1 | #ifndef _theplu_yat_statistics_fisher_ |
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2 | #define _theplu_yat_statistics_fisher_ |
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3 | |
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4 | // $Id: Fisher.h 3455 2015-12-10 06:57:14Z peter $ |
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5 | |
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6 | /* |
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7 | Copyright (C) 2004, 2005 Peter Johansson |
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8 | Copyright (C) 2006, 2007, 2008 Jari Häkkinen, Peter Johansson |
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9 | Copyright (C) 2009, 2011, 2013, 2014, 2015 Peter Johansson |
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10 | |
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11 | This file is part of the yat library, http://dev.thep.lu.se/yat |
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12 | |
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13 | The yat library is free software; you can redistribute it and/or |
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14 | modify it under the terms of the GNU General Public License as |
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15 | published by the Free Software Foundation; either version 3 of the |
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16 | License, or (at your option) any later version. |
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17 | |
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18 | The yat library is distributed in the hope that it will be useful, |
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19 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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20 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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21 | General Public License for more details. |
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22 | |
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23 | You should have received a copy of the GNU General Public License |
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24 | along with yat. If not, see <http://www.gnu.org/licenses/>. |
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25 | */ |
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26 | |
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27 | #include <yat/utility/deprecate.h> |
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28 | |
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29 | namespace theplu { |
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30 | namespace yat { |
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31 | namespace statistics { |
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32 | |
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33 | /** |
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34 | @brief Fisher's exact test. |
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35 | |
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36 | Fisher's Exact test is a procedure that you can use for data |
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37 | in a two by two contingency table: \f[ \begin{tabular}{|c|c|} |
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38 | \hline a&b \tabularnewline \hline c&d \tabularnewline \hline |
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39 | \end{tabular} \f] Fisher's Exact Test is based on exact |
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40 | probabilities from a specific distribution (the hypergeometric |
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41 | distribution). There's really no lower bound on the amount of |
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42 | data that is needed for Fisher's Exact Test. You do have to |
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43 | have at least one data value in each row and one data value in |
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44 | each column. If an entire row or column is zero, then you |
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45 | don't really have a 2 by 2 table. But you can use Fisher's |
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46 | Exact Test when one of the cells in your table has a zero in |
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47 | it. Fisher's Exact Test is also very useful for highly |
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48 | imbalanced tables. If one or two of the cells in a two by two |
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49 | table have numbers in the thousands and one or two of the |
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50 | other cells has numbers less than 5, you can still use |
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51 | Fisher's Exact Test. For very large tables (where all four |
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52 | entries in the two by two table are large), your computer may |
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53 | take too much time to compute Fisher's Exact Test. In these |
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54 | situations, though, you might as well use the Chi-square test |
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55 | because a large sample approximation (that the Chi-square test |
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56 | relies on) is very reasonable. If all elements are larger than |
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57 | 10 a Chi-square test is reasonable to use. |
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58 | |
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59 | @note The statistica assumes that each column and row sum, |
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60 | respectively, are fixed. Just because you have a 2x2 table, this |
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61 | assumtion does not necessarily match you experimental setup. See |
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62 | e.g. Barnard's test for alternative. |
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63 | */ |
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64 | |
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65 | class Fisher |
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66 | { |
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67 | |
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68 | public: |
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69 | /// |
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70 | /// Default Constructor. |
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71 | /// |
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72 | /// \param yates if true Yates's correction is used for |
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73 | /// chi-squared calculation |
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74 | /// |
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75 | Fisher(bool yates=false); |
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76 | |
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77 | /// |
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78 | /// Destructor |
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79 | /// |
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80 | virtual ~Fisher(void); |
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81 | |
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82 | |
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83 | /** |
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84 | The Chi2 score is calculated as \f$ \sum |
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85 | \frac{(O_i-E_i)^2}{E_i}\f$ where \a E is expected value and \a |
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86 | O is observed value. |
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87 | |
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88 | If indicated in constructor, Yates's correction is used, i.e., |
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89 | Chi2 is calculated as \f$ \frac{(|O_i-E_i|-0.5)^2}{E_i} \f$ |
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90 | |
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91 | |
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92 | \see expected(double&, double&, double&, double&) |
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93 | |
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94 | \return Chi2 score |
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95 | */ |
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96 | double Chi2(void) const; |
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97 | |
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98 | /** |
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99 | Calculates the expected values under the null hypothesis. |
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100 | \f$ a' = \frac{(a+c)(a+b)}{a+b+c+d} \f$, |
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101 | \f$ b' = \frac{(a+b)(b+d)}{a+b+c+d} \f$, |
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102 | \f$ c' = \frac{(a+c)(c+d)}{a+b+c+d} \f$, |
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103 | \f$ d' = \frac{(b+d)(c+d)}{a+b+c+d} \f$, |
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104 | */ |
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105 | void expected(double& a, double& b, double& c, double& d) const; |
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106 | |
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107 | /// |
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108 | /// If all elements in table is at least minimum_size(), a Chi2 |
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109 | /// approximation is used for p-value calculation. |
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110 | /// |
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111 | /// @return reference to minimum_size |
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112 | /// |
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113 | unsigned int& minimum_size(void); |
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114 | |
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115 | /// |
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116 | /// If all elements in table is at least minimum_size(), a Chi2 |
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117 | /// approximation is used for p-value calculation. |
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118 | /// |
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119 | /// @return const reference to minimum_size |
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120 | /// |
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121 | const unsigned int& minimum_size(void) const; |
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122 | |
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123 | /** |
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124 | Calculates probability to get oddsratio (or smaller). |
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125 | |
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126 | If all elements in table is at least minimum_size(), a Chi2 |
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127 | approximation is used. |
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128 | |
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129 | \since New in yat 0.11 |
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130 | */ |
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131 | double p_left(void) const; |
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132 | |
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133 | /** |
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134 | Calculates probability to get oddsratio (or greater). |
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135 | |
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136 | If all elements in table is at least minimum_size(), a Chi2 |
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137 | approximation is used. |
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138 | |
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139 | \since New in yat 0.11 |
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140 | */ |
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141 | double p_right(void) const; |
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142 | |
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143 | /** |
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144 | If all elements in table is at least minimum_size(), a Chi2 |
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145 | approximation is used. |
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146 | |
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147 | Otherwise a two-sided p-value is calculated using the |
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148 | hypergeometric distribution |
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149 | \f$ \sum_k P(k) \f$ where summation runs over \a k such that |
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150 | \f$ P(k) \le P(a) \f$. |
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151 | |
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152 | \return two-sided p-value |
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153 | */ |
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154 | double p_value(void) const; |
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155 | |
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156 | /// |
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157 | /// One-sided p-value is probability to get larger (or equal) oddsratio. |
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158 | /// |
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159 | /// If all elements in table is at least minimum_size(), a Chi2 |
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160 | /// approximation is used. |
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161 | /// |
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162 | /// @return One-sided p-value |
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163 | /// |
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164 | /// \deprecated Provided for backward compatibility with the 0.10 |
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165 | /// API. Use p_right() instead. |
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166 | /// |
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167 | double p_value_one_sided() const YAT_DEPRECATE; |
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168 | |
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169 | /** |
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170 | Function calculating odds ratio from 2x2 table |
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171 | \f[ \begin{tabular}{|c|c|} |
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172 | \hline a&b \tabularnewline \hline c&d \tabularnewline \hline |
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173 | \end{tabular} \f] as \f$ \frac{ad}{bc} \f$ |
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174 | |
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175 | Object will remember the values of \a a, \a b, \a c, and \a d. |
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176 | |
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177 | @return odds ratio. |
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178 | |
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179 | @throw If table is invalid a runtime_error is thrown. A table |
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180 | is invalid if a row or column sum is zero. |
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181 | */ |
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182 | double oddsratio(const unsigned int a, const unsigned int b, |
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183 | const unsigned int c, const unsigned int d); |
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184 | |
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185 | /** |
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186 | \return oddsratio loaded via oddsratio(4) |
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187 | |
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188 | \since New in yat 0.8 |
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189 | */ |
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190 | double oddsratio(void) const; |
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191 | |
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192 | private: |
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193 | bool calculate_p_exact(void) const; |
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194 | |
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195 | // two-sided |
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196 | double p_value_approximative(void) const; |
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197 | // two-sided |
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198 | double p_value_exact(void) const; |
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199 | // calculate two-sided p-value to get k (or fewer) wins when |
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200 | // drawing t samples out of of a population of n1 wins and n2 losses |
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201 | double p_value_exact(unsigned int k, unsigned int n1, unsigned int n2, |
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202 | unsigned int t) const; |
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203 | |
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204 | double lower_tail(unsigned int k, unsigned int n1, unsigned int n2, |
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205 | unsigned int t) const; |
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206 | |
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207 | // return P(X=k+1) / P(X=k) |
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208 | double hypergeometric_ratio(unsigned int k, unsigned int n1, |
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209 | unsigned int n2, unsigned int t) const; |
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210 | double choose_ratio(unsigned int n, unsigned int k) const; |
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211 | |
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212 | double p_left_exact(void) const; |
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213 | double p_right_exact(void) const; |
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214 | |
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215 | double yates(unsigned int o, double e) const; |
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216 | |
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217 | unsigned int a_; |
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218 | unsigned int b_; |
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219 | unsigned int c_; |
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220 | unsigned int d_; |
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221 | unsigned int minimum_size_; |
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222 | double oddsratio_; |
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223 | bool yates_; |
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224 | }; |
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225 | |
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226 | }}} // of namespace statistics, yat, and theplu |
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227 | |
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228 | #endif |
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