*z/(4*total))/total) + denominator = 1 + z*z/total + return [(phat + z*z/(2*total) - offset)/denominator, + (phat + z*z/(2*total) + offset)/denominator] +end |