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source: trunk/sources/HeuristicLab.Analysis/3.3/Statistics/SampleSizeDetermination.cs @ 11703

Last change on this file since 11703 was 11703, checked in by ascheibe, 9 years ago

#2031 moved statistic algs and unit tests to trunk

File size: 4.1 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2014 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
4 *
5 * This file is part of HeuristicLab.
6 *
7 * HeuristicLab is free software: you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation, either version 3 of the License, or
10 * (at your option) any later version.
11 *
12 * HeuristicLab is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
19 */
20#endregion
21
22using System;
23using System.Linq;
24using HeuristicLab.Common;
25
26namespace HeuristicLab.Analysis.Statistics {
27  public static class SampleSizeDetermination {
28    /// <summary>
29    /// Determines for a given sample the required sample size as described in
30    /// Göran Kauermann, Helmut Küchenhoff: Stichproben: Methoden und praktische Umsetzung mit R, section 2.27.
31    /// </summary>
32    /// <param name="samples">The pilot sample.</param>
33    /// <param name="conf">Confidence Interval.</param>
34    /// <returns>Number of required samples for the given confidence interval. </returns>
35    public static int DetermineSampleSizeByEstimatingMean(double[] samples, double conf = 0.95) {
36      if (conf < 0.0 || conf > 1.0) throw new ArgumentException("The confidence interval must be between zero and one.");
37
38      var confInterval = samples.ConfidenceIntervals(0.95);
39      double e = (confInterval.Item2 - confInterval.Item1) / 2;
40      double s = samples.StandardDeviation();
41      double z = alglib.invnormaldistribution((conf + 1) / 2);
42      double n = samples.Count();
43
44      double result = Math.Pow(s, 2) / ((Math.Pow(e, 2) / Math.Pow(z, 2)) + (Math.Pow(s, 2) / n));
45
46      result = Math.Ceiling(result);
47      if (result > int.MaxValue)
48        return int.MaxValue;
49      else
50        return (int)result;
51    }
52
53    public static int DetermineSampleSizeByEstimatingMeanForLargeSampleSizes(double[] samples, double conf = 0.95) {
54      if (conf < 0.0 || conf > 1.0) throw new ArgumentException("The confidence interval must be between zero and one.");
55
56      var confInterval = samples.ConfidenceIntervals(0.95);
57      double e = (confInterval.Item2 - confInterval.Item1) / 2;
58      double s = samples.StandardDeviation();
59      double z = alglib.invnormaldistribution((conf + 1) / 2);
60
61      double result = Math.Pow(z, 2) * (Math.Pow(s, 2) / Math.Pow(e, 2));
62
63      result = Math.Ceiling(result);
64      if (result > int.MaxValue)
65        return int.MaxValue;
66      else
67        return (int)result;
68    }
69
70    /// <summary>
71    /// Calculates Cohen's d.
72    /// </summary>
73    /// <returns>Cohen's d.
74    /// d = 0.2 means small effect
75    /// d = 0.5 means medium effect
76    /// d = 0.8 means big effect
77    /// According to Wikipedia this means: "A lower Cohen's d indicates a necessity of larger sample sizes, and vice versa."
78    /// </returns>
79    public static double CalculateCohensD(double[] d1, double[] d2) {
80      double x1, x2, s1, s2;
81
82      x1 = d1.Average();
83      x2 = d2.Average();
84      s1 = d1.Variance();
85      s2 = d2.Variance();
86
87      return Math.Abs(x1 - x2) / Math.Sqrt((s1 + s2) / 2);
88    }
89
90    /// <summary>
91    /// Calculates Hedges' g.
92    /// Hedges' g works like Cohen's d but corrects for bias.
93    /// </summary>
94    /// <returns>Hedges' g</returns>
95    public static double CalculateHedgesG(double[] d1, double[] d2) {
96      double x1, x2, s1, s2, n1, n2, s, g, c;
97
98      x1 = d1.Average();
99      x2 = d2.Average();
100      s1 = d1.Variance();
101      s2 = d2.Variance();
102      n1 = d1.Count();
103      n2 = d2.Count();
104
105      s = Math.Sqrt(((n1 - 1) * s1 + (n2 - 1) * s2) / (n1 + n2 - 2));
106      g = Math.Abs(x1 - x2) / s;
107      c = (1 - (3 / (4 * (n1 + n2) - 9))) * g;
108
109      return c;
110    }
111  }
112}
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