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import numpy |
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def chi_square_test(observed, expected, alpha=0.05, df=None): |
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"""Testing Goodness-of-fit Test with Pearson's Chi-squared Test. |
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Args: |
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observed (list of ints): List of # of counts each element is observed. |
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expected (list of floats): List of # of counts each element is expected |
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to be observed. |
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alpha (float): Significance level. Currently, |
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only 0.05 and 0.01 are acceptable. |
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df (int): Degree of freedom. If ``None``, |
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it is set to the length of ``observed`` minus 1. |
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Returns: |
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bool: ``True`` if null hypothesis is **NOT** reject. |
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Otherwise, ``False``. |
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""" |
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if df is None: |
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df = observed.size - 1 |
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if alpha == 0.01: |
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alpha_idx = 0 |
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elif alpha == 0.05: |
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alpha_idx = 1 |
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else: |
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raise ValueError('support only alpha == 0.05 or 0.01') |
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chi_square = numpy.sum((observed - expected) ** 2 / expected) |
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return chi_square < chi_square_table[alpha_idx][df] |
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chi_square_table = [ |
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[None, |
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6.635, 9.210, 11.345, 13.277, 15.086, |
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16.812, 18.475, 20.090, 21.666, 23.209, |
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24.725, 26.217, 27.688, 29.141, 30.578, |
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32.000, 33.409, 34.805, 36.191, 37.566, |
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38.932, 40.289, 41.638, 42.980, 44.314, |
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45.642, 46.963, 48.278, 49.588, 50.892, |
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52.191, 53.486, 54.776, 56.061, 57.342, |
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58.619, 59.893, 61.162, 62.428, 63.691, |
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64.950, 66.206, 67.459, 68.710, 69.957, |
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71.201, 72.443, 73.683, 74.919, 76.154, |
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77.386, 78.616, 79.843, 81.069, 82.292, |
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83.513, 84.733, 85.950, 87.166, 88.379, |
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89.591, 90.802, 92.010, 93.217, 94.422, |
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95.626, 96.828, 98.028, 99.228, 100.425, |
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101.621, 102.816, 104.010, 105.202, 106.393, |
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107.583, 108.771, 109.958, 111.144, 112.329, |
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113.512, 114.695, 115.876, 117.057, 118.236, |
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119.414, 120.591, 121.767, 122.942, 124.116, |
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125.289, 126.462, 127.633, 128.803, 129.973, |
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131.141, 132.309, 133.476, 134.642, 135.807, |
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136.971, 138.134, 139.297, 140.459, 141.620, |
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142.780, 143.940, 145.099, 146.257, 147.414, |
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148.571, 149.727, 150.882, 152.037, 153.191, |
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154.344, 155.496, 156.648, 157.800, 158.950, |
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160.100, 161.250, 162.398, 163.546, 164.694, |
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165.841, 166.987, 168.133, 169.278, 170.423, |
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171.567, 172.711, 173.854, 174.996, 176.138, |
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177.280, 178.421, 179.561, 180.701, 181.840, |
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182.979, 184.118, 185.256, 186.393, 187.530, |
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188.666, 189.802, 190.938, 192.073, 193.208, |
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194.342, 195.476, 196.609, 197.742, 198.874, |
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200.006, 201.138, 202.269, 203.400, 204.530, |
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205.660, 206.790, 207.919, 209.047, 210.176, |
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211.304, 212.431, 213.558, 214.685, 215.812, |
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216.938, 218.063, 219.189, 220.314, 221.438, |
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222.563, 223.687, 224.810, 225.933, 227.056, |
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228.179, 229.301, 230.423, 231.544, 232.665, |
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233.786, 234.907, 236.027, 237.147, 238.266, |
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239.386, 240.505, 241.623, 242.742, 243.860, |
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244.977, 246.095, 247.212, 248.329, 249.445, |
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250.561, 251.677, 252.793, 253.908, 255.023, |
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256.138, 257.253, 258.367, 259.481, 260.595, |
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261.708, 262.821, 263.934, 265.047, 266.159, |
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267.271, 268.383, 269.495, 270.606, 271.717, |
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272.828, 273.939, 275.049, 276.159, 277.269, |
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278.379, 279.488, 280.597, 281.706, 282.814, |
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283.923, 285.031, 286.139, 287.247, 288.354, |
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289.461, 290.568, 291.675, 292.782, 293.888, |
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294.994, 296.100, 297.206, 298.311, 299.417, |
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300.522, 301.626, 302.731, 303.835, 304.940], |
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[None, |
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3.841, 5.991, 7.815, 9.488, 11.070, |
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12.592, 14.067, 15.507, 16.919, 18.307, |
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19.675, 21.026, 22.362, 23.685, 24.996, |
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26.296, 27.587, 28.869, 30.144, 31.410, |
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32.671, 33.924, 35.172, 36.415, 37.652, |
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38.885, 40.113, 41.337, 42.557, 43.773, |
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44.985, 46.194, 47.400, 48.602, 49.802, |
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50.998, 52.192, 53.384, 54.572, 55.758, |
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56.942, 58.124, 59.304, 60.481, 61.656, |
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62.830, 64.001, 65.171, 66.339, 67.505, |
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68.669, 69.832, 70.993, 72.153, 73.311, |
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74.468, 75.624, 76.778, 77.931, 79.082, |
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80.232, 81.381, 82.529, 83.675, 84.821, |
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85.965, 87.108, 88.250, 89.391, 90.531, |
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91.670, 92.808, 93.945, 95.081, 96.217, |
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97.351, 98.484, 99.617, 100.749, 101.879, |
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103.010, 104.139, 105.267, 106.395, 107.522, |
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108.648, 109.773, 110.898, 112.022, 113.145, |
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114.268, 115.390, 116.511, 117.632, 118.752, |
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119.871, 120.990, 122.108, 123.225, 124.342, |
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125.458, 126.574, 127.689, 128.804, 129.918, |
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131.031, 132.144, 133.257, 134.369, 135.480, |
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136.591, 137.701, 138.811, 139.921, 141.030, |
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142.138, 143.246, 144.354, 145.461, 146.567, |
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147.674, 148.779, 149.885, 150.989, 152.094, |
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153.198, 154.302, 155.405, 156.508, 157.610, |
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158.712, 159.814, 160.915, 162.016, 163.116, |
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164.216, 165.316, 166.415, 167.514, 168.613, |
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169.711, 170.809, 171.907, 173.004, 174.101, |
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175.198, 176.294, 177.390, 178.485, 179.581, |
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180.676, 181.770, 182.865, 183.959, 185.052, |
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186.146, 187.239, 188.332, 189.424, 190.516, |
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191.608, 192.700, 193.791, 194.883, 195.973, |
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197.064, 198.154, 199.244, 200.334, 201.423, |
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202.513, 203.602, 204.690, 205.779, 206.867, |
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207.955, 209.042, 210.130, 211.217, 212.304, |
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213.391, 214.477, 215.563, 216.649, 217.735, |
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218.820, 219.906, 220.991, 222.076, 223.160, |
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224.245, 225.329, 226.413, 227.496, 228.580, |
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229.663, 230.746, 231.829, 232.912, 233.994, |
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235.077, 236.159, 237.240, 238.322, 239.403, |
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240.485, 241.566, 242.647, 243.727, 244.808, |
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245.888, 246.968, 248.048, 249.128, 250.207, |
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251.286, 252.365, 253.444, 254.523, 255.602, |
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256.680, 257.758, 258.837, 259.914, 260.992, |
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262.070, 263.147, 264.224, 265.301, 266.378, |
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267.455, 268.531, 269.608, 270.684, 271.760, |
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272.836, 273.911, 274.987, 276.062, 277.138, |
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278.213, 279.288, 280.362, 281.437, 282.511, |
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283.586, 284.660, 285.734, 286.808, 287.882]] |
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