File size: 5,990 Bytes
46a43b0 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 | from __future__ import annotations
import numpy
def chi_square_test(observed, expected, alpha=0.05, df=None):
"""Testing Goodness-of-fit Test with Pearson's Chi-squared Test.
Args:
observed (list of ints): List of # of counts each element is observed.
expected (list of floats): List of # of counts each element is expected
to be observed.
alpha (float): Significance level. Currently,
only 0.05 and 0.01 are acceptable.
df (int): Degree of freedom. If ``None``,
it is set to the length of ``observed`` minus 1.
Returns:
bool: ``True`` if null hypothesis is **NOT** reject.
Otherwise, ``False``.
"""
if df is None:
df = observed.size - 1
if alpha == 0.01:
alpha_idx = 0
elif alpha == 0.05:
alpha_idx = 1
else:
raise ValueError('support only alpha == 0.05 or 0.01')
chi_square = numpy.sum((observed - expected) ** 2 / expected)
return chi_square < chi_square_table[alpha_idx][df]
# https://www.medcalc.org/manual/chi-square-table.php
chi_square_table = [
[None,
6.635, 9.210, 11.345, 13.277, 15.086,
16.812, 18.475, 20.090, 21.666, 23.209,
24.725, 26.217, 27.688, 29.141, 30.578,
32.000, 33.409, 34.805, 36.191, 37.566,
38.932, 40.289, 41.638, 42.980, 44.314,
45.642, 46.963, 48.278, 49.588, 50.892,
52.191, 53.486, 54.776, 56.061, 57.342,
58.619, 59.893, 61.162, 62.428, 63.691,
64.950, 66.206, 67.459, 68.710, 69.957,
71.201, 72.443, 73.683, 74.919, 76.154,
77.386, 78.616, 79.843, 81.069, 82.292,
83.513, 84.733, 85.950, 87.166, 88.379,
89.591, 90.802, 92.010, 93.217, 94.422,
95.626, 96.828, 98.028, 99.228, 100.425,
101.621, 102.816, 104.010, 105.202, 106.393,
107.583, 108.771, 109.958, 111.144, 112.329,
113.512, 114.695, 115.876, 117.057, 118.236,
119.414, 120.591, 121.767, 122.942, 124.116,
125.289, 126.462, 127.633, 128.803, 129.973,
131.141, 132.309, 133.476, 134.642, 135.807,
136.971, 138.134, 139.297, 140.459, 141.620,
142.780, 143.940, 145.099, 146.257, 147.414,
148.571, 149.727, 150.882, 152.037, 153.191,
154.344, 155.496, 156.648, 157.800, 158.950,
160.100, 161.250, 162.398, 163.546, 164.694,
165.841, 166.987, 168.133, 169.278, 170.423,
171.567, 172.711, 173.854, 174.996, 176.138,
177.280, 178.421, 179.561, 180.701, 181.840,
182.979, 184.118, 185.256, 186.393, 187.530,
188.666, 189.802, 190.938, 192.073, 193.208,
194.342, 195.476, 196.609, 197.742, 198.874,
200.006, 201.138, 202.269, 203.400, 204.530,
205.660, 206.790, 207.919, 209.047, 210.176,
211.304, 212.431, 213.558, 214.685, 215.812,
216.938, 218.063, 219.189, 220.314, 221.438,
222.563, 223.687, 224.810, 225.933, 227.056,
228.179, 229.301, 230.423, 231.544, 232.665,
233.786, 234.907, 236.027, 237.147, 238.266,
239.386, 240.505, 241.623, 242.742, 243.860,
244.977, 246.095, 247.212, 248.329, 249.445,
250.561, 251.677, 252.793, 253.908, 255.023,
256.138, 257.253, 258.367, 259.481, 260.595,
261.708, 262.821, 263.934, 265.047, 266.159,
267.271, 268.383, 269.495, 270.606, 271.717,
272.828, 273.939, 275.049, 276.159, 277.269,
278.379, 279.488, 280.597, 281.706, 282.814,
283.923, 285.031, 286.139, 287.247, 288.354,
289.461, 290.568, 291.675, 292.782, 293.888,
294.994, 296.100, 297.206, 298.311, 299.417,
300.522, 301.626, 302.731, 303.835, 304.940],
[None,
3.841, 5.991, 7.815, 9.488, 11.070,
12.592, 14.067, 15.507, 16.919, 18.307,
19.675, 21.026, 22.362, 23.685, 24.996,
26.296, 27.587, 28.869, 30.144, 31.410,
32.671, 33.924, 35.172, 36.415, 37.652,
38.885, 40.113, 41.337, 42.557, 43.773,
44.985, 46.194, 47.400, 48.602, 49.802,
50.998, 52.192, 53.384, 54.572, 55.758,
56.942, 58.124, 59.304, 60.481, 61.656,
62.830, 64.001, 65.171, 66.339, 67.505,
68.669, 69.832, 70.993, 72.153, 73.311,
74.468, 75.624, 76.778, 77.931, 79.082,
80.232, 81.381, 82.529, 83.675, 84.821,
85.965, 87.108, 88.250, 89.391, 90.531,
91.670, 92.808, 93.945, 95.081, 96.217,
97.351, 98.484, 99.617, 100.749, 101.879,
103.010, 104.139, 105.267, 106.395, 107.522,
108.648, 109.773, 110.898, 112.022, 113.145,
114.268, 115.390, 116.511, 117.632, 118.752,
119.871, 120.990, 122.108, 123.225, 124.342,
125.458, 126.574, 127.689, 128.804, 129.918,
131.031, 132.144, 133.257, 134.369, 135.480,
136.591, 137.701, 138.811, 139.921, 141.030,
142.138, 143.246, 144.354, 145.461, 146.567,
147.674, 148.779, 149.885, 150.989, 152.094,
153.198, 154.302, 155.405, 156.508, 157.610,
158.712, 159.814, 160.915, 162.016, 163.116,
164.216, 165.316, 166.415, 167.514, 168.613,
169.711, 170.809, 171.907, 173.004, 174.101,
175.198, 176.294, 177.390, 178.485, 179.581,
180.676, 181.770, 182.865, 183.959, 185.052,
186.146, 187.239, 188.332, 189.424, 190.516,
191.608, 192.700, 193.791, 194.883, 195.973,
197.064, 198.154, 199.244, 200.334, 201.423,
202.513, 203.602, 204.690, 205.779, 206.867,
207.955, 209.042, 210.130, 211.217, 212.304,
213.391, 214.477, 215.563, 216.649, 217.735,
218.820, 219.906, 220.991, 222.076, 223.160,
224.245, 225.329, 226.413, 227.496, 228.580,
229.663, 230.746, 231.829, 232.912, 233.994,
235.077, 236.159, 237.240, 238.322, 239.403,
240.485, 241.566, 242.647, 243.727, 244.808,
245.888, 246.968, 248.048, 249.128, 250.207,
251.286, 252.365, 253.444, 254.523, 255.602,
256.680, 257.758, 258.837, 259.914, 260.992,
262.070, 263.147, 264.224, 265.301, 266.378,
267.455, 268.531, 269.608, 270.684, 271.760,
272.836, 273.911, 274.987, 276.062, 277.138,
278.213, 279.288, 280.362, 281.437, 282.511,
283.586, 284.660, 285.734, 286.808, 287.882]]
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