Merge branch 'body-statistics' into rails-3-develop

1 files changed, 31 insertions, 0 deletions

diff --git a/lib/confidence_intervals.rb b/lib/confidence_intervals.rb
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+++ b/lib/confidence_intervals.rb
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+# 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