1 | #region License Information |
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2 | /* HeuristicLab |
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3 | * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL) |
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4 | * |
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5 | * This file is part of HeuristicLab. |
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6 | * |
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7 | * HeuristicLab is free software: you can redistribute it and/or modify |
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8 | * it under the terms of the GNU General Public License as published by |
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9 | * the Free Software Foundation, either version 3 of the License, or |
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10 | * (at your option) any later version. |
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11 | * |
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12 | * HeuristicLab is distributed in the hope that it will be useful, |
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 | * GNU General Public License for more details. |
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16 | * |
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17 | * You should have received a copy of the GNU General Public License |
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18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>. |
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19 | */ |
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20 | #endregion |
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21 | |
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22 | using System; |
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23 | using System.Linq; |
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24 | using HeuristicLab.Common; |
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25 | |
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26 | namespace HeuristicLab.Analysis.Statistics { |
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27 | public static class SampleSizeDetermination { |
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28 | /// <summary> |
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29 | /// Determines for a given sample the required sample size as described in |
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30 | /// Göran Kauermann, Helmut Küchenhoff: Stichproben: Methoden und praktische Umsetzung mit R, section 2.27. |
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31 | /// </summary> |
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32 | /// <param name="samples">The pilot sample.</param> |
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33 | /// <param name="conf">Confidence Interval.</param> |
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34 | /// <returns>Number of required samples for the given confidence interval. </returns> |
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35 | public static int DetermineSampleSizeByEstimatingMean(double[] samples, double conf = 0.95) { |
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36 | if (conf < 0.0 || conf > 1.0) throw new ArgumentException("The confidence interval must be between zero and one."); |
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37 | |
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38 | var confInterval = samples.ConfidenceIntervals(conf); |
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39 | double e = (confInterval.Item2 - confInterval.Item1) / 2; |
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40 | double s = samples.StandardDeviation(); |
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41 | double z = alglib.invnormaldistribution((conf + 1) / 2); |
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42 | double n = samples.Count(); |
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43 | |
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44 | double result = Math.Pow(s, 2) / ((Math.Pow(e, 2) / Math.Pow(z, 2)) + (Math.Pow(s, 2) / n)); |
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45 | |
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46 | result = Math.Ceiling(result); |
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47 | if (result > int.MaxValue) |
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48 | return int.MaxValue; |
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49 | else |
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50 | return (int)result; |
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51 | } |
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52 | |
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53 | /// <summary> |
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54 | /// Calculates Cohen's d. |
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55 | /// </summary> |
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56 | /// <returns>Cohen's d. |
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57 | /// d = 0.2 means small effect |
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58 | /// d = 0.5 means medium effect |
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59 | /// d = 0.8 means big effect |
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60 | /// According to Wikipedia this means: "A lower Cohen's d indicates a necessity of larger sample sizes, and vice versa." |
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61 | /// </returns> |
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62 | public static double CalculateCohensD(double[] d1, double[] d2) { |
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63 | double x1, x2, s1, s2; |
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64 | |
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65 | x1 = d1.Average(); |
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66 | x2 = d2.Average(); |
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67 | s1 = d1.Variance(); |
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68 | s2 = d2.Variance(); |
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69 | |
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70 | return Math.Abs(x1 - x2) / Math.Sqrt((s1 + s2) / 2); |
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71 | } |
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72 | |
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73 | /// <summary> |
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74 | /// Calculates Hedges' g. |
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75 | /// Hedges' g works like Cohen's d but corrects for bias. |
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76 | /// </summary> |
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77 | /// <returns>Hedges' g</returns> |
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78 | public static double CalculateHedgesG(double[] d1, double[] d2) { |
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79 | double x1, x2, s1, s2, n1, n2, s, g, c; |
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80 | |
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81 | x1 = d1.Average(); |
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82 | x2 = d2.Average(); |
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83 | s1 = d1.Variance(); |
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84 | s2 = d2.Variance(); |
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85 | n1 = d1.Count(); |
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86 | n2 = d2.Count(); |
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87 | |
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88 | s = Math.Sqrt(((n1 - 1) * s1 + (n2 - 1) * s2) / (n1 + n2 - 2)); |
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89 | g = Math.Abs(x1 - x2) / s; |
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90 | c = (1 - (3 / (4 * (n1 + n2) - 9))) * g; |
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91 | |
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92 | return c; |
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93 | } |
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94 | } |
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95 | } |
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