1 | #include "StudentTTest.h" |
2 | |
3 | #include <cmath> |
4 | #include <iostream> |
5 | #include <iomanip> |
6 | #include <sstream> |
7 | #include <stdexcept> |
8 | |
9 | |
10 | namespace |
11 | { |
12 | /// First row corresponds to infinity size of distributions case |
13 | const double students_table[101][6] = |
14 | { |
15 | { 1.282, 1.645, 1.960, 2.326, 2.576, 3.090 }, |
16 | { 3.078, 6.314, 12.706, 31.821, 63.657, 318.313 }, |
17 | { 1.886, 2.920, 4.303, 6.965, 9.925, 22.327 }, |
18 | { 1.638, 2.353, 3.182, 4.541, 5.841, 10.215 }, |
19 | { 1.533, 2.132, 2.776, 3.747, 4.604, 7.173 }, |
20 | { 1.476, 2.015, 2.571, 3.365, 4.032, 5.893 }, |
21 | { 1.440, 1.943, 2.447, 3.143, 3.707, 5.208 }, |
22 | { 1.415, 1.895, 2.365, 2.998, 3.499, 4.782 }, |
23 | { 1.397, 1.860, 2.306, 2.896, 3.355, 4.499 }, |
24 | { 1.383, 1.833, 2.262, 2.821, 3.250, 4.296 }, |
25 | { 1.372, 1.812, 2.228, 2.764, 3.169, 4.143 }, |
26 | { 1.363, 1.796, 2.201, 2.718, 3.106, 4.024 }, |
27 | { 1.356, 1.782, 2.179, 2.681, 3.055, 3.929 }, |
28 | { 1.350, 1.771, 2.160, 2.650, 3.012, 3.852 }, |
29 | { 1.345, 1.761, 2.145, 2.624, 2.977, 3.787 }, |
30 | { 1.341, 1.753, 2.131, 2.602, 2.947, 3.733 }, |
31 | { 1.337, 1.746, 2.120, 2.583, 2.921, 3.686 }, |
32 | { 1.333, 1.740, 2.110, 2.567, 2.898, 3.646 }, |
33 | { 1.330, 1.734, 2.101, 2.552, 2.878, 3.610 }, |
34 | { 1.328, 1.729, 2.093, 2.539, 2.861, 3.579 }, |
35 | { 1.325, 1.725, 2.086, 2.528, 2.845, 3.552 }, |
36 | { 1.323, 1.721, 2.080, 2.518, 2.831, 3.527 }, |
37 | { 1.321, 1.717, 2.074, 2.508, 2.819, 3.505 }, |
38 | { 1.319, 1.714, 2.069, 2.500, 2.807, 3.485 }, |
39 | { 1.318, 1.711, 2.064, 2.492, 2.797, 3.467 }, |
40 | { 1.316, 1.708, 2.060, 2.485, 2.787, 3.450 }, |
41 | { 1.315, 1.706, 2.056, 2.479, 2.779, 3.435 }, |
42 | { 1.314, 1.703, 2.052, 2.473, 2.771, 3.421 }, |
43 | { 1.313, 1.701, 2.048, 2.467, 2.763, 3.408 }, |
44 | { 1.311, 1.699, 2.045, 2.462, 2.756, 3.396 }, |
45 | { 1.310, 1.697, 2.042, 2.457, 2.750, 3.385 }, |
46 | { 1.309, 1.696, 2.040, 2.453, 2.744, 3.375 }, |
47 | { 1.309, 1.694, 2.037, 2.449, 2.738, 3.365 }, |
48 | { 1.308, 1.692, 2.035, 2.445, 2.733, 3.356 }, |
49 | { 1.307, 1.691, 2.032, 2.441, 2.728, 3.348 }, |
50 | { 1.306, 1.690, 2.030, 2.438, 2.724, 3.340 }, |
51 | { 1.306, 1.688, 2.028, 2.434, 2.719, 3.333 }, |
52 | { 1.305, 1.687, 2.026, 2.431, 2.715, 3.326 }, |
53 | { 1.304, 1.686, 2.024, 2.429, 2.712, 3.319 }, |
54 | { 1.304, 1.685, 2.023, 2.426, 2.708, 3.313 }, |
55 | { 1.303, 1.684, 2.021, 2.423, 2.704, 3.307 }, |
56 | { 1.303, 1.683, 2.020, 2.421, 2.701, 3.301 }, |
57 | { 1.302, 1.682, 2.018, 2.418, 2.698, 3.296 }, |
58 | { 1.302, 1.681, 2.017, 2.416, 2.695, 3.291 }, |
59 | { 1.301, 1.680, 2.015, 2.414, 2.692, 3.286 }, |
60 | { 1.301, 1.679, 2.014, 2.412, 2.690, 3.281 }, |
61 | { 1.300, 1.679, 2.013, 2.410, 2.687, 3.277 }, |
62 | { 1.300, 1.678, 2.012, 2.408, 2.685, 3.273 }, |
63 | { 1.299, 1.677, 2.011, 2.407, 2.682, 3.269 }, |
64 | { 1.299, 1.677, 2.010, 2.405, 2.680, 3.265 }, |
65 | { 1.299, 1.676, 2.009, 2.403, 2.678, 3.261 }, |
66 | { 1.298, 1.675, 2.008, 2.402, 2.676, 3.258 }, |
67 | { 1.298, 1.675, 2.007, 2.400, 2.674, 3.255 }, |
68 | { 1.298, 1.674, 2.006, 2.399, 2.672, 3.251 }, |
69 | { 1.297, 1.674, 2.005, 2.397, 2.670, 3.248 }, |
70 | { 1.297, 1.673, 2.004, 2.396, 2.668, 3.245 }, |
71 | { 1.297, 1.673, 2.003, 2.395, 2.667, 3.242 }, |
72 | { 1.297, 1.672, 2.002, 2.394, 2.665, 3.239 }, |
73 | { 1.296, 1.672, 2.002, 2.392, 2.663, 3.237 }, |
74 | { 1.296, 1.671, 2.001, 2.391, 2.662, 3.234 }, |
75 | { 1.296, 1.671, 2.000, 2.390, 2.660, 3.232 }, |
76 | { 1.296, 1.670, 2.000, 2.389, 2.659, 3.229 }, |
77 | { 1.295, 1.670, 1.999, 2.388, 2.657, 3.227 }, |
78 | { 1.295, 1.669, 1.998, 2.387, 2.656, 3.225 }, |
79 | { 1.295, 1.669, 1.998, 2.386, 2.655, 3.223 }, |
80 | { 1.295, 1.669, 1.997, 2.385, 2.654, 3.220 }, |
81 | { 1.295, 1.668, 1.997, 2.384, 2.652, 3.218 }, |
82 | { 1.294, 1.668, 1.996, 2.383, 2.651, 3.216 }, |
83 | { 1.294, 1.668, 1.995, 2.382, 2.650, 3.214 }, |
84 | { 1.294, 1.667, 1.995, 2.382, 2.649, 3.213 }, |
85 | { 1.294, 1.667, 1.994, 2.381, 2.648, 3.211 }, |
86 | { 1.294, 1.667, 1.994, 2.380, 2.647, 3.209 }, |
87 | { 1.293, 1.666, 1.993, 2.379, 2.646, 3.207 }, |
88 | { 1.293, 1.666, 1.993, 2.379, 2.645, 3.206 }, |
89 | { 1.293, 1.666, 1.993, 2.378, 2.644, 3.204 }, |
90 | { 1.293, 1.665, 1.992, 2.377, 2.643, 3.202 }, |
91 | { 1.293, 1.665, 1.992, 2.376, 2.642, 3.201 }, |
92 | { 1.293, 1.665, 1.991, 2.376, 2.641, 3.199 }, |
93 | { 1.292, 1.665, 1.991, 2.375, 2.640, 3.198 }, |
94 | { 1.292, 1.664, 1.990, 2.374, 2.640, 3.197 }, |
95 | { 1.292, 1.664, 1.990, 2.374, 2.639, 3.195 }, |
96 | { 1.292, 1.664, 1.990, 2.373, 2.638, 3.194 }, |
97 | { 1.292, 1.664, 1.989, 2.373, 2.637, 3.193 }, |
98 | { 1.292, 1.663, 1.989, 2.372, 2.636, 3.191 }, |
99 | { 1.292, 1.663, 1.989, 2.372, 2.636, 3.190 }, |
100 | { 1.292, 1.663, 1.988, 2.371, 2.635, 3.189 }, |
101 | { 1.291, 1.663, 1.988, 2.370, 2.634, 3.188 }, |
102 | { 1.291, 1.663, 1.988, 2.370, 2.634, 3.187 }, |
103 | { 1.291, 1.662, 1.987, 2.369, 2.633, 3.185 }, |
104 | { 1.291, 1.662, 1.987, 2.369, 2.632, 3.184 }, |
105 | { 1.291, 1.662, 1.987, 2.368, 2.632, 3.183 }, |
106 | { 1.291, 1.662, 1.986, 2.368, 2.631, 3.182 }, |
107 | { 1.291, 1.662, 1.986, 2.368, 2.630, 3.181 }, |
108 | { 1.291, 1.661, 1.986, 2.367, 2.630, 3.180 }, |
109 | { 1.291, 1.661, 1.986, 2.367, 2.629, 3.179 }, |
110 | { 1.291, 1.661, 1.985, 2.366, 2.629, 3.178 }, |
111 | { 1.290, 1.661, 1.985, 2.366, 2.628, 3.177 }, |
112 | { 1.290, 1.661, 1.985, 2.365, 2.627, 3.176 }, |
113 | { 1.290, 1.661, 1.984, 2.365, 2.627, 3.175 }, |
114 | { 1.290, 1.660, 1.984, 2.365, 2.626, 3.175 }, |
115 | { 1.290, 1.660, 1.984, 2.364, 2.626, 3.174 }, |
116 | }; |
117 | |
118 | const double confidence_level[6] = { 80, 90, 95, 98, 99, 99.5 }; |
119 | } |
120 | |
121 | |
122 | void StudentTTest::clear() |
123 | { |
124 | data[0].clear(); |
125 | data[1].clear(); |
126 | } |
127 | |
128 | void StudentTTest::add(size_t distribution, double value) |
129 | { |
130 | if (distribution > 1) |
131 | throw std::logic_error("Distribution number for Student's T-Test must be eigther 0 or 1" ); |
132 | data[distribution].add(value); |
133 | } |
134 | |
135 | /// Confidence_level_index can be set in range [0, 5]. Corresponding values can be found above. |
136 | std::pair<bool, std::string> StudentTTest::compareAndReport(size_t confidence_level_index) const |
137 | { |
138 | if (confidence_level_index > 5) |
139 | confidence_level_index = 5; |
140 | |
141 | if (data[0].size == 0 || data[1].size == 0) |
142 | return {true, "" }; |
143 | |
144 | size_t degrees_of_freedom = (data[0].size - 1) + (data[1].size - 1); |
145 | |
146 | double table_value = students_table[degrees_of_freedom > 100 ? 0 : degrees_of_freedom][confidence_level_index]; |
147 | |
148 | double pooled_standard_deviation = sqrt(((data[0].size - 1) * data[0].var() + (data[1].size - 1) * data[1].var()) / degrees_of_freedom); |
149 | |
150 | double t_statistic = pooled_standard_deviation * sqrt(1.0 / data[0].size + 1.0 / data[1].size); |
151 | |
152 | double mean_difference = fabs(data[0].avg() - data[1].avg()); |
153 | |
154 | double mean_confidence_interval = table_value * t_statistic; |
155 | |
156 | std::stringstream ss; |
157 | if (mean_difference > mean_confidence_interval && (mean_difference - mean_confidence_interval > 0.0001)) /// difference must be more than 0.0001, to take into account connection latency. |
158 | { |
159 | ss << "Difference at " << confidence_level[confidence_level_index] << "% confidence : " ; |
160 | ss << std::fixed << std::setprecision(8) << "mean difference is " << mean_difference << ", but confidence interval is " << mean_confidence_interval; |
161 | return {false, ss.str()}; |
162 | } |
163 | else |
164 | { |
165 | ss << "No difference proven at " << confidence_level[confidence_level_index] << "% confidence" ; |
166 | return {true, ss.str()}; |
167 | } |
168 | } |
169 | |
170 | |