[Telemetry] Update the ConfindenceInterval calculation in results.html to use

tools/telemetry/third_party/WebKit/PerformanceTests/resources/statistics.js

 /*
  * Copyright (C) 2012, 2013 Apple Inc. All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
  * are met:
  * 1. Redistributions of source code must retain the above copyright
  *    notice, this list of conditions and the following disclaimer.
  * 2. Redistributions in binary form must reproduce the above copyright
  *    notice, this list of conditions and the following disclaimer in the
@@ skipping 47 matching lines @@
             - sum * sum / (numberOfSamples - 1) / numberOfSamples);
     }
 
     this.supportedConfidenceLevels = function () {
         var supportedLevels = [];
         for (var quantile in tDistributionInverseCDF)
             supportedLevels.push((1 - (1 - quantile) * 2).toFixed(2));
         return supportedLevels;
     }
 
-    // Computes the delta d s.t. (mean - d, mean + d) is the confidence interval with the specified confidence level in O(1).
-    this.confidenceIntervalDelta = function (confidenceLevel, numberOfSamples, sum, squareSum) {
+    this.quantile = function (confidenceLevel, numberOfSamples) {
         var probability = (1 - (1 - confidenceLevel) / 2);
         if (!(probability in tDistributionInverseCDF)) {
             console.warn('We only support ' + this.supportedConfidenceLevels().map(
                 function (level) { return level * 100 + '%'; } ).join(', ') + ' confidence intervals.');
             return NaN;
         }
         if (numberOfSamples < 2)
             return Number.POSITIVE_INFINITY;
 
         var cdfForProbability = tDistributionInverseCDF[probability];
         var degreesOfFreedom = numberOfSamples - 1;

[petrcermak, 2015/09/09 18:44:40]

The degrees of freedom should be changed as well. For example if get 3 samples
on 2 pages, there will be only 2*(3-1)=4 degrees of freedom (not 2*3-1=5) when
using the new calculation (because we have 2 means).

[nednguyen, 2015/09/09 22:29:06]

Done. But this is no-op change for now. I will hook up degree of freedom change
to list_of_scalar_value in the next patch.

[petrcermak, 2015/09/10 09:04:08]

Great, thanks!

 
         // tDistributionQuantile(degreesOfFreedom, confidenceLevel) * sampleStandardDeviation / sqrt(numberOfSamples) * S/sqrt(numberOfSamples)
         if (degreesOfFreedom <= 100)
-          var quantile = cdfForProbability[degreesOfFreedom - 1]; // The first entry is for the one degree of freedom.
+          return cdfForProbability[degreesOfFreedom - 1]; // The first entry is for the one degree of freedom.
         else if (degreesOfFreedom <= 300)
-          var quantile = cdfForProbability[Math.round(degreesOfFreedom / 10) + 100 - 10 - 1];
+          return cdfForProbability[Math.round(degreesOfFreedom / 10) + 100 - 10 - 1];
         else if (degreesOfFreedom <= 1300)
-          var quantile = cdfForProbability[Math.round(degreesOfFreedom / 100) + 120 - 3 - 1];
+          return cdfForProbability[Math.round(degreesOfFreedom / 100) + 120 - 3 - 1];
         else
-          var quantile = cdfForProbability[cdfForProbability.length - 1];
+          return cdfForProbability[cdfForProbability.length - 1];
+    }
+
+    // Computes the delta d s.t. (mean - d, mean + d) is the confidence interval with the specified confidence level in O(1).
+    this.confidenceIntervalDelta = function (confidenceLevel, numberOfSamples, sum, squareSum) {

[petrcermak, 2015/09/09 18:44:40]

To reduce code duplication, this function should use
confidenceIntervalDeltaFromStd:

this.confidenceIntervalDelta = function (confidenceLevel, numberOfSamples, sum,
squareSum) {
  var sampleStandardDeviation = this.sampleStandardDeviation(numberOfSamples,
sum, squareSum);
  return this.confidenceIntervalDeltaFromStd(confidenceLevel, numberOfSamples,
sampleStandardDeviation);
}

[nednguyen, 2015/09/09 22:29:06]

Done.

+        var quantile = this.quantile(confidenceLevel, numberOfSamples);
         return quantile * this.sampleStandardDeviation(numberOfSamples, sum, squareSum) / Math.sqrt(numberOfSamples);
     }
 
+    this.confidenceIntervalDeltaFromStd = function (confidenceLevel, numberOfSamples, sampleStandardDeviation) {
+        var quantile = this.quantile(confidenceLevel, numberOfSamples);
+        return quantile * sampleStandardDeviation / Math.sqrt(numberOfSamples);
+    }
+
+
     this.confidenceInterval = function (values, probability) {
         var sum = this.sum(values);
         var mean = sum / values.length;
         var delta = this.confidenceIntervalDelta(probability || 0.95, values.length, sum, this.squareSum(values));
         return [mean - delta, mean + delta];
     }
 
     // See http://en.wikipedia.org/wiki/Student's_t-distribution#Table_of_selected_values
     // This table contains one sided (a.k.a. tail) values.
     // Use TINV((1 - probability) * 2, df) in your favorite spreadsheet software to compute these.
@@ skipping 76 matching lines @@
             // Infinity
             2.326348],
     };
 
 })();
 
 if (typeof module != 'undefined') {
     for (var key in Statistics)
         module.exports[key] = Statistics[key];
 }