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

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

Index: tools/telemetry/third_party/WebKit/PerformanceTests/resources/statistics.js
diff --git a/tools/telemetry/third_party/WebKit/PerformanceTests/resources/statistics.js b/tools/telemetry/third_party/WebKit/PerformanceTests/resources/statistics.js
index f5269c2c2b8769e43c65fc1c090d548a83b54520..faa5a4aa7988bda6347bd5234711149a50ae7b58 100644
--- a/tools/telemetry/third_party/WebKit/PerformanceTests/resources/statistics.js
+++ b/tools/telemetry/third_party/WebKit/PerformanceTests/resources/statistics.js
@@ -65,8 +65,7 @@ var Statistics = new (function () {
         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, opt_degreeOfFreedom) {
         var probability = (1 - (1 - confidenceLevel) / 2);
         if (!(probability in tDistributionInverseCDF)) {
             console.warn('We only support ' + this.supportedConfidenceLevels().map(
@@ -77,20 +76,31 @@ var Statistics = new (function () {
             return Number.POSITIVE_INFINITY;
 
         var cdfForProbability = tDistributionInverseCDF[probability];
-        var degreesOfFreedom = numberOfSamples - 1;
+        var degreesOfFreedom = opt_degreeOfFreedom || numberOfSamples - 1;

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

In theory (and most probably in practice as well), opt_degreeOfFreedom could be
zero (e.g. if you did only a single measurement per page on K pages, the degrees
of freedom would be K*(1 - 1) = 0. In that case, degreesOfFreedom would
incorrectly end up being K - 1. I think you should do something along the lines
of:

var degreesOfFreedom = opt_degreeOfFreedom;
if (degreesOfFreedom === undefined)
  degreesOfFreedom = numberOfSamples - 1;

Alternatively, you could use the ternary operator:

var degreesOfFreedom = opt_degreeOfFreedom === udnefined ? numberOfSamples - 1 :
opt_degreeOfFreedom;

[nednguyen, 2015/09/10 15:11:59]

Done. I picked the first one.

 
         // 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 quantile * this.sampleStandardDeviation(numberOfSamples, sum, squareSum) / Math.sqrt(numberOfSamples);
+          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) {
+        var sampleStandardDeviation = this.sampleStandardDeviation(numberOfSamples, sum, squareSum);
+        return this.confidenceIntervalDeltaFromStd(confidenceLevel, numberOfSamples, sampleStandardDeviation);
+    }
+
+    this.confidenceIntervalDeltaFromStd = function (confidenceLevel, numberOfSamples, sampleStandardDeviation, opt_degreeOfFreedom) {
+        var quantile = this.quantile(confidenceLevel, numberOfSamples, opt_degreeOfFreedom);
+        return quantile * sampleStandardDeviation / Math.sqrt(numberOfSamples);
+    }
+
+
     this.confidenceInterval = function (values, probability) {
         var sum = this.sum(values);
         var mean = sum / values.length;