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T_test.h added, some fixes

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This commit is contained in:
dimarub2000 2019-08-21 11:53:41 +03:00
parent 9caa69ce88
commit 086dd815ac
3 changed files with 242 additions and 203 deletions
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229
dbms/programs/benchmark/Benchmark.cpp
View File

@ -32,6 +32,7 @@
#include <Client/Connection.h>
#include <Common/InterruptListener.h>
#include <Common/Config/configReadClient.h>
#include <Common/T_test.h>
/** A tool for evaluating ClickHouse performance.
@ -41,6 +42,8 @@
namespace DB
{
using Ports = std::vector<UInt16>;
namespace ErrorCodes
{
extern const int BAD_ARGUMENTS;
@ -50,8 +53,7 @@ namespace ErrorCodes
class Benchmark : public Poco::Util::Application
{
public:
Benchmark(unsigned concurrency_, double delay_,
const std::vector<std::string> & hosts_, const std::vector<UInt16> & ports_,
Benchmark(unsigned concurrency_, double delay_, Strings && hosts_, Ports && ports_,
bool cumulative_, bool secure_, const String & default_database_,
const String & user_, const String & password_, const String & stage,
bool randomize_, size_t max_iterations_, double max_time_,
@ -68,24 +70,17 @@ public:
connections.reserve(connections_cnt);
comparison_info_total.reserve(connections_cnt);
comparison_info_per_interval.reserve(connections_cnt);
comparison_relative.data.resize(connections_cnt);
for (size_t i = 0; i < connections_cnt; ++i)
{
UInt16 cur_port = i >= ports_.size() ? 9000 : ports_[i];
std::string cur_host = i >= hosts_.size() ? "localhost" : hosts_[i];
connections.emplace_back(std::make_shared<ConnectionPool>(concurrency, cur_host, cur_port, default_database_, user_, password_, "benchmark", Protocol::Compression::Enable, secure));
connections.emplace_back(std::make_unique<ConnectionPool>(concurrency, cur_host, cur_port, default_database_, user_, password_, "benchmark", Protocol::Compression::Enable, secure));
comparison_info_per_interval.emplace_back(std::make_shared<Stats>());
comparison_info_total.emplace_back(std::make_shared<Stats>());
}
if (confidence > 5)
{
std::cerr << "Confidence can't be set to " + toString(confidence) + ". It was set to 5 instead." << '\n';
confidence = 5;
}
global_context.makeGlobalContext();
std::cerr << std::fixed << std::setprecision(3);
@ -140,7 +135,9 @@ private:
using Queue = ConcurrentBoundedQueue<Query>;
Queue queue;
ConnectionPoolPtrs connections;
using ConnectionPoolUniq = std::unique_ptr<ConnectionPool>;
using ConnectionPoolUniqs = std::vector<ConnectionPoolUniq>;
ConnectionPoolUniqs connections;
bool randomize;
bool cumulative;
@ -192,180 +189,10 @@ private:
}
};
struct RelativeAnalysis
{
struct RelativeStats
{
size_t cnt = 0;
double sum = 0;
double squares_sum = 0;
void add(double seconds)
{
++cnt;
sum += seconds;
squares_sum += seconds * seconds;
}
double avg() const
{
return sum / cnt;
}
double var() const
{
return (squares_sum - (sum * sum / cnt)) / static_cast<double>(cnt - 1);
}
};
const std::vector<double> confidence_level = { 80, 90, 95, 98, 99, 99.5 };
const std::vector<std::vector<double>> students_table = {
/* inf */ { 1.282, 1.645, 1.960, 2.326, 2.576, 3.090 },
/* 1. */ { 3.078, 6.314, 12.706, 31.821, 63.657, 318.313},
/* 2. */ { 1.886, 2.920, 4.303, 6.965, 9.925, 22.327 },
/* 3. */ { 1.638, 2.353, 3.182, 4.541, 5.841, 10.215 },
/* 4. */ { 1.533, 2.132, 2.776, 3.747, 4.604, 7.173 },
/* 5. */ { 1.476, 2.015, 2.571, 3.365, 4.032, 5.893 },
/* 6. */ { 1.440, 1.943, 2.447, 3.143, 3.707, 5.208 },
/* 7. */ { 1.415, 1.895, 2.365, 2.998, 3.499, 4.782 },
/* 8. */ { 1.397, 1.860, 2.306, 2.896, 3.355, 4.499 },
/* 9. */ { 1.383, 1.833, 2.262, 2.821, 3.250, 4.296 },
/* 10. */ { 1.372, 1.812, 2.228, 2.764, 3.169, 4.143 },
/* 11. */ { 1.363, 1.796, 2.201, 2.718, 3.106, 4.024 },
/* 12. */ { 1.356, 1.782, 2.179, 2.681, 3.055, 3.929 },
/* 13. */ { 1.350, 1.771, 2.160, 2.650, 3.012, 3.852 },
/* 14. */ { 1.345, 1.761, 2.145, 2.624, 2.977, 3.787 },
/* 15. */ { 1.341, 1.753, 2.131, 2.602, 2.947, 3.733 },
/* 16. */ { 1.337, 1.746, 2.120, 2.583, 2.921, 3.686 },
/* 17. */ { 1.333, 1.740, 2.110, 2.567, 2.898, 3.646 },
/* 18. */ { 1.330, 1.734, 2.101, 2.552, 2.878, 3.610 },
/* 19. */ { 1.328, 1.729, 2.093, 2.539, 2.861, 3.579 },
/* 20. */ { 1.325, 1.725, 2.086, 2.528, 2.845, 3.552 },
/* 21. */ { 1.323, 1.721, 2.080, 2.518, 2.831, 3.527 },
/* 22. */ { 1.321, 1.717, 2.074, 2.508, 2.819, 3.505 },
/* 23. */ { 1.319, 1.714, 2.069, 2.500, 2.807, 3.485 },
/* 24. */ { 1.318, 1.711, 2.064, 2.492, 2.797, 3.467 },
/* 25. */ { 1.316, 1.708, 2.060, 2.485, 2.787, 3.450 },
/* 26. */ { 1.315, 1.706, 2.056, 2.479, 2.779, 3.435 },
/* 27. */ { 1.314, 1.703, 2.052, 2.473, 2.771, 3.421 },
/* 28. */ { 1.313, 1.701, 2.048, 2.467, 2.763, 3.408 },
/* 29. */ { 1.311, 1.699, 2.045, 2.462, 2.756, 3.396 },
/* 30. */ { 1.310, 1.697, 2.042, 2.457, 2.750, 3.385 },
/* 31. */ { 1.309, 1.696, 2.040, 2.453, 2.744, 3.375 },
/* 32. */ { 1.309, 1.694, 2.037, 2.449, 2.738, 3.365 },
/* 33. */ { 1.308, 1.692, 2.035, 2.445, 2.733, 3.356 },
/* 34. */ { 1.307, 1.691, 2.032, 2.441, 2.728, 3.348 },
/* 35. */ { 1.306, 1.690, 2.030, 2.438, 2.724, 3.340 },
/* 36. */ { 1.306, 1.688, 2.028, 2.434, 2.719, 3.333 },
/* 37. */ { 1.305, 1.687, 2.026, 2.431, 2.715, 3.326 },
/* 38. */ { 1.304, 1.686, 2.024, 2.429, 2.712, 3.319 },
/* 39. */ { 1.304, 1.685, 2.023, 2.426, 2.708, 3.313 },
/* 40. */ { 1.303, 1.684, 2.021, 2.423, 2.704, 3.307 },
/* 41. */ { 1.303, 1.683, 2.020, 2.421, 2.701, 3.301 },
/* 42. */ { 1.302, 1.682, 2.018, 2.418, 2.698, 3.296 },
/* 43. */ { 1.302, 1.681, 2.017, 2.416, 2.695, 3.291 },
/* 44. */ { 1.301, 1.680, 2.015, 2.414, 2.692, 3.286 },
/* 45. */ { 1.301, 1.679, 2.014, 2.412, 2.690, 3.281 },
/* 46. */ { 1.300, 1.679, 2.013, 2.410, 2.687, 3.277 },
/* 47. */ { 1.300, 1.678, 2.012, 2.408, 2.685, 3.273 },
/* 48. */ { 1.299, 1.677, 2.011, 2.407, 2.682, 3.269 },
/* 49. */ { 1.299, 1.677, 2.010, 2.405, 2.680, 3.265 },
/* 50. */ { 1.299, 1.676, 2.009, 2.403, 2.678, 3.261 },
/* 51. */ { 1.298, 1.675, 2.008, 2.402, 2.676, 3.258 },
/* 52. */ { 1.298, 1.675, 2.007, 2.400, 2.674, 3.255 },
/* 53. */ { 1.298, 1.674, 2.006, 2.399, 2.672, 3.251 },
/* 54. */ { 1.297, 1.674, 2.005, 2.397, 2.670, 3.248 },
/* 55. */ { 1.297, 1.673, 2.004, 2.396, 2.668, 3.245 },
/* 56. */ { 1.297, 1.673, 2.003, 2.395, 2.667, 3.242 },
/* 57. */ { 1.297, 1.672, 2.002, 2.394, 2.665, 3.239 },
/* 58. */ { 1.296, 1.672, 2.002, 2.392, 2.663, 3.237 },
/* 59. */ { 1.296, 1.671, 2.001, 2.391, 2.662, 3.234 },
/* 60. */ { 1.296, 1.671, 2.000, 2.390, 2.660, 3.232 },
/* 61. */ { 1.296, 1.670, 2.000, 2.389, 2.659, 3.229 },
/* 62. */ { 1.295, 1.670, 1.999, 2.388, 2.657, 3.227 },
/* 63. */ { 1.295, 1.669, 1.998, 2.387, 2.656, 3.225 },
/* 64. */ { 1.295, 1.669, 1.998, 2.386, 2.655, 3.223 },
/* 65. */ { 1.295, 1.669, 1.997, 2.385, 2.654, 3.220 },
/* 66. */ { 1.295, 1.668, 1.997, 2.384, 2.652, 3.218 },
/* 67. */ { 1.294, 1.668, 1.996, 2.383, 2.651, 3.216 },
/* 68. */ { 1.294, 1.668, 1.995, 2.382, 2.650, 3.214 },
/* 69. */ { 1.294, 1.667, 1.995, 2.382, 2.649, 3.213 },
/* 70. */ { 1.294, 1.667, 1.994, 2.381, 2.648, 3.211 },
/* 71. */ { 1.294, 1.667, 1.994, 2.380, 2.647, 3.209 },
/* 72. */ { 1.293, 1.666, 1.993, 2.379, 2.646, 3.207 },
/* 73. */ { 1.293, 1.666, 1.993, 2.379, 2.645, 3.206 },
/* 74. */ { 1.293, 1.666, 1.993, 2.378, 2.644, 3.204 },
/* 75. */ { 1.293, 1.665, 1.992, 2.377, 2.643, 3.202 },
/* 76. */ { 1.293, 1.665, 1.992, 2.376, 2.642, 3.201 },
/* 77. */ { 1.293, 1.665, 1.991, 2.376, 2.641, 3.199 },
/* 78. */ { 1.292, 1.665, 1.991, 2.375, 2.640, 3.198 },
/* 79. */ { 1.292, 1.664, 1.990, 2.374, 2.640, 3.197 },
/* 80. */ { 1.292, 1.664, 1.990, 2.374, 2.639, 3.195 },
/* 81. */ { 1.292, 1.664, 1.990, 2.373, 2.638, 3.194 },
/* 82. */ { 1.292, 1.664, 1.989, 2.373, 2.637, 3.193 },
/* 83. */ { 1.292, 1.663, 1.989, 2.372, 2.636, 3.191 },
/* 84. */ { 1.292, 1.663, 1.989, 2.372, 2.636, 3.190 },
/* 85. */ { 1.292, 1.663, 1.988, 2.371, 2.635, 3.189 },
/* 86. */ { 1.291, 1.663, 1.988, 2.370, 2.634, 3.188 },
/* 87. */ { 1.291, 1.663, 1.988, 2.370, 2.634, 3.187 },
/* 88. */ { 1.291, 1.662, 1.987, 2.369, 2.633, 3.185 },
/* 89. */ { 1.291, 1.662, 1.987, 2.369, 2.632, 3.184 },
/* 90. */ { 1.291, 1.662, 1.987, 2.368, 2.632, 3.183 },
/* 91. */ { 1.291, 1.662, 1.986, 2.368, 2.631, 3.182 },
/* 92. */ { 1.291, 1.662, 1.986, 2.368, 2.630, 3.181 },
/* 93. */ { 1.291, 1.661, 1.986, 2.367, 2.630, 3.180 },
/* 94. */ { 1.291, 1.661, 1.986, 2.367, 2.629, 3.179 },
/* 95. */ { 1.291, 1.661, 1.985, 2.366, 2.629, 3.178 },
/* 96. */ { 1.290, 1.661, 1.985, 2.366, 2.628, 3.177 },
/* 97. */ { 1.290, 1.661, 1.985, 2.365, 2.627, 3.176 },
/* 98. */ { 1.290, 1.661, 1.984, 2.365, 2.627, 3.175 },
/* 99. */ { 1.290, 1.660, 1.984, 2.365, 2.626, 3.175 },
/* 100. */ { 1.290, 1.660, 1.984, 2.364, 2.626, 3.174 }
};
std::vector<RelativeStats> data;
bool report(size_t confidence_index)
{
if (data.size() != 2) /// Works for two connections only
return true;
size_t i = (data[0].cnt - 1) + (data[1].cnt - 1);
double t = students_table[i > 100 ? 0 : i][confidence_index];
double spool = (data[0].cnt - 1) * data[0].var() + (data[1].cnt - 1) * data[1].var();
spool = sqrt(spool / i);
double s = spool * sqrt(1.0 / data[0].cnt + 1.0 / data[1].cnt);
double d = data[1].avg() - data[0].avg();
double e = t * s;
std::cerr << '\n';
if (fabs(d) > e)
{
std::cerr << std::setprecision(1) << "Difference at " << confidence_level[confidence_index] << "% confidence\n" << std::setprecision(6);
std::cerr << "\t" << d << " +/- " << e << "\n";
std::cerr << "\t" << d * 100 / data[0].avg() << "% +/- " << e * 100 / data[0].avg() << "%\n";
std::cerr << "\t(Student's t, pooled s = " << spool << ")\n" << std::setprecision(3);
return false;
}
else
{
std::cerr << std::setprecision(1) << "No difference proven at " << confidence_level[confidence_index] << "% confidence\n" << std::setprecision(3);
return true;
}
}
};
RelativeAnalysis comparison_relative;
using MultiStats = std::vector<std::shared_ptr<Stats>>;
MultiStats comparison_info_per_interval;
MultiStats comparison_info_total;
T_test t_test;
Stopwatch total_watch;
Stopwatch delay_watch;
@ -434,8 +261,6 @@ private:
{
printNumberOfQueriesExecuted(queries_executed);
cumulative ? report(comparison_info_total) : report(comparison_info_per_interval);
comparison_relative.report(confidence);
delay_watch.restart();
}
}
@ -482,7 +307,6 @@ private:
printNumberOfQueriesExecuted(queries_executed);
report(comparison_info_total);
comparison_relative.report(confidence);
}
@ -549,7 +373,7 @@ private:
comparison_info_per_interval[connection_index]->add(seconds, progress.read_rows, progress.read_bytes, info.rows, info.bytes);
comparison_info_total[connection_index]->add(seconds, progress.read_rows, progress.read_bytes, info.rows, info.bytes);
comparison_relative.data[connection_index].add(seconds);
t_test.add(connection_index, seconds);
}
void report(MultiStats & infos)
@ -557,9 +381,9 @@ private:
std::lock_guard lock(mutex);
std::cerr << "\n";
for (size_t i = 1; i <= infos.size(); ++i)
for (size_t i = 0; i < infos.size(); ++i)
{
const auto & info = infos[i - 1];
const auto & info = infos[i];
/// Avoid zeros, nans or exceptions
if (0 == info->queries)
@ -568,7 +392,7 @@ private:
double seconds = info->work_time / concurrency;
std::cerr
<< "connection " << i << ", "
<< connections[i]->getDescription() << ", "
<< "queries " << info->queries << ", "
<< "QPS: " << (info->queries / seconds) << ", "
<< "RPS: " << (info->read_rows / seconds) << ", "
@ -577,13 +401,8 @@ private:
<< "result MiB/s: " << (info->result_bytes / seconds / 1048576) << "."
<< "\n";
}
std::cerr << "\n\t\t";
for (size_t i = 1; i <= infos.size(); ++i)
std::cerr << "connection " << i << "\t";
std::cerr << "\n";
auto print_percentile = [&](double percent)
{
std::cerr << percent << "%\t\t";
@ -602,6 +421,8 @@ private:
print_percentile(99.9);
print_percentile(99.99);
std::cerr << "\n" << t_test.compareAndReport(confidence).second << "\n";
if (!cumulative)
{
for (auto & info : infos)
@ -627,11 +448,11 @@ private:
json_out << "{\n";
for (size_t i = 1; i <= infos.size(); ++i)
for (size_t i = 0; i < infos.size(); ++i)
{
const auto & info = infos[i - 1];
const auto & info = infos[i];
json_out << double_quote << "connection_" + toString(i) << ": {\n";
json_out << double_quote << connections[i]->getDescription() << ": {\n";
json_out << double_quote << "statistics" << ": {\n";
print_key_value("QPS", info->queries / info->work_time);
@ -653,7 +474,7 @@ private:
print_percentile(*info, 99.99, false);
json_out << "}\n";
json_out << (i == infos.size() ? "}\n" : "},\n");
json_out << (i == infos.size() - 1 ? "}\n" : "},\n");
}
json_out << "}\n";
@ -693,8 +514,8 @@ int mainEntryClickHouseBenchmark(int argc, char ** argv)
("timelimit,t", value<double>()->default_value(0.), "stop launch of queries after specified time limit")
("randomize,r", value<bool>()->default_value(false), "randomize order of execution")
("json", value<std::string>()->default_value(""), "write final report to specified file in JSON format")
("host,h", value<std::vector<std::string>>()->default_value(std::vector<std::string>{"localhost"}, "localhost"), "note that more than one host can be described")
("port,p", value<std::vector<UInt16>>()->default_value(std::vector<UInt16>{9000}, "9000"), "note that more than one port can be described")
("host,h", value<Strings>()->multitoken(), "")
("port,p", value<Ports>()->multitoken(), "")
("cumulative", "prints cumulative data instead of data per interval")
("secure,s", "Use TLS connection")
("user", value<std::string>()->default_value("default"), "")
@ -721,12 +542,14 @@ int mainEntryClickHouseBenchmark(int argc, char ** argv)
print_stacktrace = options.count("stacktrace");
UseSSL use_ssl;
Ports ports = options.count("port") ? options["port"].as<Ports>() : Ports({9000});
Strings hosts = options.count("host") ? options["host"].as<Strings>() : Strings({"localhost"});
Benchmark benchmark(
options["concurrency"].as<unsigned>(),
options["delay"].as<double>(),
options["host"].as<std::vector<std::string>>(),
options["port"].as<std::vector<UInt16>>(),
std::move(hosts),
std::move(ports),
options.count("cumulative"),
options.count("secure"),
options["database"].as<std::string>(),

4
dbms/src/Client/ConnectionPool.h
View File

@ -88,6 +88,10 @@ public:
{
return host;
}
std::string getDescription() const
{
return host + ":" + toString(port);
}
protected:
/** Creates a new object to put in the pool. */

212
dbms/src/Common/T_test.h Normal file
View File

@ -0,0 +1,212 @@
#pragma once
#include <vector>
#include <cmath>
#include <iostream>
#include <iomanip>
#include <sstream>
/**
* About:
* This is implementation of Independent two-sample t-test
* Read about it on https://en.wikipedia.org/wiki/Student%27s_t-test (Equal or unequal sample sizes, equal variance)
*
* Usage:
* It's it used to assume with some level of confidence that two distributions don't differ.
* Values can be added with T_test.add(0/1, value) and after compared and reported with compareAndReport().
*/
struct T_test
{
struct DistributionData
{
size_t size = 0;
double sum = 0;
double squares_sum = 0;
void add(double value)
{
++size;
sum += value;
squares_sum += value * value;
}
double avg() const
{
return sum / size;
}
double var() const
{
return (squares_sum - (sum * sum / size)) / static_cast<double>(size - 1);
}
void clear()
{
size = 0;
sum = 0;
squares_sum = 0;
}
};
std::vector<DistributionData> data;
const std::vector<std::vector<double>> students_table =
{
/* inf */ { 1.282, 1.645, 1.960, 2.326, 2.576, 3.090 },
/* 1. */ { 3.078, 6.314, 12.706, 31.821, 63.657, 318.313},
/* 2. */ { 1.886, 2.920, 4.303, 6.965, 9.925, 22.327 },
/* 3. */ { 1.638, 2.353, 3.182, 4.541, 5.841, 10.215 },
/* 4. */ { 1.533, 2.132, 2.776, 3.747, 4.604, 7.173 },
/* 5. */ { 1.476, 2.015, 2.571, 3.365, 4.032, 5.893 },
/* 6. */ { 1.440, 1.943, 2.447, 3.143, 3.707, 5.208 },
/* 7. */ { 1.415, 1.895, 2.365, 2.998, 3.499, 4.782 },
/* 8. */ { 1.397, 1.860, 2.306, 2.896, 3.355, 4.499 },
/* 9. */ { 1.383, 1.833, 2.262, 2.821, 3.250, 4.296 },
/* 10. */ { 1.372, 1.812, 2.228, 2.764, 3.169, 4.143 },
/* 11. */ { 1.363, 1.796, 2.201, 2.718, 3.106, 4.024 },
/* 12. */ { 1.356, 1.782, 2.179, 2.681, 3.055, 3.929 },
/* 13. */ { 1.350, 1.771, 2.160, 2.650, 3.012, 3.852 },
/* 14. */ { 1.345, 1.761, 2.145, 2.624, 2.977, 3.787 },
/* 15. */ { 1.341, 1.753, 2.131, 2.602, 2.947, 3.733 },
/* 16. */ { 1.337, 1.746, 2.120, 2.583, 2.921, 3.686 },
/* 17. */ { 1.333, 1.740, 2.110, 2.567, 2.898, 3.646 },
/* 18. */ { 1.330, 1.734, 2.101, 2.552, 2.878, 3.610 },
/* 19. */ { 1.328, 1.729, 2.093, 2.539, 2.861, 3.579 },
/* 20. */ { 1.325, 1.725, 2.086, 2.528, 2.845, 3.552 },
/* 21. */ { 1.323, 1.721, 2.080, 2.518, 2.831, 3.527 },
/* 22. */ { 1.321, 1.717, 2.074, 2.508, 2.819, 3.505 },
/* 23. */ { 1.319, 1.714, 2.069, 2.500, 2.807, 3.485 },
/* 24. */ { 1.318, 1.711, 2.064, 2.492, 2.797, 3.467 },
/* 25. */ { 1.316, 1.708, 2.060, 2.485, 2.787, 3.450 },
/* 26. */ { 1.315, 1.706, 2.056, 2.479, 2.779, 3.435 },
/* 27. */ { 1.314, 1.703, 2.052, 2.473, 2.771, 3.421 },
/* 28. */ { 1.313, 1.701, 2.048, 2.467, 2.763, 3.408 },
/* 29. */ { 1.311, 1.699, 2.045, 2.462, 2.756, 3.396 },
/* 30. */ { 1.310, 1.697, 2.042, 2.457, 2.750, 3.385 },
/* 31. */ { 1.309, 1.696, 2.040, 2.453, 2.744, 3.375 },
/* 32. */ { 1.309, 1.694, 2.037, 2.449, 2.738, 3.365 },
/* 33. */ { 1.308, 1.692, 2.035, 2.445, 2.733, 3.356 },
/* 34. */ { 1.307, 1.691, 2.032, 2.441, 2.728, 3.348 },
/* 35. */ { 1.306, 1.690, 2.030, 2.438, 2.724, 3.340 },
/* 36. */ { 1.306, 1.688, 2.028, 2.434, 2.719, 3.333 },
/* 37. */ { 1.305, 1.687, 2.026, 2.431, 2.715, 3.326 },
/* 38. */ { 1.304, 1.686, 2.024, 2.429, 2.712, 3.319 },
/* 39. */ { 1.304, 1.685, 2.023, 2.426, 2.708, 3.313 },
/* 40. */ { 1.303, 1.684, 2.021, 2.423, 2.704, 3.307 },
/* 41. */ { 1.303, 1.683, 2.020, 2.421, 2.701, 3.301 },
/* 42. */ { 1.302, 1.682, 2.018, 2.418, 2.698, 3.296 },
/* 43. */ { 1.302, 1.681, 2.017, 2.416, 2.695, 3.291 },
/* 44. */ { 1.301, 1.680, 2.015, 2.414, 2.692, 3.286 },
/* 45. */ { 1.301, 1.679, 2.014, 2.412, 2.690, 3.281 },
/* 46. */ { 1.300, 1.679, 2.013, 2.410, 2.687, 3.277 },
/* 47. */ { 1.300, 1.678, 2.012, 2.408, 2.685, 3.273 },
/* 48. */ { 1.299, 1.677, 2.011, 2.407, 2.682, 3.269 },
/* 49. */ { 1.299, 1.677, 2.010, 2.405, 2.680, 3.265 },
/* 50. */ { 1.299, 1.676, 2.009, 2.403, 2.678, 3.261 },
/* 51. */ { 1.298, 1.675, 2.008, 2.402, 2.676, 3.258 },
/* 52. */ { 1.298, 1.675, 2.007, 2.400, 2.674, 3.255 },
/* 53. */ { 1.298, 1.674, 2.006, 2.399, 2.672, 3.251 },
/* 54. */ { 1.297, 1.674, 2.005, 2.397, 2.670, 3.248 },
/* 55. */ { 1.297, 1.673, 2.004, 2.396, 2.668, 3.245 },
/* 56. */ { 1.297, 1.673, 2.003, 2.395, 2.667, 3.242 },
/* 57. */ { 1.297, 1.672, 2.002, 2.394, 2.665, 3.239 },
/* 58. */ { 1.296, 1.672, 2.002, 2.392, 2.663, 3.237 },
/* 59. */ { 1.296, 1.671, 2.001, 2.391, 2.662, 3.234 },
/* 60. */ { 1.296, 1.671, 2.000, 2.390, 2.660, 3.232 },
/* 61. */ { 1.296, 1.670, 2.000, 2.389, 2.659, 3.229 },
/* 62. */ { 1.295, 1.670, 1.999, 2.388, 2.657, 3.227 },
/* 63. */ { 1.295, 1.669, 1.998, 2.387, 2.656, 3.225 },
/* 64. */ { 1.295, 1.669, 1.998, 2.386, 2.655, 3.223 },
/* 65. */ { 1.295, 1.669, 1.997, 2.385, 2.654, 3.220 },
/* 66. */ { 1.295, 1.668, 1.997, 2.384, 2.652, 3.218 },
/* 67. */ { 1.294, 1.668, 1.996, 2.383, 2.651, 3.216 },
/* 68. */ { 1.294, 1.668, 1.995, 2.382, 2.650, 3.214 },
/* 69. */ { 1.294, 1.667, 1.995, 2.382, 2.649, 3.213 },
/* 70. */ { 1.294, 1.667, 1.994, 2.381, 2.648, 3.211 },
/* 71. */ { 1.294, 1.667, 1.994, 2.380, 2.647, 3.209 },
/* 72. */ { 1.293, 1.666, 1.993, 2.379, 2.646, 3.207 },
/* 73. */ { 1.293, 1.666, 1.993, 2.379, 2.645, 3.206 },
/* 74. */ { 1.293, 1.666, 1.993, 2.378, 2.644, 3.204 },
/* 75. */ { 1.293, 1.665, 1.992, 2.377, 2.643, 3.202 },
/* 76. */ { 1.293, 1.665, 1.992, 2.376, 2.642, 3.201 },
/* 77. */ { 1.293, 1.665, 1.991, 2.376, 2.641, 3.199 },
/* 78. */ { 1.292, 1.665, 1.991, 2.375, 2.640, 3.198 },
/* 79. */ { 1.292, 1.664, 1.990, 2.374, 2.640, 3.197 },
/* 80. */ { 1.292, 1.664, 1.990, 2.374, 2.639, 3.195 },
/* 81. */ { 1.292, 1.664, 1.990, 2.373, 2.638, 3.194 },
/* 82. */ { 1.292, 1.664, 1.989, 2.373, 2.637, 3.193 },
/* 83. */ { 1.292, 1.663, 1.989, 2.372, 2.636, 3.191 },
/* 84. */ { 1.292, 1.663, 1.989, 2.372, 2.636, 3.190 },
/* 85. */ { 1.292, 1.663, 1.988, 2.371, 2.635, 3.189 },
/* 86. */ { 1.291, 1.663, 1.988, 2.370, 2.634, 3.188 },
/* 87. */ { 1.291, 1.663, 1.988, 2.370, 2.634, 3.187 },
/* 88. */ { 1.291, 1.662, 1.987, 2.369, 2.633, 3.185 },
/* 89. */ { 1.291, 1.662, 1.987, 2.369, 2.632, 3.184 },
/* 90. */ { 1.291, 1.662, 1.987, 2.368, 2.632, 3.183 },
/* 91. */ { 1.291, 1.662, 1.986, 2.368, 2.631, 3.182 },
/* 92. */ { 1.291, 1.662, 1.986, 2.368, 2.630, 3.181 },
/* 93. */ { 1.291, 1.661, 1.986, 2.367, 2.630, 3.180 },
/* 94. */ { 1.291, 1.661, 1.986, 2.367, 2.629, 3.179 },
/* 95. */ { 1.291, 1.661, 1.985, 2.366, 2.629, 3.178 },
/* 96. */ { 1.290, 1.661, 1.985, 2.366, 2.628, 3.177 },
/* 97. */ { 1.290, 1.661, 1.985, 2.365, 2.627, 3.176 },
/* 98. */ { 1.290, 1.661, 1.984, 2.365, 2.627, 3.175 },
/* 99. */ { 1.290, 1.660, 1.984, 2.365, 2.626, 3.175 },
/* 100. */ { 1.290, 1.660, 1.984, 2.364, 2.626, 3.174 }
};
const std::vector<double> confidence_level = { 80, 90, 95, 98, 99, 99.5 };
T_test()
{
data.resize(2);
}
void clear()
{
data[0].clear();
data[1].clear();
}
void add(size_t distribution, double value)
{
if (distribution > 1)
return;
data[distribution].add(value);
}
/// Confidence_level_index can be set in range [0, 5]. Corresponding values can be found above.
std::pair<bool, std::string> compareAndReport(size_t confidence_level_index = 5) const
{
if (confidence_level_index > 5)
confidence_level_index = 5;
if (data[0].size == 0 || data[1].size == 0)
return {true, ""};
size_t degrees_of_freedom = (data[0].size - 1) + (data[1].size - 1);
double table_value = students_table[degrees_of_freedom > 100 ? 0 : degrees_of_freedom][confidence_level_index];
double pooled_standard_deviation = sqrt(((data[0].size - 1) * data[0].var() + (data[1].size - 1) * data[1].var()) / degrees_of_freedom);
double t_statistic = pooled_standard_deviation * sqrt(1.0 / data[0].size + 1.0 / data[1].size);
double mean_difference = fabs(data[0].avg() - data[1].avg());
double mean_confidence_interval = table_value * t_statistic;
std::stringstream ss;
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.
{
ss << "Difference at " << confidence_level[confidence_level_index] << "% confidence : ";
ss << std::fixed << std::setprecision(8) << "mean difference is " << mean_difference << ", but confidence interval is " << mean_confidence_interval;
return {false, ss.str()};
}
else
{
ss << "No difference proven at " << confidence_level[confidence_level_index] << "% confidence";
return {true, ss.str()};
}
}
};