applied_statistics

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Lecture 10. Mann-Whitney.ipynb 
1587 строк · 481.3 Кб
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{
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 "cells": [
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  {
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   "cell_type": "code",
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   "execution_count": 1,
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   "metadata": {},
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   "outputs": [],
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   "source": [
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    "from scipy.stats import (\n",
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    "    norm, binom, expon, t, chi2, pareto, ttest_1samp, ttest_ind, sem, bernoulli, mannwhitneyu, uniform, gamma\n",
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    ")\n",
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    "from tqdm import tqdm_notebook\n",
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    "import scipy.stats as stats\n",
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    "from statsmodels.stats.proportion import proportion_confint\n",
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    "from statsmodels.stats.api import CompareMeans, DescrStatsW\n",
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    "import numpy as numpy\n",
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    "import math\n",
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    "from seaborn import distplot\n",
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    "from matplotlib import pyplot\n",
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    "import pandas as pd\n",
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    "import seaborn\n",
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    "from statsmodels.stats.api import CompareMeans, DescrStatsW\n",
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    "import warnings\n",
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    "warnings.filterwarnings('ignore')\n",
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    "numpy.random.seed(42)\n",
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    "\n"
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   ]
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  },
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  {
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   "cell_type": "code",
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   "execution_count": 2,
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   "metadata": {},
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   "outputs": [],
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   "source": [
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    "def inverse_plot_colorscheme():\n",
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    "    import cycler\n",
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    "    def invert(color_to_convert): \n",
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    "        table = str.maketrans('0123456789abcdef', 'fedcba9876543210')\n",
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    "        return '#' + color_to_convert[1:].lower().translate(table).upper()\n",
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    "    update_dict = {}\n",
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    "    for key, value in pyplot.rcParams.items():\n",
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    "        if value == 'black':\n",
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    "            update_dict[key] = 'white'\n",
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    "        elif value == 'white':\n",
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    "            update_dict[key] = 'black'\n",
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    "    \n",
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    "    old_cycle = pyplot.rcParams['axes.prop_cycle']\n",
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    "    new_cycle = []\n",
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    "    for value in old_cycle:\n",
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    "        new_cycle.append({\n",
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    "            'color': invert(value['color'])\n",
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    "        })\n",
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    "    pyplot.rcParams.update(update_dict)\n",
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    "    pyplot.rcParams['axes.prop_cycle'] = cycler.Cycler(new_cycle)\n",
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    "    lec = pyplot.rcParams['legend.edgecolor']\n",
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    "    lec = str(1 - float(lec))\n",
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    "    pyplot.rcParams['legend.edgecolor'] = lec"
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   ]
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  },
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  {
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   "cell_type": "code",
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   "execution_count": 3,
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   "metadata": {},
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   "outputs": [],
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   "source": [
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    "inverse_plot_colorscheme()"
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   ]
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  },
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  {
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   "cell_type": "markdown",
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   "metadata": {},
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   "source": [
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    "# Критерий Манна-Уитни."
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   ]
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  },
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  {
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   "cell_type": "markdown",
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   "metadata": {},
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   "source": [
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    "Давайте в этот раз придумаем новый критерий однородности, проверяющий смещение одной выборки относительно другой. Напомним нулевую гипотезу у критерия однородности:\n",
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    "\n",
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    "$$\n",
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    "    H_0: F = G,\\ vs. H_1: F \\neq G\n",
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    "$$\n",
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    "где $F$, $G$ – функции распределения 2-ух выборок.\n",
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    "\n",
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    "Для начала рассмотрим простой пример с 2 нормальными распределениями, где одно смещено относительно другого. Наш критерий должен будет детектирвоать, что это разные распределения.\n"
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   ]
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  },
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  {
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   "cell_type": "code",
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   "execution_count": 4,
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   "metadata": {},
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   "outputs": [],
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   "source": [
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    "distr_a = norm(loc=1, scale=1)\n",
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    "distr_b = norm(loc=3, scale=1)"
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   ]
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  },
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  {
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   "cell_type": "markdown",
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   "metadata": {},
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   "source": [
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    "Визуализируем:"
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   ]
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  },
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  {
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   "cell_type": "code",
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   "execution_count": 5,
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   "metadata": {},
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   "outputs": [
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    {
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     "data": {
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\n",
115
      "text/plain": [
116
       "<Figure size 720x360 with 1 Axes>"
117
      ]
118
     },
119
     "metadata": {
120
      "needs_background": "dark"
121
     },
122
     "output_type": "display_data"
123
    }
124
   ],
125
   "source": [
126
    "x = numpy.linspace(-4, 6, 1000)\n",
127
    "\n",
128
    "pyplot.figure(figsize=(10, 5))\n",
129
    "pyplot.title(\"2 нормальных распределения со смещением\", fontsize=12)\n",
130
    "pyplot.plot(x, distr_a.pdf(x), label='A')\n",
131
    "pyplot.plot(x, distr_b.pdf(x), label='B')\n",
132
    "pyplot.xlabel(f'X', fontsize=12)\n",
133
    "pyplot.ylabel('Плотность', fontsize=12)\n",
134
    "pyplot.grid(linewidth=0.2)\n",
135
    "pyplot.legend(fontsize=12)\n",
136
    "pyplot.show()\n"
137
   ]
138
  },
139
  {
140
   "cell_type": "markdown",
141
   "metadata": {},
142
   "source": [
143
    "Что является \"сердцем\" любого критерия? Правильно, его статистика! Ее-то нам и надо придумать. Во время всех предыдущих лекций мы опирались на **значения** элементов выборок, в этот раз предлагается посмотреть не на сами значения, а на их **порядок** относительно друг друга.\n",
144
    "\n",
145
    "Давайте сгенерируем выборки из наших искусственных нормальных распределений, и попытаемся их визуализировать."
146
   ]
147
  },
148
  {
149
   "cell_type": "code",
150
   "execution_count": 6,
151
   "metadata": {},
152
   "outputs": [
153
    {
154
     "data": {
155
      "image/png": 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\n",
156
      "text/plain": [
157
       "<Figure size 1440x720 with 4 Axes>"
158
      ]
159
     },
160
     "metadata": {
161
      "needs_background": "dark"
162
     },
163
     "output_type": "display_data"
164
    }
165
   ],
166
   "source": [
167
    "numpy.random.seed(8)\n",
168
    "sample_a = distr_a.rvs(50)\n",
169
    "sample_no_shift = distr_a.rvs(50)\n",
170
    "sample_b = distr_b.rvs(50)\n",
171
    "\n",
172
    "fig = pyplot.figure(figsize=(20, 10))\n",
173
    "\n",
174
    "ax = fig.subplots(nrows=2, ncols=2)\n",
175
    "\n",
176
    "pyplot.subplot(2, 2, 1)\n",
177
    "pyplot.title(\"2 нормальных распределения без смещения\", fontsize=12)\n",
178
    "pyplot.plot(x, distr_a.pdf(x), lw=5, label='A')\n",
179
    "pyplot.plot(x, distr_a.pdf(x), linestyle='--', lw=3, label='B')\n",
180
    "pyplot.xlabel(f'X', fontsize=12)\n",
181
    "pyplot.ylabel('Плотность', fontsize=12)\n",
182
    "pyplot.grid(linewidth=0.2)\n",
183
    "pyplot.legend(fontsize=12)\n",
184
    "\n",
185
    "\n",
186
    "pyplot.subplot(2, 2, 2)\n",
187
    "pyplot.title(\"2 нормальных распределения со смещением\", fontsize=12)\n",
188
    "pyplot.plot(x, distr_a.pdf(x), label='A')\n",
189
    "pyplot.plot(x, distr_b.pdf(x), label='B')\n",
190
    "pyplot.xlabel(f'X', fontsize=12)\n",
191
    "pyplot.ylabel('Плотность', fontsize=12)\n",
192
    "pyplot.grid(linewidth=0.2)\n",
193
    "pyplot.legend(fontsize=12)\n",
194
    "\n",
195
    "\n",
196
    "\n",
197
    "pyplot.subplot(2, 2, 3)\n",
198
    "# pyplot.title(\"2 нормальных распределения без смещения\", fontsize=12)\n",
199
    "pyplot.scatter(sample_a, [0] * len(sample_a), label='A')\n",
200
    "pyplot.scatter(sample_no_shift, [0] * len(sample_no_shift), alpha=0.5, label='B')\n",
201
    "pyplot.xlabel(f'Значения в выборках', fontsize=12)\n",
202
    "pyplot.grid(linewidth=0.2)\n",
203
    "pyplot.legend(fontsize=12)\n",
204
    "\n",
205
    "pyplot.subplot(2, 2, 4)\n",
206
    "# pyplot.title(\"2 нормальных распределения со смещением\", fontsize=12)\n",
207
    "pyplot.scatter(sample_a, [0] * len(sample_a), label='A')\n",
208
    "pyplot.scatter(sample_b, [0] * len(sample_b), alpha=0.5, label='B')\n",
209
    "pyplot.xlabel(f'Значения в выборках', fontsize=12)\n",
210
    "pyplot.grid(linewidth=0.2)\n",
211
    "pyplot.legend(fontsize=12)\n",
212
    "pyplot.show()\n"
213
   ]
214
  },
215
  {
216
   "cell_type": "markdown",
217
   "metadata": {},
218
   "source": [
219
    "Мы видим, что в случае равенства распредений (отсутсвия смещения) значения перемешаны между собой. Это левая картинка. А когда присутствует смещение распределений (правая картинка) все значения в выборке $B$ больше, чем значения в выборке $A$. Отсюда мы видим простое правило: если все точки одного распределения \"часто\" левее второго распределения, то это 2 разных распределения. Где понятие \"часто\" предстоит определить.\n",
220
    "\n",
221
    "**Идея:** давайте посчитаем число пар, где синий элемент больше рыжего, если таких пар очень много или мало, то одна выборка будет смещена относительно другой. \n",
222
    "\n",
223
    "Наш критерий на языке математики это:\n",
224
    "$$\n",
225
    "\\begin{align}\n",
226
    "    U = \\sum_{i}^N\\sum_{j}^M I[A_i < B_j]\n",
227
    "\\end{align}\n",
228
    "$$\n",
229
    "\n",
230
    "где $A_1, ..., A_N$ &mdash; первая выборка, $B_1, ..., B_M$ &mdash; вторая выборка, $I$ &mdash; функция-индикатор, которая равна 1, если выполнено условие в скобках, и 0 иначе. \n",
231
    "\n",
232
    "Напишем код для подсчета."
233
   ]
234
  },
235
  {
236
   "cell_type": "code",
237
   "execution_count": 7,
238
   "metadata": {},
239
   "outputs": [],
240
   "source": [
241
    "def calculate_U(A, B):\n",
242
    "    \"\"\"\n",
243
    "        Функция для подсчета статистики U\n",
244
    "    \"\"\"\n",
245
    "    U = 0\n",
246
    "    for A_elem in A:\n",
247
    "        for B_elem in B:\n",
248
    "            U += A_elem < B_elem\n",
249
    "    return U"
250
   ]
251
  },
252
  {
253
   "cell_type": "code",
254
   "execution_count": 8,
255
   "metadata": {},
256
   "outputs": [
257
    {
258
     "data": {
259
      "text/plain": [
260
       "2205"
261
      ]
262
     },
263
     "execution_count": 8,
264
     "metadata": {},
265
     "output_type": "execute_result"
266
    }
267
   ],
268
   "source": [
269
    "calculate_U(sample_a, sample_b)"
270
   ]
271
  },
272
  {
273
   "cell_type": "markdown",
274
   "metadata": {},
275
   "source": [
276
    "Ага, теперь нам надо понять, 2205 это много или мало? Давайте посчитаем мат. ожидание U, если у нас нет никакого смещения. В этом случае для любой пары вероятность, что одно значение будет больше второго, равна 0.5.\n",
277
    "\n",
278
    "$$\n",
279
    "\\begin{align}\n",
280
    "    \\mathbb{E} U = \\sum_{i}^N\\sum_{j}^M \\mathbb{P}[A_i < B_j] \\cdot I[A_i < B_j] = \\sum_{i}^N\\sum_{j}^M \\mathbb{P}[A_i < B_j] = \\sum_{i}^N\\sum_{j}^M \\dfrac{1}{2} = \\dfrac{NM}{2}\n",
281
    "\\end{align}\n",
282
    "$$\n",
283
    "\n",
284
    "В нашем случае мат. ожидание равно:\n"
285
   ]
286
  },
287
  {
288
   "cell_type": "code",
289
   "execution_count": 9,
290
   "metadata": {},
291
   "outputs": [
292
    {
293
     "data": {
294
      "text/plain": [
295
       "1250.0"
296
      ]
297
     },
298
     "execution_count": 9,
299
     "metadata": {},
300
     "output_type": "execute_result"
301
    }
302
   ],
303
   "source": [
304
    "len(sample_a) * len(sample_b) / 2"
305
   ]
306
  },
307
  {
308
   "cell_type": "markdown",
309
   "metadata": {},
310
   "source": [
311
    "Мы видим, что отличие есть. Понятно, что чем оно больше, тем вероятней есть смещение одной выборки относительно другой. Теперь осталось это выразить статистически: как распределена $U$ относительно мат. ожидания, когда выборки из одного распределения? Тогда мы сможем понять, насколько текущее отличие больше.  \n",
312
    "Cгенерируем распределение $U$ с помощью Монте-Карло:"
313
   ]
314
  },
315
  {
316
   "cell_type": "code",
317
   "execution_count": 10,
318
   "metadata": {},
319
   "outputs": [
320
    {
321
     "data": {
322
      "application/vnd.jupyter.widget-view+json": {
323
       "model_id": "d379da3d2513485eaf59fdd04d0e7c17",
324
       "version_major": 2,
325
       "version_minor": 0
326
      },
327
      "text/plain": [
328
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
329
      ]
330
     },
331
     "metadata": {},
332
     "output_type": "display_data"
333
    },
334
    {
335
     "data": {
336
      "image/png": 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\n",
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      "text/plain": [
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       "<Figure size 720x360 with 1 Axes>"
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      ]
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     },
341
     "metadata": {
342
      "needs_background": "dark"
343
     },
344
     "output_type": "display_data"
345
    }
346
   ],
347
   "source": [
348
    "numpy.random.seed(35)\n",
349
    "alpha=0.05\n",
350
    "sample_size = 50\n",
351
    "N_exps = 1000\n",
352
    "\n",
353
    "statistics = []\n",
354
    "\n",
355
    "for i in tqdm_notebook(range(N_exps)):\n",
356
    "    # Генерирую выборку из одного распределения\n",
357
    "    A = distr_a.rvs(sample_size)\n",
358
    "    B = distr_a.rvs(sample_size)\n",
359
    "    \n",
360
    "    U = calculate_U(A, B)\n",
361
    "\n",
362
    "    statistics.append(U)\n",
363
    "    \n",
364
    "EU = len(A) * len(B) / 2\n",
365
    "pyplot.figure(figsize=(10, 5))\n",
366
    "pyplot.title(\"Визуализация $U$\", fontsize=12)\n",
367
    "pyplot.vlines(EU, 0, 120, color='white', label='$\\mathbb{E}_{H0}$U')\n",
368
    "pyplot.hist(statistics, bins='auto')\n",
369
    "pyplot.xlabel(f'X', fontsize=12)\n",
370
    "pyplot.ylabel('Плотность', fontsize=12)\n",
371
    "pyplot.grid(linewidth=0.2)\n",
372
    "pyplot.legend(fontsize=14)\n",
373
    "pyplot.show()\n"
374
   ]
375
  },
376
  {
377
   "cell_type": "markdown",
378
   "metadata": {},
379
   "source": [
380
    "Что теперь мы можем сделать? Взять квантили этого распределения как критические области и наш критерий готов. "
381
   ]
382
  },
383
  {
384
   "cell_type": "code",
385
   "execution_count": 11,
386
   "metadata": {},
387
   "outputs": [
388
    {
389
     "data": {
390
      "text/plain": [
391
       "array([ 955.925, 1532.05 ])"
392
      ]
393
     },
394
     "execution_count": 11,
395
     "metadata": {},
396
     "output_type": "execute_result"
397
    }
398
   ],
399
   "source": [
400
    "numpy.quantile(statistics, [0.025, 0.975])"
401
   ]
402
  },
403
  {
404
   "cell_type": "markdown",
405
   "metadata": {},
406
   "source": [
407
    "Мы уже знаем, что в задаче с двумя нормальными распределениями он точно отверг гипотезу $H_0$ об однородности выборок: там значение 2205 > 1532.05.\n",
408
    "\n",
409
    "Минус текущего решения – оно будет подходить только для текущей задачи. Если мы поменяем распределения или размеры выборок – все изменится.\n",
410
    "Но тут на помощь приходит теория: было доказано, что если выборки $A$ и $B$ из одного распределения, то\n",
411
    "\n",
412
    "$$\n",
413
    "\\begin{align}\n",
414
    "    &U \\overset{d}\\rightarrow \\mathcal{N}(\\mathbb{E}U, \\mathbb{D}U), \\text{где}\\\\\n",
415
    "    &U^{(*)} = \\sum_{i}^N\\sum_{j}^M I[A_i < B_j],\\\\\n",
416
    "    &\\mathbb{E} U = \\dfrac{NM}{2},\\\\\n",
417
    "    &\\mathbb{D}U = \\dfrac{NM(N + M + 1)}{12}\n",
418
    "\\end{align}\n",
419
    "$$\n",
420
    "\n",
421
    "----\n",
422
    "\n",
423
    "Мы рассмотрели выше примеры, когда в выборке нет пересекающихся значений. Для непрерывных распределений это нормально, но что делать в случае дискретных распределений? Как считать пару $I[A_i < B_j]$, особенно если в выборках будет только одно значение? В этом случае нужно скорректировать формулу $U = \\sum_{i}^N\\sum_{j}^M I[A_i < B_j] + \\sum_{i}^N\\sum_{j}^M \\dfrac{1}{2}I[A_i = B_j]$. Тогда мат. ожидание $U$ даже в случае выборок из одинаковых значений будет равно $\\dfrac{NM}{2}$, что нам и нужно. Кроме этого применяется поправка к формуле дисперсии. И критерий остается валидным.\n",
424
    "\n",
425
    "При малых размерах выборок используются табличные значения."
426
   ]
427
  },
428
  {
429
   "cell_type": "code",
430
   "execution_count": 12,
431
   "metadata": {},
432
   "outputs": [],
433
   "source": [
434
    "def mann_whitney_distribution(A, B):\n",
435
    "    \"\"\"Функция, возвращающая распределение для статистики U.\"\"\"\n",
436
    "    N = len(A)\n",
437
    "    M = len(B)\n",
438
    "    DU = N * M * (N + M + 1) / 12\n",
439
    "    return norm(loc=N * M / 2, scale=DU ** (1/2))"
440
   ]
441
  },
442
  {
443
   "cell_type": "markdown",
444
   "metadata": {},
445
   "source": [
446
    "Покажем, что теория соотносится с практикой:"
447
   ]
448
  },
449
  {
450
   "cell_type": "code",
451
   "execution_count": 13,
452
   "metadata": {},
453
   "outputs": [
454
    {
455
     "data": {
456
      "image/png": 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\n",
457
      "text/plain": [
458
       "<Figure size 720x360 with 1 Axes>"
459
      ]
460
     },
461
     "metadata": {
462
      "needs_background": "dark"
463
     },
464
     "output_type": "display_data"
465
    }
466
   ],
467
   "source": [
468
    "x = numpy.linspace(min(statistics), max(statistics), 1000)\n",
469
    "distrib = mann_whitney_distribution(A, B)\n",
470
    "\n",
471
    "EU = len(A) * len(B) / 2\n",
472
    "pyplot.figure(figsize=(10, 5))\n",
473
    "pyplot.title(\"Визуализация $U$\", fontsize=12)\n",
474
    "pyplot.hist(statistics, density=True, bins='auto')\n",
475
    "pyplot.plot(x, distrib.pdf(x), label=\"Теоретическое распределение\")\n",
476
    "pyplot.vlines(EU, 0, 0.003, color='white', label='$\\mathbb{E}_{H0}$U')\n",
477
    "pyplot.xlabel(f'X', fontsize=12)\n",
478
    "pyplot.ylabel('Плотность', fontsize=12)\n",
479
    "pyplot.grid(linewidth=0.2)\n",
480
    "pyplot.legend(fontsize=12)\n",
481
    "pyplot.show()"
482
   ]
483
  },
484
  {
485
   "cell_type": "markdown",
486
   "metadata": {},
487
   "source": [
488
    "Видим достаточно точное совпадение, все отлично. Мы имеем статистику критерия, понимание, как она распределена при $H_0$, а значит, можем посчитать p-value. Критерий готов! \n",
489
    "\n",
490
    "Кроме того, теоретические свойства этого критерия работают для любых непрерывных распределений, а не только для нормальных. Это не параметрический криетрий.\n",
491
    "\n",
492
    "Минус текущего нашего решения – оно долго работает, а точнее за квадратичное время.  \n",
493
    "\n",
494
    "**Идея как ускорить работу критерия:** давайте упорядочим все элементы на графике ниже. Самый левый элемент &mdash; первый, следующий &mdash; второй и т.д. Эти номера назовем рангами.\n",
495
    "Будем опираться на ранги синей выборки. "
496
   ]
497
  },
498
  {
499
   "cell_type": "code",
500
   "execution_count": 42,
501
   "metadata": {},
502
   "outputs": [
503
    {
504
     "data": {
505
      "image/png": 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\n",
506
      "text/plain": [
507
       "<Figure size 1440x216 with 1 Axes>"
508
      ]
509
     },
510
     "metadata": {
511
      "needs_background": "dark"
512
     },
513
     "output_type": "display_data"
514
    }
515
   ],
516
   "source": [
517
    "sample_a = [1, 5, 8, 20]\n",
518
    "sample_b = [2, 3, 6]\n",
519
    "\n",
520
    "ranks_b = stats.rankdata(sample_a + sample_b)[len(sample_b):]\n",
521
    "\n",
522
    "pyplot.figure(figsize=(20, 3))\n",
523
    "pyplot.title(\"Пример рангов\", fontsize=12)\n",
524
    "pyplot.scatter(sample_a, [0] * len(sample_a), label='A')\n",
525
    "\n",
526
    "pyplot.scatter(sample_b, [0] * len(sample_b), alpha=0.5, label='B')\n",
527
    "for elem, rank in zip(sorted(sample_b), sorted(ranks_b)):\n",
528
    "    pyplot.text(elem - 0.03, 0.01, int(rank), c='blue')\n",
529
    "\n",
530
    "\n",
531
    "pyplot.xlabel(f'Значения в выборках', fontsize=12)\n",
532
    "pyplot.grid(linewidth=0.2)\n",
533
    "pyplot.legend(fontsize=12)\n",
534
    "pyplot.show()"
535
   ]
536
  },
537
  {
538
   "cell_type": "markdown",
539
   "metadata": {},
540
   "source": [
541
    "$R_j$ – ранг $B_j$ в выборке $(A_1,\\ ...,\\ A_N,\\ B_1,\\ ...,\\ B_M)$.\n",
542
    "\n",
543
    "$V = R_1 +\\ ...\\ + R_M$. Идея $V$: чем смещенней одна выборка относительно другой, тем больше/меньше сумма рангов у одной выборки.\n",
544
    "\n",
545
    "В случае, если в выборке есть повторения, то ранг – число элементов меньше текущего плюс число элементов, равных текущему, деленное на 2. Но ранги начинаются с 1, поэтому к формуле прибавляется 1.\n",
546
    "\n",
547
    "Например, в выборке [1, 1, 2, 3, 4, 4, 4] ранги будут равны [1.5, 1.5, 3, 4, 6, 6, 6].\n",
548
    "\n",
549
    "**Утверждение:** $U = V - \\dfrac{M (M + 1)}{2}$.\n",
550
    "\n",
551
    "\n",
552
    "То есть мы можем переписать наш критерий, вычисляя статистику $U$ по формуле $V - \\dfrac{M (M + 1)}{2}$. Зачем? Потому что это быстрее: чтобы посчитать все ранги, достаточно отсортировать выборку размера $N + M$ за время $(N + M)\\log(N + M)$, что сильно быстрее квадратичного времени $NM$.\n",
553
    "\n",
554
    "Поэтому **критерий Манна-Уитни часто называют критерием сумм рангов**.\n",
555
    "\n",
556
    "\n",
557
    "Итоговый критерий реализован в питоне [scipy.stats.mannwhitneyu](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html)."
558
   ]
559
  },
560
  {
561
   "cell_type": "code",
562
   "execution_count": null,
563
   "metadata": {},
564
   "outputs": [],
565
   "source": [
566
    "distr_a = norm(loc=1, scale=1)\n",
567
    "distr_b = norm(loc=3, scale=1)\n",
568
    "\n",
569
    "numpy.random.seed(8)\n",
570
    "sample_a = distr_a.rvs(50)\n",
571
    "sample_no_shift = distr_a.rvs(50)\n",
572
    "sample_b = distr_b.rvs(50)\n",
573
    "\n",
574
    "mannwhitneyu(sample_a, sample_b).pvalue\n"
575
   ]
576
  },
577
  {
578
   "cell_type": "markdown",
579
   "metadata": {},
580
   "source": [
581
    "Мы видим, что критерий нашел смещение, все отлично."
582
   ]
583
  },
584
  {
585
   "cell_type": "code",
586
   "execution_count": null,
587
   "metadata": {},
588
   "outputs": [],
589
   "source": [
590
    "mannwhitneyu(sample_a, sample_no_shift).pvalue"
591
   ]
592
  },
593
  {
594
   "cell_type": "markdown",
595
   "metadata": {},
596
   "source": [
597
    "И не нашел смещения, когда его нет."
598
   ]
599
  },
600
  {
601
   "cell_type": "markdown",
602
   "metadata": {},
603
   "source": [
604
    "### Алгоритм критерия Манна-Уитни\n",
605
    "\n",
606
    "Проверяемая гипотеза: $H_0: F=G,\\ vs.\\\\ H_1: F \\neq G$\n",
607
    "- Вычисляются ранги выборки $A_1,\\ ...\\ A_N,\\ B_1,\\ ...\\ B_M$.\n",
608
    "- Сохраняются все ранги выборки $B$: это выборка $R$.\n",
609
    "- Берется сумма рангов выборки $B$ в списке $A \\& B$: $V = R_1 +\\ ...\\ + R_M$. Считается статистика $U = V - \\dfrac{M (M + 1)}{2}$\n",
610
    "- Считается мат. ожидание выборки, дисперсия выборки при корректности $H_0$:\n",
611
    "$$\n",
612
    "\\begin{align}\n",
613
    "    &\\mathbb{E} U = \\dfrac{NM}{2},\\\\\n",
614
    "    &\\mathbb{D} U = \\dfrac{NM(N + M + 1)}{12}\n",
615
    "\\end{align}\n",
616
    "$$\n",
617
    "\n",
618
    "\n",
619
    "- $U \\overset{d}\\rightarrow \\mathcal{N}(\\mathbb{E}U, \\mathbb{D}U)$. По этому распределению считаются квантили.\n",
620
    "- При малых значениях выборок используют табличные значения.\n",
621
    "- Если в выборках есть повторения, то в дисперсии используется поправка.\n",
622
    "\n",
623
    "\n",
624
    "В чем главная прелесть данного критерия? Он не зависит от шумов в данных! Неважно, есть ли выбросы в вашей выборке, критерию это не важно: главное, сколько элементов меньше них.\n",
625
    "\n",
626
    "-------"
627
   ]
628
  },
629
  {
630
   "cell_type": "markdown",
631
   "metadata": {},
632
   "source": [
633
    "## При каких H1 Манн-Уитни будет мощным критерием?\n",
634
    "\n",
635
    "\n",
636
    "Рассмотрим с вами 2 ситуации: \n",
637
    "\n",
638
    "- Смещение 2 выборок\n",
639
    "- Изменение дисперсии у выборок\n",
640
    "\n",
641
    "\n",
642
    "Визуализируем эти 2 случая:"
643
   ]
644
  },
645
  {
646
   "cell_type": "code",
647
   "execution_count": 28,
648
   "metadata": {},
649
   "outputs": [
650
    {
651
     "data": {
652
      "image/png": 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\n",
653
      "text/plain": [
654
       "<Figure size 1440x360 with 2 Axes>"
655
      ]
656
     },
657
     "metadata": {
658
      "needs_background": "dark"
659
     },
660
     "output_type": "display_data"
661
    }
662
   ],
663
   "source": [
664
    "distr = norm(loc=1, scale=1)\n",
665
    "distr_shift = norm(loc=3, scale=1)\n",
666
    "\n",
667
    "distr_scaled = norm(loc=1, scale=3)\n",
668
    "\n",
669
    "\n",
670
    "fig = pyplot.figure(figsize=(20, 5))\n",
671
    "\n",
672
    "ax = fig.subplots(nrows=1, ncols=2)\n",
673
    "x = numpy.linspace(-3, 6, 1000)\n",
674
    "pyplot.subplot(1, 2, 1)\n",
675
    "pyplot.title(\"2 нормальных распределения со смещением\", fontsize=12)\n",
676
    "pyplot.plot(x, distr.pdf(x), label='A')\n",
677
    "pyplot.plot(x, distr_shift.pdf(x), label='B')\n",
678
    "pyplot.xlabel(f'X', fontsize=12)\n",
679
    "pyplot.ylabel('Плотность', fontsize=12)\n",
680
    "pyplot.grid(linewidth=0.2)\n",
681
    "pyplot.legend(fontsize=12)\n",
682
    "\n",
683
    "pyplot.subplot(1, 2, 2)\n",
684
    "x = numpy.linspace(-4, 6, 1000)\n",
685
    "pyplot.title(\"2 нормальных распределения c изменением дисперсии\", fontsize=12)\n",
686
    "pyplot.plot(x, distr.pdf(x), label='A')\n",
687
    "pyplot.plot(x, distr_scaled.pdf(x), label='B')\n",
688
    "pyplot.xlabel(f'X', fontsize=12)\n",
689
    "pyplot.ylabel('Плотность', fontsize=12)\n",
690
    "pyplot.grid(linewidth=0.2)\n",
691
    "pyplot.legend(fontsize=12)\n",
692
    "pyplot.show()\n"
693
   ]
694
  },
695
  {
696
   "cell_type": "markdown",
697
   "metadata": {},
698
   "source": [
699
    "Давайте оценим мощность критерия в каждом из этих 2 случаев. Как? С помощью механики Монте-Карло!\n",
700
    "\n",
701
    "\n",
702
    "#### Случай 1: смещение выборок"
703
   ]
704
  },
705
  {
706
   "cell_type": "code",
707
   "execution_count": 29,
708
   "metadata": {},
709
   "outputs": [
710
    {
711
     "data": {
712
      "application/vnd.jupyter.widget-view+json": {
713
       "model_id": "",
714
       "version_major": 2,
715
       "version_minor": 0
716
      },
717
      "text/plain": [
718
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
719
      ]
720
     },
721
     "metadata": {},
722
     "output_type": "display_data"
723
    },
724
    {
725
     "name": "stdout",
726
     "output_type": "stream",
727
     "text": [
728
      "Mann-whitneyu power: 1.0, (0.9962, 1.0)\n"
729
     ]
730
    }
731
   ],
732
   "source": [
733
    "numpy.random.seed(8)\n",
734
    "# Заводим счетчики количества отвергнутых гипотез для Манна-Уитни и для t-test\n",
735
    "mann_bad_cnt = 0\n",
736
    " \n",
737
    "# Прогоняем критерии 1000 раз\n",
738
    "sz = 1000\n",
739
    "for i in tqdm_notebook(range(sz)):\n",
740
    "    # Генерируем распределение\n",
741
    "    test = distr.rvs(1000)\n",
742
    "    control = distr_shift.rvs(1000)\n",
743
    "     \n",
744
    "    # Считаем p-value\n",
745
    "    mann_pvalue = mannwhitneyu(control, test, alternative='two-sided').pvalue\n",
746
    "    \n",
747
    "    # Отвергаем критерий на уровне 5%\n",
748
    "    if mann_pvalue < 0.05:\n",
749
    "        mann_bad_cnt += 1\n",
750
    "\n",
751
    "\n",
752
    "# Строим доверительный интервал для уровня значимости критерия (или для FPR критерия)\n",
753
    "left_mann, right_mann = proportion_confint(count = mann_bad_cnt, nobs = sz, alpha=0.05, method='wilson')\n",
754
    "# Выводим результаты\n",
755
    "print(f\"Mann-whitneyu power: {round(mann_bad_cnt / sz, 4)}, ({round(left_mann, 4)}, {round(right_mann, 4)})\")"
756
   ]
757
  },
758
  {
759
   "cell_type": "markdown",
760
   "metadata": {},
761
   "source": [
762
    "Мы видим мощность 1. А в случае с увеличением дисперсии?\n",
763
    "\n",
764
    "#### Случай 2: Разные дисперсии. Смещения нет"
765
   ]
766
  },
767
  {
768
   "cell_type": "code",
769
   "execution_count": 30,
770
   "metadata": {},
771
   "outputs": [
772
    {
773
     "data": {
774
      "application/vnd.jupyter.widget-view+json": {
775
       "model_id": "",
776
       "version_major": 2,
777
       "version_minor": 0
778
      },
779
      "text/plain": [
780
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
781
      ]
782
     },
783
     "metadata": {},
784
     "output_type": "display_data"
785
    },
786
    {
787
     "name": "stdout",
788
     "output_type": "stream",
789
     "text": [
790
      "Mann-whitneyu power: 0.071, (0.0567, 0.0886)\n"
791
     ]
792
    }
793
   ],
794
   "source": [
795
    "numpy.random.seed(8)\n",
796
    "# Заводим счетчики количества отвергнутых гипотез для Манна-Уитни и для t-test\n",
797
    "mann_bad_cnt = 0\n",
798
    " \n",
799
    "# Прогоняем критерии 1000 раз\n",
800
    "sz = 1000\n",
801
    "for i in tqdm_notebook(range(sz)):\n",
802
    "    # Генерируем распределение\n",
803
    "    test = distr.rvs(1000)\n",
804
    "    control = distr_scaled.rvs(1000)\n",
805
    "     \n",
806
    "    # Считаем p-value\n",
807
    "    mann_pvalue = mannwhitneyu(control, test, alternative='two-sided').pvalue\n",
808
    "    \n",
809
    "    # Отвергаем критерий на уровне 5%\n",
810
    "    if mann_pvalue < 0.05:\n",
811
    "        mann_bad_cnt += 1\n",
812
    "\n",
813
    "\n",
814
    "# Строим доверительный интервал для уровня значимости критерия (или для FPR критерия)\n",
815
    "left_mann, right_mann = proportion_confint(count = mann_bad_cnt, nobs = sz, alpha=0.05, method='wilson')\n",
816
    "# Выводим результаты\n",
817
    "print(f\"Mann-whitneyu power: {round(mann_bad_cnt / sz, 4)}, ({round(left_mann, 4)}, {round(right_mann, 4)})\")"
818
   ]
819
  },
820
  {
821
   "cell_type": "markdown",
822
   "metadata": {},
823
   "source": [
824
    "Мы видим очень маленькую мощность, близкую к 0.05!\n",
825
    "\n",
826
    "\n",
827
    "**Вывод:** Манн-Уитни хорошо работает в случае смещения выборок, но не в случае разных дисперсий у теста и контроля. Что логично вытекает из того, как мы строили критерий. "
828
   ]
829
  },
830
  {
831
   "cell_type": "markdown",
832
   "metadata": {},
833
   "source": [
834
    "### Односторонний критерий Манна-Уитни\n",
835
    "\n",
836
    "Теперь давайте обсудим, как с помощью текущего критерия определять, в какую сторону произошло смещение?\n",
837
    "\n",
838
    "Давайте посмотрим 2 ситуации: смещение синей выборки $B$ влево и вправо относительно рыжей выборки $A$. Где тогда будет значение статистики $U$?"
839
   ]
840
  },
841
  {
842
   "cell_type": "code",
843
   "execution_count": 17,
844
   "metadata": {},
845
   "outputs": [
846
    {
847
     "data": {
848
      "image/png": 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\n",
849
      "text/plain": [
850
       "<Figure size 1440x720 with 4 Axes>"
851
      ]
852
     },
853
     "metadata": {
854
      "needs_background": "dark"
855
     },
856
     "output_type": "display_data"
857
    }
858
   ],
859
   "source": [
860
    "numpy.random.seed(8)\n",
861
    "x = numpy.linspace(-4, 6, 1000)\n",
862
    "\n",
863
    "distr_a = norm(loc=1, scale=1)\n",
864
    "distr_b_right = norm(loc=1.5, scale=1)\n",
865
    "distr_b_left = norm(loc=0.5, scale=1)\n",
866
    "\n",
867
    "sample_a = distr_a.rvs(100)\n",
868
    "sample_b_right = distr_b_right.rvs(150)\n",
869
    "sample_b_left = distr_b_left.rvs(150)\n",
870
    "\n",
871
    "N = len(sample_a)\n",
872
    "M = len(sample_b_right)\n",
873
    "EU = N * M / 2\n",
874
    "DU = numpy.sqrt(N * M * (N + M + 1) / 12)\n",
875
    "mann_whitney_dist = norm(loc=EU, scale=DU)\n",
876
    "mw_x = numpy.linspace(EU - 3 * DU, EU + 3 * DU, 1000)\n",
877
    "\n",
878
    "\n",
879
    "fig = pyplot.figure(figsize=(20, 10))\n",
880
    "\n",
881
    "ax = fig.subplots(nrows=2, ncols=2)\n",
882
    "\n",
883
    "pyplot.subplot(2, 2, 1)\n",
884
    "pyplot.title(\"Cмещение синей выборки влево\", fontsize=12)\n",
885
    "pyplot.plot(x, distr_a.pdf(x), label='A')\n",
886
    "pyplot.plot(x, distr_b_left.pdf(x), label='B')\n",
887
    "pyplot.xlabel(f'X', fontsize=12)\n",
888
    "pyplot.ylabel('Плотность', fontsize=12)\n",
889
    "pyplot.grid(linewidth=0.2)\n",
890
    "pyplot.legend(fontsize=12)\n",
891
    "\n",
892
    "\n",
893
    "pyplot.subplot(2, 2, 3)\n",
894
    "u = calculate_U(sample_a, sample_b_left)\n",
895
    "pyplot.title(\"Распределение Манна-Уитни при H0\", fontsize=12)\n",
896
    "pyplot.plot(mw_x, mann_whitney_dist.pdf(mw_x), c='white', label='$U_{H0}$ dist')\n",
897
    "pyplot.scatter(u, 0, c='red', label='u')\n",
898
    "\n",
899
    "pyplot.xlabel(f'X', fontsize=12)\n",
900
    "pyplot.ylabel('Плотность', fontsize=12)\n",
901
    "pyplot.grid(linewidth=0.2)\n",
902
    "pyplot.legend(fontsize=12)\n",
903
    "\n",
904
    "\n",
905
    "pyplot.subplot(2, 2, 2)\n",
906
    "pyplot.title(\"Cмещение синей выборки вправо\", fontsize=12)\n",
907
    "pyplot.plot(x, distr_a.pdf(x), label='A')\n",
908
    "pyplot.plot(x, distr_b_right.pdf(x), label='B')\n",
909
    "pyplot.xlabel(f'X', fontsize=12)\n",
910
    "pyplot.ylabel('Плотность', fontsize=12)\n",
911
    "pyplot.grid(linewidth=0.2)\n",
912
    "pyplot.legend(fontsize=12)\n",
913
    "\n",
914
    "pyplot.subplot(2, 2, 4)\n",
915
    "u = calculate_U(sample_a, sample_b_right)\n",
916
    "pyplot.title(\"Распределение Манна-Уитни при H0\", fontsize=12)\n",
917
    "pyplot.plot(mw_x, mann_whitney_dist.pdf(mw_x), c='white', label='$U_{H0}$ dist')\n",
918
    "pyplot.scatter(u, 0, c='red', label='u')\n",
919
    "\n",
920
    "pyplot.xlabel(f'X', fontsize=12)\n",
921
    "pyplot.ylabel('Плотность', fontsize=12)\n",
922
    "pyplot.grid(linewidth=0.2)\n",
923
    "pyplot.legend(fontsize=12)\n",
924
    "\n",
925
    "\n",
926
    "pyplot.show()"
927
   ]
928
  },
929
  {
930
   "cell_type": "markdown",
931
   "metadata": {},
932
   "source": [
933
    "В первом случае значение статистики U будет маленьким, а во втором – большим, что логично: в одном случае все ранги синей выборки маленькие, а в другом – большие. Поэтому и статистика $U$ будет либо в левом хвосте (если синее распределение левее), либо в правом хвосте (наоборот).\n",
934
    "\n",
935
    "В критерии Манна-Уитни это также реализовано через альтернативу:"
936
   ]
937
  },
938
  {
939
   "cell_type": "code",
940
   "execution_count": 18,
941
   "metadata": {},
942
   "outputs": [
943
    {
944
     "data": {
945
      "text/plain": [
946
       "0.005465026978270606"
947
      ]
948
     },
949
     "execution_count": 18,
950
     "metadata": {},
951
     "output_type": "execute_result"
952
    }
953
   ],
954
   "source": [
955
    "mannwhitneyu(sample_b_right, sample_a, alternative='greater').pvalue"
956
   ]
957
  },
958
  {
959
   "cell_type": "code",
960
   "execution_count": 19,
961
   "metadata": {},
962
   "outputs": [
963
    {
964
     "data": {
965
      "text/plain": [
966
       "4.6704977909583455e-05"
967
      ]
968
     },
969
     "execution_count": 19,
970
     "metadata": {},
971
     "output_type": "execute_result"
972
    }
973
   ],
974
   "source": [
975
    "mannwhitneyu(sample_b_left, sample_a, alternative='less').pvalue"
976
   ]
977
  },
978
  {
979
   "cell_type": "markdown",
980
   "metadata": {},
981
   "source": [
982
    "Таким образом вы можете проверять, распределение левее или правее вашего изначального рыжего распределения.\n",
983
    "\n",
984
    "Теперь давайте рассмотрим еще 1 пример."
985
   ]
986
  },
987
  {
988
   "cell_type": "code",
989
   "execution_count": 34,
990
   "metadata": {},
991
   "outputs": [
992
    {
993
     "data": {
994
      "image/png": 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\n",
995
      "text/plain": [
996
       "<Figure size 720x360 with 1 Axes>"
997
      ]
998
     },
999
     "metadata": {
1000
      "needs_background": "dark"
1001
     },
1002
     "output_type": "display_data"
1003
    }
1004
   ],
1005
   "source": [
1006
    "distr_a = expon(loc=0, scale=6)\n",
1007
    "distr_b = gamma(a=4, scale=1)\n",
1008
    "x = numpy.linspace(0, 30, 1000)\n",
1009
    "\n",
1010
    "fig = pyplot.figure(figsize=(10, 5))\n",
1011
    "pyplot.title(\"Что левее? Плотность распределения\", fontsize=12)\n",
1012
    "\n",
1013
    "pyplot.plot(x, distr_a.pdf(x), c='white', label='A')\n",
1014
    "pyplot.plot(x, distr_b.pdf(x), c='yellow', label='B')\n",
1015
    "pyplot.xlabel(f'X', fontsize=12)\n",
1016
    "pyplot.ylabel('Плотность', fontsize=12)\n",
1017
    "pyplot.grid(linewidth=0.2)\n",
1018
    "pyplot.legend(fontsize=12)\n",
1019
    "pyplot.show()"
1020
   ]
1021
  },
1022
  {
1023
   "cell_type": "code",
1024
   "execution_count": 35,
1025
   "metadata": {},
1026
   "outputs": [
1027
    {
1028
     "data": {
1029
      "text/plain": [
1030
       "6.0"
1031
      ]
1032
     },
1033
     "execution_count": 35,
1034
     "metadata": {},
1035
     "output_type": "execute_result"
1036
    }
1037
   ],
1038
   "source": [
1039
    "distr_a.expect()"
1040
   ]
1041
  },
1042
  {
1043
   "cell_type": "code",
1044
   "execution_count": 36,
1045
   "metadata": {},
1046
   "outputs": [
1047
    {
1048
     "data": {
1049
      "text/plain": [
1050
       "4.000000000000001"
1051
      ]
1052
     },
1053
     "execution_count": 36,
1054
     "metadata": {},
1055
     "output_type": "execute_result"
1056
    }
1057
   ],
1058
   "source": [
1059
    "distr_b.expect()"
1060
   ]
1061
  },
1062
  {
1063
   "cell_type": "markdown",
1064
   "metadata": {},
1065
   "source": [
1066
    "Какое в этом случае распределение будет левее по мнению Манна-Уитни?"
1067
   ]
1068
  },
1069
  {
1070
   "cell_type": "code",
1071
   "execution_count": 23,
1072
   "metadata": {},
1073
   "outputs": [
1074
    {
1075
     "data": {
1076
      "application/vnd.jupyter.widget-view+json": {
1077
       "model_id": "77cc034ca2e341709da58820471819a3",
1078
       "version_major": 2,
1079
       "version_minor": 0
1080
      },
1081
      "text/plain": [
1082
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
1083
      ]
1084
     },
1085
     "metadata": {},
1086
     "output_type": "display_data"
1087
    },
1088
    {
1089
     "name": "stdout",
1090
     "output_type": "stream",
1091
     "text": [
1092
      "Power for alternative 'Less': (A < B): 0.0%\n",
1093
      "Power for alternative 'Greater': power (A > B): 91.1%\n"
1094
     ]
1095
    }
1096
   ],
1097
   "source": [
1098
    "numpy.random.seed(8)\n",
1099
    "# Заводим счетчики количества отвергнутых гипотез для Манна-Уитни и для t-test\n",
1100
    "mann_bad_cnt_left = 0\n",
1101
    "mann_bad_cnt_right = 0\n",
1102
    "\n",
1103
    " \n",
1104
    "# Прогоняем критерии 1000 раз\n",
1105
    "sz = 1000\n",
1106
    "for i in tqdm_notebook(range(sz)):\n",
1107
    "    # Генерируем распределение\n",
1108
    "    A = distr_a.rvs(1000)\n",
1109
    "    B = distr_b.rvs(1000)\n",
1110
    "     \n",
1111
    "    # Считаем p-value\n",
1112
    "    mann_pvalue_left = mannwhitneyu(A, B, alternative='less').pvalue  # H1: A < B \n",
1113
    "    mann_pvalue_right = mannwhitneyu(A, B, alternative='greater').pvalue  # H1: A > B\n",
1114
    "\n",
1115
    "    \n",
1116
    "    # отвергаем критерий на уровне 5%\n",
1117
    "    if mann_pvalue_left < 0.05:\n",
1118
    "        mann_bad_cnt_left += 1\n",
1119
    "\n",
1120
    "    if mann_pvalue_right < 0.05:\n",
1121
    "        mann_bad_cnt_right += 1\n",
1122
    "    \n",
1123
    "\n",
1124
    "print(f\"Power for alternative 'Less': (A < B): {round(mann_bad_cnt_left / sz * 100, 1)}%\")\n",
1125
    "print(f\"Power for alternative 'Greater': power (A > B): {round(mann_bad_cnt_right / sz * 100, 1)}%\")\n"
1126
   ]
1127
  },
1128
  {
1129
   "cell_type": "markdown",
1130
   "metadata": {},
1131
   "source": [
1132
    "Критерий Манна-Уитни посчитал, что белое распределение правее желтого. Правда ли это? Здесь зависит от того, как мы **формально** определяем, что значит левее или правее. \n",
1133
    "\n",
1134
    "В данном случае поступим просто: определим \"правее\" – это значит, что Манн-Уитни чаще будет отвергать нулевую гипотезу в пользу альтернативы \"greater\". Нам надо понять, есть ли у этого правила какое-то применение на практике?\n",
1135
    "\n",
1136
    "Посмотрим на другой пример:"
1137
   ]
1138
  },
1139
  {
1140
   "cell_type": "code",
1141
   "execution_count": 37,
1142
   "metadata": {},
1143
   "outputs": [
1144
    {
1145
     "data": {
1146
      "image/png": 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UP38+bNwIzzzjn/JFRESyCiVxkm6RkXDPPfDNN+b5p/7y7rtQrZpp9RMREZGUKYmTdGvWDAoWNPO6+dNXX8HBg+beOBEREUmZkjhJt44d4ehRWLTIv9eJjzfTlzRpAmXK+PdaIiIi/rB7927Onj3L6dOnOXHiBLNmzaJkyZKOXkNJnKRLrlzQogXExDg3N1xaxowBy4KHH/b/tURERPyhdevWFChQgGLFinH48GGGDx/uaPlK4iRd6teHqKjMPSfVFwcOwKxZ8OCDEB5uBeaiIiIifnDhwgWmTp1K5cqVHS03kElcM2AbsAN4IYX9DYGfgQSgvdf2RsB6r+U8cI+97zNgt9e+mn6IW4CWLeHiRTN6NFBGjYJrroGWLf04ikJERMTP8uTJw7333svKlSsdLTeXo6WlLgz4ELgb2A+sAWKALV7H7AV6AM8mO/cHLiVnV2GSwHle+/sCUx2PWC7TsiUsXQpnzgTumvPmwe7d0L37Bb79VrP/iohI6oYOhZp+bspZv963QXfffvstCQkJ5MuXj6NHj9K0aVNH4wlUS9wtmORrF3AR+Bpom+yY34GNQFIa5bQH5gBnnQ9RUlO6NFSpEriuVI+kJPjkE7j99gTKlg3AjXgiIiIOuueee4iOjiZ37tz07t2bJUuWcM011zhWfqBa4koA+7ze7wfqZqCcTsB7yba9DrwMLMR0015Iq4CwsDCio6MzcOn0iYqK8lvZbunQ4TxwjmXLChIdHRbQa3/zTRKvvXaS7t1zsHOn//5u2UlW/I66TXXqLNWn87JinebMmZOwsEu/Sc8m78fzk7AwLrtu2seG/X1sTEwMiYmJNGzYkOnTp//j2Jw5c/qcn4TSwIZiQDVgrte2fkAloA6mq/X5VM7tCawF1hYuXNifMWZJd98dz86dOdm5M7AJHMDhwzn58cc8tGt3hhw5NMBBRERCU+vWrYmOjubXX391rMxAtcQdAEp5vS9pb/NFR+AbwPsud88j2C8A4/jn/XQeo+2Fw4cPW3FxcT5e2neBuEYg5MoFt94Kn3/u3mf68st8jBmTSPXqf7J4sSshZElZ5TsaTFSnzlJ9Oi8r1ek111xDYiDmvErDla7/7bffkpiYiGVZ7Nmzh+7du7Np06YUj01KSvL57xOoJG4NUB4og0neOgFdfCyjM6blzVsxTCKXAzNi9ZfMhSnJ1akD+fP7f4LftMyZE87p09CtG0riREQkJJQJwGz1gepOTQB6Y7pCtwKTgc3AIKCNfUwdzL1yHYCP7f0epTEteUuSlTsB2GQvhYHBfok+G2vUyKyXJK/5ADp3LgfffhtB+/aQN697cYiIiASTQLXEAXxnL95e9nq9BtPNmpLfMYMjkrsz82FJWho1gg0b4Phxd+P4+usI7r//Iu3awYQJ7sYiIiISDEJpYIMEWEQE3Habu12pHitX5mL3btOlKiIiIkriJA316kGePPDDD25HApaVg4kToXFjKFLE7WhERETcpyROUtWokXnY/dKlbkdiTJpk5uf5z3/cjkRERMR9SuIkVXfcAbGxcPKk25EYmzbBli1w771uRyIiIm6Lj48nT548bofhiDx58hAf7/tzwpXEOSxnzpyUK1fO7TAyLVcuqFs3eFrhPCZNgoYNoVgxtyMRERE3HTlyhBIlSoR8IpcnTx5KlCjBkSNHfD43kKNTs4X33nuP5s2bc/3113Pu3Dm3w8mwmjXN/XDLl7sdyeUmTYJXX4UOHeCDD9yORkRE3HL69GkAihcvTnh4eECvnTOnaQNLSkrrce/pEx8fz+HDh//+PL5QEuewr776im7duvHoo48ydOhQt8PJsPr1zXrFCnfjSG7bNli/3nSpKokTEcneTp8+naHkJ7M8zzh1+wkY6k512KpVq1iyZAnPPfccuXPndjucDKtfH/bsgYMH3Y7kn77+2sR33XVuRyIiIuIeJXF+MGTIEK699loefvhht0PJsPr1g68r1WPyZLPu2NHdOERERNykJM4Pli9fzpIlS3j++eeJjIx0OxyflSwJpUoFbxK3ezesWqVRqiIikr0pifOTV199lRIlSvDQQw+5HYrPbr3VrIM1iQOYOhVq11aXqoiIZF9K4vzkhx9+YNmyZbzwwgtERES4HY5P6teHv/6CjRvdjiR133xj1u3auRuHiIiIW5TE+dGrr75KqVKl6NGjh9uh+KR+fVizBhIS3I4kdTt3woYN8O9/ux2JiIiIO5TE+dGCBQtYsWIF/fv3D/gcNhkVHg41asDq1W5HcmXffAP/+hcULep2JCIiIoGnJM7PBg0axPXXX0+3bt3cDiVdqlaFyEhYu9btSK5s+nTImRPatHE7EhERkcBTEudn33//PatXr+bFF18kV67gn1v55pvNOhSSuE2bYMcOdamKiEj2pCQuAAYOHEiZMmV48MEH3Q7limrXhhMnzDQeoWD6dGjcGAoVcjsSERGRwFISFwBz5sxh+fLlvPTSS0E/b1zt2rBundtRpN8330BEBLRs6XYkIiIigaUkLkBefPFFSpYsyaOPPup2KKmKiIBq1UIriVu1yjwaTF2qIiKS3SiJC5DFixezYMEC+vfvT758+dwOJ0XVqplELhTuh/OwLNMa16wZ5MnjdjQiIiKBoyQugAYMGEDRokV58skn3Q4lRaE0qMHb9OmQLx80aeJ2JCIiIoGjJC6AVq1axcyZM+nbty+FgvBO/Nq14fhx2LPH7Uh8s3SpiVtdqiIikp0oiQuwl156iejoaJ599lm3Q/mH2rVDrxUOzJMlZs6E1q0hBGZxERERcUQgk7hmwDZgB/BCCvsbAj8DCUD7ZPsSgfX2EuO1vQywyi5zEhD0DyndsGEDkyZN4qmnnqJw4cJuh/O3yEgz0W8oDWrwNmMGREebJziIiIhkB4FK4sKAD4HmQGWgs732thfoAUxM4fxzQE178Z6f/y1gKFAOiAMecjJof3nllVfIkycPL7yQUi7rjurVzSO3QrElDmD+fDh/Xk9vEBGR7CNQSdwtmNayXcBF4GugbbJjfgc2AknpLDMHcCcw1X7/OXBPZgMNhG3btjF+/Hh69epFiRIl3A4HgFq1zPrnn92NI6P++gsWLjRdqiIiItlBoO4gKgHs83q/H6jrw/m5gbWYrtb/Ad8CVwN/2ts8ZV4xIwoLCyM6OtqHS/smKioqXccNHTqULl268NZbb/HEE0/4LZ70uuWWvzh5Mp5TpwoRHZ3D7XAuk946XbDgAi1bnqVevYJs2xbm56hCV3rrU9JPdeos1afzVKfOCpb6DJWBDdcDtYEuwDCgrI/n98QkgWuD5T60/fv388knn9C5c2duvPFGt8OhSpVENm8OwzRwhqZ588IBaNYs3uVIRERE/C9QLXEHgFJe70va23w5H0x37GLgJmAaEIX5DAlXKHO0vXD48GErLi7Oh0tnTHqu8fLLL9O1a1f69+9Pq1at/B5TanLkgMqV4bPP0he3W64UW1wcrFkDd999joEDzwUoqtAVzH/rUKU6dZbq03mqU2e5XZ+BaolbA5THjCaNADpx+SjTtEQDngeOFgZuA7YAFvADl0aydgdmOBRvQMTFxfHGG2/QsmVLGjVq5FocpUtDgQKwcaNrITgmJgbq1YOiRd2ORERExL8ClcQlAL2BucBWYDKwGRjEpdGmdTD3tXUAPrb3A9yI6QrdgEna/odJ4gCeB/pgBk1cDXzq58/huOHDh7Nnzx7efvttcuRwpyuzRg2z3rDBlcs7KiYGcuaEli3djkRERMS/Ajk16nf24u1lr9drMF2iyS0HqqVS5i7MyNeQdeHCBV566SXGjx9Px44dmTRpUsBjqF4dkpJg8+YrHxvsNm40T5xo0wbGjXM7GhEREf8JlYENWdqECRNYv349b7zxBhERgZ+vuEYN2L4dzp4N+KX9IibGPEc1d263IxEREfEfJXFBICkpieeff54bbriBxx57LODXr149a9wP5xETA3nzQuPGbkciIiLiP0rigsS8efOYP38+L730EoUKFQrYdfPnh3Llssb9cB5LlsCpU3p6g4iIZG1K4oLIc889R3R0NC+99FLArlm1qllnpZa4+HiYM8c8vcGlsSIiIiJ+pyQuiKxfv56xY8fy5JNPUr58+YBcMyuNTPU2cyYUKwa1a7sdiYiIiH8oiQsyAwYM4Ny5c7zzzjsBuV6NGvDnn7B3b0AuFzDffQcJCepSFRGRrEtJXJA5fPgwr7/+Om3atOGuu+7y+/Wy2qAGj7g4WLZMSZyIiGRdSuKC0LBhw9i5cydDhw4lLMy/D3KvWhU2bfLrJVwTE2OS1NKl3Y5ERETEeUrigtDFixd59tlnqVq1Kj179vTbdUqWhEKFssYkvymJsR/s1rq1u3GIiIj4g5K4IPXtt9/yww8/MGjQIKKiovxyjcqVzTqrJnE7d8KWLUriREQka1ISF8SeeuopoqOjeeWVV/xSfpUqZp1Vkzgwo1TvuAMKFnQ7EhEREWcpiQtiGzduZMyYMfTq1YtKlSo5Xn6VKnDkCBw/7njRQSMmBsLDoWlTtyMRERFxlpK4IDdgwADOnDnDiBEjHC+7cuWs3QoHsHIlHD2qUaoiIpL1KIkLcseOHePFF1+kcePGdOzY0dGyK1c294xlZUlJMHs2tGgBfh7oKyIiElBK4kLAxx9/zLp163jvvffInz+/I2WWKJG1R6Z6i4mBq66C225zOxIRERHnKIkLAUlJSTz++OOUKFHCsUEO2WFQg8e8eXDhgrpURUQka1ESFyJWr17NJ598wlNPPUUVTwaWCZ7pRbJ6dyrAX3/BokVK4kREJGtREhdC+vXrx8mTJx0Z5OAZmXrsmAOBhYCZM6F8eahY0e1IREREnKEkLoQcP36cfv36cccdd9ClS5dMlZUdBjV4mznTrDXxr4iIZBVK4kLMmDFjWLVqFe+++y4FMzGDbZUq2eN+OI/9+yE2Vl2qIiKSdSiJCzGWZdGrVy+KFCnC66+/nqEystPIVG8xMVC/Plx9tduRiIiIZJ6SuBC0bt06hg8fzuOPP069evV8Pj87DWrwFhNj5opr0cLtSERERDJPSVyIeumll9i/fz+jR48mPDzcp3Oz0/Qi3n7+GQ4cUJeqiIhkDYFM4poB24AdwAsp7G8I/AwkAO29ttcEVgCbgY3AvV77PgN2A+vtpabTQQerM2fO0KtXL6pVq0bfvn19OrdyZfMoquwyMtXbzJnmOaoREW5HIiIikjmBSuLCgA+B5kBloLO99rYX6AFMTLb9LNANqIJJBIcBUV77+2KSt5qYRC7bmDVrFpMnT+all16ifPny6T4vuw1q8DZzJhQoAHfc4XYkIiIimZMrQNe5BdMCt8t+/zXQFvC+K+t3e52U7NzfvF4fBI4ARYA/MxJIWFgY0dHRGTk1XaKioq58kINefvllmjZtyqeffkrbtm3TcYZFlSonmTo1gujovH6PzwlO1mlsrMVff/1Jhw6RrFkTGp/faYH+jmYHqlNnqT6dpzp1VrDUZ6Ba4koA+7ze77e3+eoWIALY6bXtdUw361AgMpXzegJrgbWFCxfOwGWD15EjR3jllVdo0KBBuuaOK1rUolAhi99+y563Q54/n4PFi8Np1uwiYLkdjoiISIYFqiXOCcWAL4DuXGqt6wf8gUnsRgPPA4NSOHe0vXD48GErLi7O78EG4hoeH3zwAf/+978ZNGgQU6ZM4ciRI6keW62aWcfGniMu7lyAInSGU3U6bRq0bAnXXfcnGzY4UmRICuR3NLtQnTpL9ek81amz3K7PQDXHHABKeb0vaW9Lr4LAbOBFYKXX9kOY5pQLwDhMS122Y1kWPXv2JF++fFd8JFelSmb9668BCCxIzZ4NSUl6eoOIiIS2QCVxa4DyQBlMq1knICad50YA3wDjganJ9hWz1zmAe4BfMh1piNq2bRsDBw6kQ4cOtG/fPtXjKlaEs2fNEwyyqyNHYNUqTTUiIiKhLVBJXALQG5gLbAUmY6YMGQR4fkrrYO6V6wB8bO8H6IiZfqQH/5xKZAKwyV4KA4P9+zGC25AhQ1izZg0jR46kSJEiKR5TqRJs2wZWNr8dLCYG6tSBYsWufKyIiEgwykwSVwGo5MPx39nnlMUMRgB4mUstcmsw3QcKrWMAACAASURBVKz5gKsxU4oAfAmEc2kaEe+pRO4EqgFVgfuAMxn4HFlGYmIiPXr0oGDBgql2q1asaJK47G7mTLNu1crdOERERDIqo0lcH0witYaUJ+4Vl2zZsoWBAwfSsWPHf3SrRkZCmTLZ+344j82bYdcudamKiEjoymgS9zim+/NG4BHnwhEneHerek+pUq4c5MypljiPmTOhcWPImz2nixMRkRCX0STuasw9a/sJrWlKsoXExEQeeOABChYsyIcffvj3do1MvVxMDOTJA3fd5XYkIiIivvMlibvBa8mBGWla1scyJEA2b97Mq6++SseOHenQoQNg7ocD+O23NE7MRn78EU6e1FQjIiISmnxJwHYA2+11QcxTE7YD1/ohLnHA22+/zerVqxk1ahTFixenUiXYu9dMMSIQHw9z5pjBDTlyuB2NiIiIb3xJ4nJiHmSfM9kS5oe4xAGJiYncd999REZGMm7cOI1MTUFMDFx7rZluREREJJT4ksRpFGoI2r59O3369KFJk7upXj1cSVwyc+ZAQoJGqYqISOjxJYnr77coxK9Gjx7NvHnjyZ07npMn1fvt7c8/zb1xSuJERCTU+JLE6a6hEDZq1FMA3Hvvy0RERLgcTXCZOROqVYPSpd2OREREJP18SeLyAntTWSTIFS36JwDlyrVi0KBBLkcTXDxPb9AoVRERCSW+zPF2AbjfX4GIf1WqBH/9BV9+OYu+ffvy3XffsXTpUrfDCgo7dsDWrSaJGz7c7WhERETSx5eWuARgSSqLBDnPyNQ+fZ5lx44dTJgwgauuusrtsIJGTAzccQcULOh2JCIiIunjSxK3y29RiN9VqmSSuLNnz9KpUyeKFCnCZ5995nZYQWPGDAgPh5Yt3Y5EREQkfXxJ4uoB4cm2hQORzoUj/pA7N1x//aXHbcXGxtK3b19at27Nk08+6W5wQWLlSjh0CNq1czsSERGR9PEliZsH3Jxs283AXOfCEX8oX/6fD74fPnw4MTExDBkyhFq1arkXXJCwLPjmG2jRwiS9IiIiwc6XJK46sCrZttVADefCEX/wPDM1+YPvH3jgAQ4fPsykSZMoUKBA4AMLMt98A/nyQZMmbkciIiJyZb4kcX8C1yTbdg3wl3PhiD9UqmTW27dfvv3EiRN06dKFMmXK8NFHHwU+sCCzeDHExcG//+12JCIiIlfmSxI3DZgIVMXMGVcNGA9M9kNc4qCKFWHPnpQffL9s2TIGDhxI165defDBBwMfXBBJSDCjVFu3hly+TL4jIiLiAl+SuBeBrZgu1DOYrtVtQD8/xCUO8oxMTc0bb7zBwoULGTFiBDVqZO/e8enT4aqr4Pbb3Y5EREQkbb4kceeBXkA+TDdqPqA3ZhJgCWIVK/7zfjhvSUlJdO7cmRMnTjBt2jSioqICF1yQmTfPTIqsLlUREQl2viRxAOWBl4DB9rq84xGJo669FgoUgN9+S/u4o0eP0qFDB6677jrGjx9PjhzZ81G558/DnDlwzz2QTatARERChC9JXGtgHVAJOAFUBNYCbfwQlzjEMzI1re5UjxUrVtCnTx9at25Nv37Zt5d8+nQoXhzq1nU7EhERkdT5ksS9AbQFumDug+tqv38jnec3w9xDtwN4IYX9DYGfMY/3ap9sX3dgu71099p+M7DJLvMDQG0nyVSoYNZXaonzGDFiBBMnTuS1117jrrvu8l9gQWz2bLh4UV2qIiIS3HxJ4koCPybbtszefiVhwIdAc6Ay0Nlee9sL9MCMgPV2FfAKUBe4xX4dbe/7CHgY061bHpMoipcKFUwX4b596T/n4YcfZsuWLUycOJGSJdPz581aTp2ChQuVxImISHDzJYlbDzyTbFsfe/uV3IJpLdsFXAS+xrTiefsd2AgkJdveFJiP6cKNs183A4oBBYGVgIWZ7uSedH2SbKRCBTM/nGWl/5yzZ8/yn//8h8jISKZOnUpERIT/AgxS06dD2bJQvbrbkYiIiKTMl9mwHgNmAv8H7ANKAWcx98pdSQn7HI/9mJa19Ejp3BL2sj+F7WkKCwsjOjr6SodlWLCN7KxU6SS//hpGdHR+n847evQovXv3Zvz48YwdO5YnnnjCTxFemRt1umRJEklJJ+nSJTf79uUJ+PX9Kdi+o1mB6tRZqk/nqU6dFSz16UtL3K/AjcC9wLtAR/v9Vj/E5bSemEEYawsXLux2LAGTK5dFmTJJ7NgRlqHzZ82axZAhQ+jatSuPPPKIw9EFt2PHcrJiRS5atYp3OxQREZEU+TovfQL/vC8uPQ5gWu48Strb0nvuHcnOXWxvL5lse2pljrYXDh8+bMXFxaXz0hkXiGtcSblyEB4OGzeeJy7ufIbKeP755ylXrhyDBw9m7dq1LFiwwOEo0y/QdTplCgwbBldfHceOHQG9dEAEw3c0q1GdOkv16TzVqbPcrk9fWuJ2Y+5pS2m5kjWYgQdlgAigExCTzuvOBZpgBjNE26/nAoeAU0A9zKjUbsCMdJaZLfg6MjUllmVx//33s3nzZiZNmkS5cuWcCS4ETJ9u1h06uBuHiIhISnxJ4v6LGQnaEyhiv/YsV5KAebrDXEz362RgMzCIS/PM1cHc19YB+NjeD2ZAw2uYRHCNfc4Je9/jwBjMoImdwBwfPk+W50QSB/DXX3/Rtm1bkpKSmDFjBgULFsx8cCFg3z5Yvhw6dnQ7EhERkX/ypTt1odfr+GTv0+M7e/H2stfrNaQ+XclYe0luLVDVxziyjYoV4fhxs2TW77//Tvv27Zk/fz4TJkz4O6nL6iZNgvffNwlxZpNhERERJ/n62C0JIU4nHkuWLOGJJ56gVatWvPnmm84VHMSmTjVrtcaJiEiw8aUl7kGv15HJ3qfUSiYuq1DBTFrrpI8//pjq1avz3HPPsX37dsaMGePsBYLMwYPw448miRs82O1oRERELvElibvf6/Vqr/cWSuKCTr58ULKkf7oAn3zyScqUKcNHH33E3r17mTdvnvMXCSKTJsGIEXDjjbA1FCbUERGRbMGX7tRGqSx3+iEuySTPIFJ/JHGJiYl07NiRX375hSlTplA9iz/WYNo0SEpSl6qIiAQXX5K42X6LQhxXsaJZb9vmn/LPnDlDy5YtOXXqFLNnz6Z48eL+uVAQ+OMPWLpUSZyIiAQXX5K4Bn6LQhznmV7En5PUHjx4kBYtWlCwYEFmz55N/vy+PdorlEyaBJUrQ5UqbkciIiJi+JLE5cRM1ntDCosEmQoVYO9eOHfOv9fZtGkTHTp0oGrVqkyePJmwsIw94ivYTZ8OiYlw771uRyIiImL4ksTlxUyqm3zZ7oe4JJMCOa/ZvHnzePzxx2nevDkff/xxYC4aYEeOwOLF6lIVEZHg4UsSdwYIs8/xXrJm00uIq1DBf/fDpeSTTz7h1Vdf5aGHHuKNN94I3IUDaPJkc69hjRpuRyIiIuJbEpfDb1GIo4oUgejowD9hYODAgXz00Uf069ePp59+OrAXD4Bp0yA+Hrp0cTsSERER35K4z/wVhDjLqWemZkTv3r2ZMmUK7733Hvfff/+VTwghx4/D99+bJC6nnnUiIiIu8+Wn6AnM5MANgc722pfJgiVA3EzikpKSuO+++1iwYAFjx46lRYsWgQ/Cj7780kyi3LCh25GIiEh250sSVwnYCkwEnrTXvwI3+iEuyYQKFeDiRdizx53rX7x4kXbt2rF+/XqmTJlC/fr13QnED2bOhNOn4b773I5ERESyO1+SuJHAaKAUcCtQEhhlb5cgUqGCmR8uMdG9GM6cOUPz5s3Zt28fs2fPpmbNmu4F46Bz58y9ce3bQ2Sk29GIiEh25ksSVxN4D/OsVI9h9nYJIhUrutOVmtyxY8do0qQJJ0+eZP78+VTJIjPlTpgAhQpBq1ZuRyIiItmZL0ncQeD2ZNsa2NslSOTMaZ6bGgxJHMDevXu58847uXDhAgsXLqSi53lgIWzRIjh0CLp2dTsSERHJznxJ4voDMcDXwFv2OsbeLkHiuutMN1+wJHEAu3btonHjxgAsXLiQG24I7Yd8JCXBxInQsqWZykVERMQNviRxMUAt4BeggL2+GZjhh7gkg9wcmZqWbdu20bhxYyIjI1m0aBHXXXed2yFlyoQJEBFh7o0TERFxg6+zXf0GDAYet9dBliqIJ4kL5NMa0mvz5s00adKEQoUKsXDhQooXL+52SBkWGwtbtmiUqoiIuMeXJG5pGosEiYoV4eRJ86zPYBQbG0vTpk0pWrQoixcvpmTJkm6HlGETJpj54kK8UVFEREKUL0lcHeDTVBYJEoF88H1GrV69+u9EbsmSJSHbtTphgllnsQdTiIhIiPAliYsHPk9lkSARCkkcwMqVK7nrrruIjo5myZIllClTxu2QfLZnDyxcCA88ADn0ZGEREQkwX5K4cKAH0BVoAZTzR0CScblzm669UEjiANauXUvjxo0pUKAAS5YsoVy50PtKjRsHZctCgwZuRyIiItmNL0ncKuABoDcwFDM6dROQ3om/mgHbgB3ACynsjwQm2ftXAaXt7V2B9V5LEpcmGF5sl+nZVzT9HyfrKVvWzBMXjIMaUhMbG0ujRo3InTs3S5YsCbl55KZPN/cgPvig25GIiEh240sSdwdmst9bMYlbQcz0Ih+m49ww+7jmQGWgs7329hAQh2nhG4qZiw5gAiZpqwncD+zGJGweXb32B+nt/IHhyX9CpSXOY9OmTdxxxx3kzJmTJUuWUK1aNbdDSrdz5+Crr6BDByhQwO1oREQkO/F1ihFvF4HXgOXpOPYWTAvbLvu8r4G2yY5py6X766YCjYHkdxp1ts+VFHimF9m+3d04MmLLli3cfvvtXLx4kaVLl1K/fn23Q0q3ceMgb17o2NHtSEREJDvJlY5jnJhCpASwz+v9fqBuGsckACeBq4FjXsfcyz+Tv3FAIjANM3edRRrCwsKI9uM0+1FRUX4r+0qqVfuLQ4fiCQ+PCsknCRw9epQWLVowffp05s+fT/fu3Vm4cKGrdZoe27db/PrrKXr2zMH06QXdDueKgr0+Q5Hq1FmqT+epTp0VLPWZniSuDvCovwNJh7rAWcy9eB5dgQOYJ0hMw3S3jk/h3J72QuHChf0bpYvKlk1k584wt8PIlAMHDtCyZUumTJnCxIkTeeyxx1i0aJHbYV1BDiZMiOS1185RoUIiv/0W2n8DEREJEZZlXWk5lY5jrrTcalnWXK/3/ezF+5i59nFYlpXLsqxjlmXl8No/1LKs/mlco4dlWSOuFMuaNWssTGudX5bo6GgrOjrar9dIbTlyBGvUqMBf1x9LwYIFrcWLF1uJiYlWnz59XKvT9C5Fi2LFx2P973/ux3Klxc3vaFZdVKeqz2BfVKehW5+WZa1NLafJzD1xvlgDlAfKABFAJ8yzWL3FAN3t1+2BRfYHAHPvXkcuvx8uF+BpVgsHWnF5K122Eh0NRYqE3qCG1Jw6dYpmzZoxa9Ys3n33Xfr27et2SGk6cgRmzYLu3SE83O1oREQkOwhUEpeAmZpkLrAVmAxsBgYBbexjPsXcA7cD6MPl05A0xNwvt8trW6Rd3kbMaNUDwCd++wRBLlgffJ8Z58+f5z//+Q9fffUV/fr145NPPiFXrvTcAeCO0aPh2muhbfK7NkVERPwgPb+IuYBG/HOkqLf03LT0nb14e9nr9XmgQyrnLgbqJdv2F3BzOq6bLWTFJA4gISGBXr16sX//fvr27UvJkiXp0KEDZ86ccTu0f5g7F37/HR59FKZOdTsaERHJ6tKTxB0Bxqax3wJucCYcyagKFSAhAXbvdjsS/3jzzTfZunUro0ePZunSpbRs2ZJDhw65HdZlkpLg44/hzTdD5/FnIiISutLTnVoacy9baosSuCBQsaJJ4OLj3Y7Ef8aNG0fLli0pV64cK1eupEqVKm6H9A9jx5q/wSOPuB2JiIhkdYG6J078rFIl2LrV7Sj8b968eTRo0ICwsDB++ukn7rzzTrdDusyRI+ZRXD16mGfZioiI+IuSuCwgLMx03/36q9uRBMaGDRuoV68ee/bsYe7cuTz22GNuh3SZUaPgqqvMo7hERET8RUlcFlC6NERGZo+WOI/9+/fzr3/9i++++46RI0cycuTIoBm5unixSagfDYYpskVEJMtSEpcFVKpk1tmlJc7j9OnTtGvXjjfffJPHHnuM+fPnc/XVV7sdFmBa4+rXh+rV3Y5ERESyKiVxWYAnidu2zd043JCUlET//v3p2rUr9erVY/Xq1UEx4GH8eDh7Fnr3djsSERHJqpTEZQGVKsHhwxAX53Yk7pk4cSINGzYkd+7crFixgjZt2lz5JD+KizOJ3P33QxZ+XK+IiLhISVwWUKlS9utKTcmaNWuoU6cOW7duZcaMGQwePJicOd37in/wgRmh2rOnayGIiEgWpiQuC1ASd8nBgwdp2LAhY8aM4cUXX+T777+nsEtNYVu3wvffQ69eep6qiIg4T0lciLv6atNdpyTukgsXLvDwww/z0EMP0aBBA37++WduueUWV2IZNgyKF9d0IyIi4jwlcSHOM6ghO00vkl5jx46lfv36JCQk8OOPP7oyn9y8eeZv89RTAb+0iIhkcUriQtyNN5q1WuJSFhsby80338z8+fMZOXIkX3zxBfnz5w/Y9S0L3n8f6tSB224L2GVFRCQbUBIX4ipVgnPnYO9etyMJXnFxcbRu3ZoBAwbQuXNn1q1bR61atQJ2/S++gBMn1BonIiLOUhIX4ipVMvPDWZbbkQQ3y7J4/fXXufPOO8mbNy8rVqzgqQBlVWfPwujR0K4dlC0bkEuKiEg2oCQuxGlkqm+WLl1KjRo1+O677xg6dCizZs0KyOjV99+H+Hjo29fvlxIRkWxCSVwIi4yEMmWUxPnqxIkTtGvXjl69etG4cWM2bNhAo0aN/HrNP/6Azz6DHj2gWDG/XkpERLIJJXEhrHx5yJlTSVxGjRw5krp163Ly5EkWLFjAO++8Q2RkpN+uN2QI5MoFTz/tt0uIiEg2oiQuhGl6kczbuHEjtWvXZtSoUTzzzDOsW7eOm266yS/X2rULJk2CRx+FqCi/XEJERLIRJXEhrFIlSEqC7dvdjiS0nT17ll69etG0aVOioqJYtWoVL774ImFhYY5f63//gwIFoHdvx4sWEZFsRklcCLvxRjO1yLlzbkeSNcybN49q1aoxZcoUBg8ezE8//USFChUcvcamTTBzJvzf/0HevI4WLSIi2YySuBBWpQps3ux2FFlLXFwcXbt2pWPHjpQrV47Y2FieeeYZR1vl3nzTPCrt4YcdK1JERLKhQCZxzYBtwA7ghRT2RwKT7P2rgNL29tLAOWC9vYzyOudmYJN9zgdADufDDk5hYaY7VUmcf0yZMoVq1ar9PeBhxYoVVKtWzZGyV6yARYvg+echTx5HihQRkWwoUElcGPAh0ByoDHS2194eAuKAcsBQ4C2vfTuBmvbyqNf2j4CHgfL20swPsQelcuXMFCNK4vzn0KFDtG3blo4dO3L99dezbt06XnvtNUdGsL7yiplqxIXHuYqISBYRqCTuFkxr2S7gIvA10DbZMW2Bz+3XU4HGpN2yVgwoCKwELGA8cI9zIQe3KlXM+pdf3I0jO5gyZQo33ngjEydOZMCAAcTGxlK/fv1MlblsGcybBy+8APnyORSoiIhkK7kCdJ0SwD6v9/uBumkckwCcBK6235cBYoFTwADgR/v4/cnKLHGlQMLCwoiOjvYx/PSLCtDcEbVrnyMp6Tx//BFFdHTW7kUOVJ2mxbIsnn76aWbOnMl7773Hjz/+yLhx4xg8eDAnT57MUJnvvJPAvHmnee653AwbFrh+1WCoz6xGdeos1afzVKfOCpb6DIWBDYeA64CbgD7AREwLnC96AmuBtYF4xFIgVKqUyJ49OTl3LmsncMFm0aJF3HbbbYwePZoePXqwevVq7r333gyVtXZtLubNy8UTT1ygQAE9/FZERHxkWVYgllsty5rr9b6fvXgfM9c+DsuyclmWdcyyrBwplLXYsqzalmUVsyzrV6/tnS3L+vhKsaxZs8bCdL/6ZYmOjraio6P9eg3A2rQJa8YM/14jWJZA1amvS82aNa3ly5dblmVZS5YssapWrepzGbVqma/mK6+oPkN5UZ2qPoN9UZ2Gbn1alrU2tZwmUC1xazADD8oAEUAnICbZMTFAd/t1e2CR/QGKYAZGANxgl7ML00J3CqiHuXeuGzDDb58giISHQ8WKuh/ObevXr+e2227joYceonLlysTGxvLOO++QP3/+dJfx888wbRo8+ywULerHYEVEJMsJVBKXAPQG5gJbgcnAZmAQ0MY+5lPMPXA7MN2mnmlIGgIbMdOLTMWMTj1h73scGGOfsxOY4+fPERTKlzeJnEamus+yLMaOHUvFihX59NNPefrpp/n111/p2rUrOXKkr6u7Xz8z0njgQP/GKiIiWUyAulODZskK3akdOpiPU6OG+03KgVhCqRugTp061urVqy3LsqxVq1ZZt956a7rOGz4cKz4eq2JF1WcoLqpT1WewL6rT0K3PYOhOFQdVqQKJifDrr25HIsmtWbOGunXr0q1bN0qUKMHy5cv56quvuO6669I8b9AgOHvWPFtVREQkPZTEhaCqVWHnTrhwwe1IJCWWZfHFF19QoUIFBg4cSJs2bdi2bRuvv/56qvfLHT0Kb70F99wD//pXgAMWEZGQpCQuBFWpokENoeDs2bO8+uqrVKhQgcmTJ9O/f3927NhBr169CA8P/8fxQ4fC/v1mnVP/MkVE5Ar0UxFiIiLMI7c0qCF0HDhwgO7du1OnTh22bNnCiBEj/h78kNMrWzt3Dp57DmrXhgcfdDFgEREJCUriQkylSpArl5K4ULR27VruvPNOmjRpQlxcHF9++SXr16+nVatWfx/z1VewdCm8+Sb48cEiIiKSBSiJCzE1apj1hg3uxiEZN3/+fOrUqUPHjh2JjIxk5syZLFu2jAYNGgDQu7dJ4F57zeVARUQkqCmJCzE1aphut+3b3Y5EMsOyLKZMmUKVKlV4+OGHKV26NEuXLmXBggVERzdk5Eh49NFLSbuIiEhySuJCTM2asGmTmWJEQl9CQgJjxoyhXLlyPP3001SuXJklS5ZQq9ZMTp8O56OPNMhBRERSpp+HEFOjhrpSs6Lz588zbNgwbrjhBp544glKl76JqKhPufVWeP/9im6HJyIiQUhJXAgpXhwKF1YSl5WdP3+eESNGULZsWXr1WsG5c7fTu/cB1q6dTuvWrdP9KC8REcn6lMSFkJo1zXr9enfjEP+7cOECI0d+RI0ay7lw4Tw33jicmJgZbN68mQceeICIiAi3QxQREZcpiQshnpvcN250Nw4JnO3b43n++QTy5v2B4cPrc/78ecaOHcvu3bvp27cvBQsWdDtEERFxiZK4EFKzpnnc1unTbkcigTR8OKxcCV26rKRly1rcfffdbN68mbfffpt9+/bx9ttvU6pUKbfDFBGRAFMSF0I0qCF7SkqC7t0hTx4YOxYWLFhAkyZNqFWrFrNnz6ZPnz7s3r2bKVOm/D3XnIiIZH1K4kJE3rxQvrzuh8uufvsNnn0WmjWDxx4z22JjY+nSpQs33HADQ4YMoVGjRixdupT169fz4IMPkjt3bneDFhERv1ISFyKqVzfzhaklLvv66COYMwfeeQcqVLi0fe/evfTr149SpUrx3//+F4BPP/2U/fv38+abb6qrVUQki1ISFyJq1zbrdevcjUPc9eCD5okdEydC8gGq586d49NPP6VmzZrcfvvtLF68mL59+7J7925mzpxJmzZtCAsLcydwERFxnJK4EFGnDhw6BAcOuB2JuOmPP+CBB+Dmm+Hdd1M/bunSpbRv354bbriBN954g1q1ajFjxgz27NlD//791TonIpIFKIkLEXXqwJo1bkchwWDmTBgyBHr3ho4d0z527969vPzyy1x33XW0bduW9evX06dPH2JjY5kzZw7t2rUjV65cgQlcREQcpSQuBBQoABUrKomTS/r3h59+gjFjLr8/LjWJiYnExMTQqlUratSowZAhQ6hSpQrTp0/n4MGDDBs2jFq1avk/cBERcYySuBBw881mUMPatW5HIsEiIQHuvRcuXIBp0yB//vSfe+DAAd566y3KlClDq1at+OGHH3j00UdZt24dv/zyC8899xzFixf3X/AiIuIIJXEhwDOoQS1x4u3AAejUCSpVggkTTKLvi8TERGbPns29997LtddeyyOPPMKff/7JW2+9xb59+5g7dy5du3Ylb968/vkAIiKSKUriQkCdOrB7Nxw/7nYkEmwWLoSnnoI2bWDw4IyX8+effzJ69Gj+9a9/Ua5cOV577TXKly/Pl19+yZEjR/j6669p166d5p4TEQkigUzimgHbgB3ACynsjwQm2ftXAaXt7XcD64BN9vpOr3MW22Wut5eizoftvjp11JUqqfvwQxg1Cvr1g65dM1/ezp07GThwIGXLlqVhw4Z8/vnnNGrUiOnTp3PkyBG+/PJLWrduTUTyOU5ERCSwLMsKxBJmWdZOy7JusCwrwrKsDZZlVU52zOOWZY2yX3eyLGuS/fomy7KK26+rWpZ1wOucxZZl1fYlljVr1liA35bo6GgrOjrasfIKFzah9+3rv5iDfXG6TrPikisX1qJFWOfPY91xh/P1GRYWZjVu3NgaPXq0dezYMcuyLCsuLs4aN26c1aJFCysyMtL1OnBz0XdU9Rnsi+o0dOvTsqy1qeU0gWqJuwXTwrYLuAh8DbRNdkxb4HP79VSgMZADiAUO2ts3A3kwrXbZQp06Zq374SQtCQnw73/D9u0wYwbUrOls+YmJiSxcuJCePXty7bXX0qxZM7755hvuueceZs+ezdGjR5k0aRKdO3emUKFCzl5cRERSFKgJokoA+7ze7wfqpnFMAnASuBo45nXMf4CfgQte28YBicA0YDAmc01VWFgY3MaTigAAFphJREFU0dHRPoafflFRUY6W17jxORISzrN9exTR0TkcLTtUOF2nWVmnTkl8//0pvv8emjUrwJ49/3xCgxP1uXr1alavXk2/fv1o0KABLVq0oHnz5nTs2JH4+HiWLVvG7NmzmTNnDocOHcr09YKdvqPOUn06T3XqrGCpz1Aa2FAFeAt4xGtbV6Aa0MBe7k/l3J7AWmBt4cKF/Rmj4+rWTWDjxjDOns2eCZz45uDBnLRvX4DwcJg27QzFiiX59XoXL15k4cKFPPPMM1SpUoUmTZrw4YcfUrJkSd555x02b97M/Pnz6du3LzfddBM5cuh7LCLimADdE3erZVlzvd73sxfvY+bax2FZVi7Lso5ZlpXDfl/SsqzfLMu6LY1r9LAsa0RWuicuPBzr7Fms995zv//fzUX3cvi+3HIL1smTWNu2YRUr5k59VqxY0Xr++eetFStWWImJiZZlWdbhw4etzz//3OrUqZN11VVXuV5PTi36jqo+g31RnYZufQbDPXFrgPJAGSAC6ATEJDsmBuhuv24PLLI/QBQwGzOi9Sev43MBnma1cKAV8IsfYnfNTTdBnjxmZn4RX6xeDc2aQbFisGgRXHtt4GPYtm0bb731FrfeeivXXHMNXbt2Zd68ebRo0YKvvvqKI0eOsHz5cgYMGMDNN9+sVjoRER8FKolLAHoDc4GtwGTMIIVBQBv7mE8x98DtAPpwaRqS3kA54GUun0ok0i5vo73tAPCJ/z9K4Nx2m1kriZOMWLECmjeHkiXhhx/M2i3Hjh1j4sSJ3H///VxzzTXUrVuXwYMHExYWxquvvsratWs5cuQIkydP5pFHHqFcuXLuBSsiEiJyWJbldgwBtXbtWquOZ8inH3gGTcTFxWW6rGnToHp1KF8+00WFNCfrNDu67TaYPRtOnoQmTeDIkeCqzyJFitC0aVPuuusuGjduTEk729y7dy8LFy5k0aJFLFy4MKgHSOg76izVp/NUp84KZH1alrUOqJ3SvlAa2JCt5MgBt98OP/7odiQS6n76yXyXIiJg2TKoVSvB7ZAuc/ToUb788kt69OhBqVKlqFChAo899hirV6+mTZs2fPHFFxw8eJAtW7YwfPhwOnTowLVu9A+LiAQZJXFBqmZNuPpq81glkczasMG0yJ06BTNmnKZly4tuh5Sq7du3M2rUKDp06ECRIkWoVasWzz77LL///jsPPPAAkydP5tChQ+zYsYNx48bx4IMPUj67N1eLSLYUqHnixEeNG5v1okXuxiFZx65dJpGbNSuML774i1Kl4M033Y4qbZZlERsbS2xsLO+++y65cuWiZs2aNGjQgAYNGvx/e3ceHEd55nH8Oxpd1ki2ZAsJW7ZlELYF+ADvyobEUCkoFggYhw1rQ0EVJiyHSQKEsOHYcISqAEk41hXYAOvY3IfjhV2nQsI6lXWAxDgWAh+AbdnGsj2sRhbW6L5mNPvHOxrNSCMkjXqmZ6Tfp+qt7n67p/XoVY/mme5+3+aSSy5h1apVANTW1vL++++Hys6dO+nu7rb3FxARiSMlcUnq/PPh008hiW8DkhRUWwvLluWxZk0bDz/cxbx5cP310NFhd2TD4/P5qKyspLKykieffBKA8vJyli5dGkrsrrjiCgA6Ojqoqqrigw8+YNu2bWzbto2amho7wxcRsZSSuCSUmQnnnAPr1tkdiYxFHR0Obroph6qqLh55BE47DVasMI/sSkV79uxhz549rF27FoCSkhLOPvtslixZwllnncXq1au54447APB4PKGEbtu2bWzfvp2mpiY7wxcRiZmSuCR01lngcul+OIknB48+Cjt3wosvQlUV3HwzvPKK3XGNntvtZuPGjWzcuBGA9PR05s+fz5IlS0LlsssuC21fXV1NVVUVH330UWhaX18/2O5FRJKGkrgkdOml0NWl++Ek/t5+GxYuhFdfhZdfNpfxb7sNmpvtjsw6Pp8vdF/dM888A5jnHlZUVFBRUcGZZ55JRUUFK1euDL3myJEjVFVVRSR3brfbrl9BRCQqJXFJaNky2LJlbH2QSvJyu+G88+CBB+Dee00id+ON8M47dkcWP16vl82bN7N58+ZQXX5+PmeccQaLFi0KlWXLlpGWZjrx19fXs3v3bnbt2sWuXbvYvXs3u3fvpllvVBGxiZK4JDN7NpSXw1NP2R2JjCd+P9x/vxkUeN06+MMfYP16uOMO8Hrtji4xvF4vW7ZsYcuWLaE6l8vFggULWLRoEQsWLGD+/PmsWrWKvLy80DaHDh1iz549fPbZZ2zfvp1du3axd+9e9YwVkbhTEpdkli0z09/+1t44ZHzatg0WLYL77oO77oJLLoF77jEJ3Th7uAsAra2tbN26la1bt4bqHA4HpaWlzJs3j/nz5zN//nwWLlzI+eefT0ZGBmAu4R48eDDU6SK8aMR8EbGKHrtlsdE+imPLFsjPN4P9iqHHxVhruO15xhnwy1/C0qVQWQm33mqexyoDFRQUkJGRQVFREfPmzeP0009n7ty5lJeXM2fOHLKyskLbHjt2bEBit3fvXmpqavD5kutpGnbRe956alNrJctjt3QmLolMn26GFnnwQbsjEYGPPzbH41VXwS9+AX/9q3me7/33mzEMJVJ3d3foPrlwaWlpzJo1i/Ly8lBiV15ezvLly7nhhhtC2/l8Pg4fPsyBAwfYv38/Bw4ciChtbW2J/pVEJMkpiUsiV10FaWmml6BIsnjtNdi0CX74Q1Muv9z0Zv3JT2D/frujS349PT0cPHiQgwcP8vbbb0esmzx5MnPnzmXu3LmUlZWFyooVK5gyZUrEtrW1tRHJ3eeff05NTQ01NTW43W78fn8ify0RSQK6nGqx0Zxi3bHD9EhdutTqqFKbLgNYazTtOXky/OhH8P3vQ3Y2vPUWPPYYfPCB1VGmlngco5MmTaKsrIxTTjklIsErKytjxowZEdv6fD7cbncoqetfDh8+TEeqPJYDvefjQW1qLV1OlQgLFpiyerXdkYgM7vhxuPtuePJJk8jdcgt8+9vw/vumbtMm0G1d1mhsbAyNVddfdnY2M2fOpLS0dEA599xzmT59Ok6nM+I1Ho+Hmpoajh49itvtjihffPEFbreblpaWRP16ImIBJXFJ4pZboL0dNmywOxKRoXk88OMfwyOPwHe+Az/4gblfrrYWnn8e1q6FAwfsjnLs6ujoYN++fezbty/qeqfTSUlJSdQkb+7cuZx33nnk5+cPeF1TU9OABC+8eDwePB4PXV1d8f4VRWQYdDnVYrGcYp0yBY4cMY8/uvnmeEWWunQZwFrxaE+nEy66CG64wQxLkp5uelq//jq8+SYcO2bZj0pKqXiM5uTkUFJSElGmTZsWsTx16tTQsCnhvF5vKKGrra0NzUcrsVzGTcX2THZqU2vpcqqE3HQTTJgAa9bYHYlIbPx+M1Dw734HU6fCddfBNdfAM8/A00+bR8ht2GAut9bV2R2tALS1tVFdXU11dfWg2zgcDoqKikIJXnFxcaiceOKJFBcXs2DBAoqLi0Mfav01Njbi8Xioq6ujvr6e+vp6vvzyy9B8/2XveBldWsQCOhNnsZFm5y6X6eG3Y4c5kyED6RuktRLZnvPmwcqVpsyebeo+/NA8s/X3vzeDC/f0xD2MuNMxCpmZmRFJXv+Er6ioiClTplBYWMiUKVMixs4L5/f7aWho4Pjx43g8nogE7/jx43i9XhoaGmhoaAjNe71evF4vPWPhYIoTHaPW0pk4AeD22+HEE82wDSJjze7dptx3HyxcaC61XnyxeUbrffdBQwP85S/w7rvw3nsmwdPTqlJTV1cXR44c4ciRI8PaPjc3N5TQFRYWRsyXlJQwefJkJk6cyMknn0xFRQWFhYWDJn69GhsboyZ5/RO+hoYGmpubaWpqoqmpKTSve/0k1SiJs9HMmaan31tvaYgGGft27DDl4YfNU0kuuMCUc86BSy8127S1mbNzlZVQVWVKdfX4fOTXWNfS0kJLSwuHDh0asG6wsxw5OTkUFBSQn59PQUFBxHy0urKyslBdbm7ukDF1dnZGJHfhCd5Q862trbS0tNDa2kprayttbW06MyhxpyTOJg4HPPecmb/9dntjEUk0rxd+8xtTAIqKzPiI55wDX/ta3zh0YMZO/Phj2LkT9uzpK0eP2he/2KOtrY22tjbcbveIX5uenh6R8OXl5TFx4sTQtP9873JxcTGzZ88OLbtcrmH/zPb29gHJXf8y1Lr29vYBpaOjg/b2drp12nrcUxJnkwcegAsvNL1RDx+2OxoRe9XVmV6sb75pltPT4dRTYdGivnL11eYMXq+WFpPMVVdDTY0phw71zespVRLO5/OF7q0bDafTGTUBdLlcoZKbmxux3H/dtGnTBtRnZmaOOBa/3z8gsYuW7LW3t9PT00N7ezuNjY0Dtuvs7AyVrq6uiOVodb3LXV1djLf76pNNIpO4i4A1gBNYCzzab30W8CLwd8CXwErgUHDdPcD1gB+4FXhnmPtMSnfeaZK49evh2WftjkYk+fh8sGuXKS+80FdfXAzl5X3l1FOhosIMONz/M7C+Hr74woxdV1trxrbrna+tNYljQ4MpSvhkuPx+f6gjhZUyMjKiJn05OTlkZ2czYcKEiDKcusLCwlBdTk5OxDZWCU/ohkr+eut6S3d3t21lrCSfiUrinMDTwAXAUWA7sAkIf4z29UADcApwJfAzTCJ3WnD5dGAa8EdgTvA1Q+0zqcycaR4kvmIFvPEG3Hij3RGJpBaPx5Q//zmy3uEwQ5uUlsKsWWZaWmrqiothzhzTgaj3Em1/XV19CV14aWyE1lZz1m+waUsLpKf76epy4HRCZyd0dKiDhoxMd3d3XJLDXv3vM8zKygole1lZWaGSmZkZsTzcuqG2mThxYkRdRkZG1NL/SSPx4vf78fl8Q5bBtuvdx+rVq9m7d29CYo4mUUncYmA/cDC4/DqwnMiEaznwYHB+I/AU4AjWvw50Ap8H97M4uN1Q+xzA6XQOOp6RFRYvzqG0tJvubhcZGQGys2HGjB4WL/bx9a/76O6Ghx7KZs2abPLyHHGLYyyJNrK8xG6stmd7e9/9ctEFyMuD4uIeiop6OOGEAPn5ASZNCpCf30N+fiBUpk0LcNppAXJzA7hcAYY+cdEUtbajwySInZ2OqNPubgd+vxlnz+cDv9+Bz2eGXfH5wOfrW9+7jc/nCFtvXhMIECo9PZFTMx+5zcD14dPo++s/H9GyUU5qDNxm4P+7wU6G5OSYj6a2NteQP2t4P3vk2wznNanE5TKDNre2ht/T1x0sQ/P7zRnreJ+1djgcOJ1O0tPTcTqdwZKO05nWry62bdLT+9alpaWFpr3zfctOnM7I9ZmZTiZMMMsZGRmkpaUxc2YedXXxyymGkqgkrgQI73d+FFjyFdv4gEZgSrA+vO/m0WAdw9hnrxuDhcLCwhGGPjIrVzZz3XWR/9B9Pti3L43HH8/mpZeycLvT4hqDiETjoLkZmpud7N8/sm/7aWkBXC7IyTFJnZmCy2WWCwsnkJUVwO9vIysLMjMDZGaaqVmGrKzAgKnTae7/y8w0805ngPT08CnBbQJh82Y5La133pyJTNAJjARptTuAMUhtGg89PXnY2b1gvHRseC5Y8Hg8gXgOzvfEE5NYvz6P+vpmurrMt/DaWuju7gE6gkVioUEqraX2HJkvvxx8XUGBuSGvoaE9QdF8tbQ0k9j1TsPno9UNtb5/XThHlAsK/etGus2kSRMB8yxXK/c73G2G85pUM3FiHgBNTc02RzI29LZnZWWzrffUJiqJcwMzwpanB+uibXM0GNckTAeHr3rtUPtMOLc7Dbc7DX0+iohdeocn8/vtjSNWBQXmtKL+j1qnoMB83KtNrdHbnnZ3ikrUdb3twGzgJCAT01FhU79tNgHXBuevAP4EBIL1V2J6r54U3M/fhrlPERERkTEpUWfifMD3MEODOIF1wCfAQ0AlJvn6NfASprPCcUxSRnC7DZgOCz7gu5ihRhhknyIiIiJjXiLviXs7WMLdHzbfAfzTIK/9abAMZ58iIiIiY566SYqIiIikICVxIiIiIilISZyIiIhIClISJyIiIpKClMSJiIiIpCAlcSIiIiIpSEmciIiISApyBAIBu2NItGNATZx/RiFQH+efMd6oTa2l9rSe2tRaak/rqU2tlaj2LAVOiLZiPCZxiVAJ/L3dQYwxalNrqT2tpza1ltrTempTa9nenrqcKiIiIpKClMSJiIiIpCAlcfHxnN0BjEFqU2upPa2nNrWW2tN6alNr2d6euidOREREJAXpTJyIiIhIClISZ72LgL3AfuBum2MZCw4Bu4CPMT2BZOTWAXXA7rC6ycBmoDo4LbAhrlQWrU0fBNyYY/Vj4JuJDytlzQD+F/gU+AS4LViv4zQ2g7Xng+gYjVU28DdgB6ZNfxKsPwnYhvnMfwPITGRQupxqLSewD7gAOApsB67CvJEkNocwXbg1tlHszgVagBeBecG6nwPHgUcxXzYKgLtsiS41RWvTB4N1j9kUUyqbGixVQB7wIfAtYBU6TmMxWHuuQMdorByAC9N+GcD7mOT4DuBN4HXgGUyS96tEBaUzcdZajMnGDwJdmD/qclsjEoF3MR+E4ZYDLwTnX8D8g5fhi9amErv/wyQcAM3AZ0AJOk5jNVh7SuwCmAQOTBKXEaw7D9gYrE/4MaokzlolwJGw5aPojTNaAeB/MN8kb7Q5lrGkGPOPHqA2uCyj9z1gJ+Zyqy79xWYWcCbmEpWO09GbRV97go7R0XBiLkPXYS7vHwC8gC+4PuGf+UriJNktBRYBFwPfxVzGEmsFgkVG51dAGXAGJvF43N5wUlIu8J/A7UBTv3U6Tkeuf3vqGB0dP6btpmOuvJXbG46SOKu5MTeU9poerJPY9bZfHfAW5o0jo+fB3DNDcFpnYyxjhQfzT74H+A90rI5UBibheAVzjxHoOB2NwdpTx+joeTEdR84G8oH0YH3CP/OVxFlrOzAb01slE7gS2GRrRKnNhbkpt3f+H4jsDSix2wRcG5y/FvhvG2MZK6aGzV+OjtWRcAC/xty79URYvY7T2AzWnjpGY3cCJmEDmIDpwPgZJpm7Ilif8GNUvVOt903g3zDXztcBP7U3nJR2MubsG5hvOq+i9ozFa8A3gELMN/EHgP8CNgAzgRpMrzXdqD980dr0G5hLLQFMr+qb6LufS77aUuA9zHBCPcG6ezH3cek4HbnB2vMqdIzGagGm44ITcwJsA/AQ5nPqdcxwOB8B1wCdiQpKSZyIiIhICtLlVBEREZEUpCROREREJAUpiRMRERFJQUriRERERFKQkjgRERGRFKQkTkRERCQFKYkTEYlNLmasravD6vKAw/QN/ikiEjcaJ05EJHYXAi8DpwHHMM+mLAb+0c6gRGR8UBInIjI6zwNZwLOYZ1WeDtTaGZCIjA9K4kRERqcA+BTzwPF/AdbbG46IjBe6J05EZHQagE+AHOBNm2MRkXFESZyIyOhcA8wC/gj8zN5QRGQ80eVUEZHYFWHOwq0A9gTnlwPv2RmUiIwPSuJERGK3AWgEbggu/zNwJ7AQ6LQrKBEZH5TEiYjE5lvAv2OGF/GG1f8J2Ar8qx1Bicj4oSROREREJAWpY4OIiIhIClISJyIiIpKClMSJiIiIpCAlcSIiIiIpSEmciIiISApSEiciIiKSgpTEiYiIiKQgJXEiIiIiKUhJnIiIiEgK+n9E4BC5VxqSPQAAAABJRU5ErkJggg==\n",
1147
      "text/plain": [
1148
       "<Figure size 720x360 with 1 Axes>"
1149
      ]
1150
     },
1151
     "metadata": {
1152
      "needs_background": "dark"
1153
     },
1154
     "output_type": "display_data"
1155
    },
1156
    {
1157
     "data": {
1158
      "application/vnd.jupyter.widget-view+json": {
1159
       "model_id": "f319c5725e8742229aa2a352bf40d445",
1160
       "version_major": 2,
1161
       "version_minor": 0
1162
      },
1163
      "text/plain": [
1164
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
1165
      ]
1166
     },
1167
     "metadata": {},
1168
     "output_type": "display_data"
1169
    },
1170
    {
1171
     "name": "stdout",
1172
     "output_type": "stream",
1173
     "text": [
1174
      "Less power A < B: 86.2%\n",
1175
      "Greater power A > B: 0.0%\n"
1176
     ]
1177
    }
1178
   ],
1179
   "source": [
1180
    "distr_a = expon(loc=0, scale=6)\n",
1181
    "distr_b = gamma(a=5, scale=1)\n",
1182
    "x = numpy.linspace(0, 30, 1000)\n",
1183
    "\n",
1184
    "fig = pyplot.figure(figsize=(10, 5))\n",
1185
    "\n",
1186
    "pyplot.title(\"Что левее? Плотность распределения\", fontsize=12)\n",
1187
    "\n",
1188
    "pyplot.plot(x, distr_a.pdf(x), c='white', label='A')\n",
1189
    "pyplot.plot(x, distr_b.pdf(x), c='yellow', label='B')\n",
1190
    "pyplot.xlabel(f'X', fontsize=12)\n",
1191
    "pyplot.ylabel('Плотность', fontsize=12)\n",
1192
    "pyplot.grid(linewidth=0.2)\n",
1193
    "pyplot.legend(fontsize=12)\n",
1194
    "pyplot.show()\n",
1195
    "\n",
1196
    "\n",
1197
    "numpy.random.seed(8)\n",
1198
    "# Заводим счетчики количества отвергнутых гипотез для Манна-Уитни и для t-test\n",
1199
    "mann_bad_cnt_left = 0\n",
1200
    "mann_bad_cnt_right = 0\n",
1201
    "\n",
1202
    " \n",
1203
    "# Прогоняем критерии 1000 раз\n",
1204
    "sz = 1000\n",
1205
    "for i in tqdm_notebook(range(sz)):\n",
1206
    "    # Генерируем распределение\n",
1207
    "    A = distr_a.rvs(1000)\n",
1208
    "    B = distr_b.rvs(1000)\n",
1209
    "     \n",
1210
    "    # Считаем p-value\n",
1211
    "    mann_pvalue_left = mannwhitneyu(A, B, alternative='less').pvalue\n",
1212
    "    mann_pvalue_right = mannwhitneyu(A, B, alternative='greater').pvalue\n",
1213
    "\n",
1214
    "    \n",
1215
    "    # Отвергаем критерий на уровне 5%\n",
1216
    "    if mann_pvalue_left < 0.05:\n",
1217
    "        mann_bad_cnt_left += 1\n",
1218
    "\n",
1219
    "    if mann_pvalue_right < 0.05:\n",
1220
    "        mann_bad_cnt_right += 1\n",
1221
    "    \n",
1222
    "\n",
1223
    "print(f\"Less power A < B: {round(mann_bad_cnt_left / sz * 100, 1)}%\")\n",
1224
    "print(f\"Greater power A > B: {round(mann_bad_cnt_right / sz * 100, 1)}%\")\n"
1225
   ]
1226
  },
1227
  {
1228
   "cell_type": "code",
1229
   "execution_count": 38,
1230
   "metadata": {},
1231
   "outputs": [
1232
    {
1233
     "data": {
1234
      "text/plain": [
1235
       "6.0"
1236
      ]
1237
     },
1238
     "execution_count": 38,
1239
     "metadata": {},
1240
     "output_type": "execute_result"
1241
    }
1242
   ],
1243
   "source": [
1244
    "distr_a.expect()"
1245
   ]
1246
  },
1247
  {
1248
   "cell_type": "code",
1249
   "execution_count": 39,
1250
   "metadata": {},
1251
   "outputs": [
1252
    {
1253
     "data": {
1254
      "text/plain": [
1255
       "5.0"
1256
      ]
1257
     },
1258
     "execution_count": 39,
1259
     "metadata": {},
1260
     "output_type": "execute_result"
1261
    }
1262
   ],
1263
   "source": [
1264
    "distr_b.expect()"
1265
   ]
1266
  },
1267
  {
1268
   "cell_type": "markdown",
1269
   "metadata": {},
1270
   "source": [
1271
    "Теперь белое распределение левее желтого по правилам Манна-Уитни. Сравним 2 картины между собой."
1272
   ]
1273
  },
1274
  {
1275
   "cell_type": "code",
1276
   "execution_count": 27,
1277
   "metadata": {},
1278
   "outputs": [
1279
    {
1280
     "data": {
1281
      "image/png": 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\n",
1282
      "text/plain": [
1283
       "<Figure size 1440x360 with 2 Axes>"
1284
      ]
1285
     },
1286
     "metadata": {
1287
      "needs_background": "dark"
1288
     },
1289
     "output_type": "display_data"
1290
    }
1291
   ],
1292
   "source": [
1293
    "distr_a = expon(loc=0, scale=6)\n",
1294
    "distr_b_2 = gamma(a=5, scale=1)\n",
1295
    "distr_b_1 = gamma(a=4, scale=1)\n",
1296
    "\n",
1297
    "x = numpy.linspace(0, 30, 1000)\n",
1298
    "\n",
1299
    "fig = pyplot.figure(figsize=(20, 5))\n",
1300
    "\n",
1301
    "ax = fig.subplots(nrows=1, ncols=2)\n",
1302
    "\n",
1303
    "pyplot.subplot(1, 2, 1)\n",
1304
    "pyplot.title(\"Белое распределение правее желтого\", fontsize=15)\n",
1305
    "pyplot.plot(x, distr_a.pdf(x), c='white', label='A')\n",
1306
    "pyplot.plot(x, distr_b_1.pdf(x), c='yellow', label='B')\n",
1307
    "pyplot.xlabel(f'X', fontsize=12)\n",
1308
    "pyplot.ylabel('Плотность', fontsize=12)\n",
1309
    "pyplot.grid(linewidth=0.2)\n",
1310
    "pyplot.legend(fontsize=12)\n",
1311
    "\n",
1312
    "\n",
1313
    "pyplot.subplot(1, 2, 2)\n",
1314
    "pyplot.title(\"Белое распределение левее желтого\", fontsize=15)\n",
1315
    "pyplot.plot(x, distr_a.pdf(x), c='white', label='A')\n",
1316
    "pyplot.plot(x, distr_b_2.pdf(x), c='yellow', label='B')\n",
1317
    "pyplot.xlabel(f'X', fontsize=12)\n",
1318
    "pyplot.ylabel('Плотность', fontsize=12)\n",
1319
    "pyplot.grid(linewidth=0.2)\n",
1320
    "pyplot.legend(fontsize=12)\n",
1321
    "pyplot.show()\n"
1322
   ]
1323
  },
1324
  {
1325
   "cell_type": "markdown",
1326
   "metadata": {},
1327
   "source": [
1328
    "В первом случае Манн-Уитни считает, что белое распределение правее желтого, а во втором – наоборот. \n",
1329
    "\n",
1330
    "Вернемся к вопросу: Есть ли у этого правила \"правее\" Манна-Уитни какое-то реальное применение? \n",
1331
    "\n",
1332
    "1) На текущем примере односторонняя гипотеза не применима: 2 картинки практически идентичны, а результаты критерия абсолютно разные. Сложно придумать простую интерпретацию, которая объясняла бы это различие в результатах. Особенно в реальных бизнес-задачах.\n",
1333
    "2) Но если бы вы получили 2 нормальных распределения со смещением, как мы смотрели выше, то односторонний критерий Манна-Уитни бы работал валидно и имел понятную интерпретацию: 2 распределения имеют одинаковую форму, но имеют смещенные мат. ожидания.\n",
1334
    "\n",
1335
    "Главное отличие в этих примерах в том, что в одном случае была понятная интерпретация результатов, а в другом – нет.\n",
1336
    "\n",
1337
    "Поэтому, главное что нужно вынести из этого раздела: очень осторожно относитесь к односторонним гипотезам Манна-Уитни. Подумайте, есть ли у правила определения \"лево-право\" критерия Манна-Уитни понятная бизнес-интерпретация в вашем примере."
1338
   ]
1339
  },
1340
  {
1341
   "cell_type": "markdown",
1342
   "metadata": {},
1343
   "source": [
1344
    "## Работает ли Манн-Уитни для других нулевых гипотез?\n",
1345
    "\n",
1346
    "Что мы знаем про Манна-Уитни? Это критерий, который вообще не смотрит на значения элементов, а значит устойчив к шумам. Поэтому было бы интересно применить его к решению других задач, где шумы могут помешать получить стат. значимые результаты. Мы рассмотрим с вами 3 гипотезы и посмотрим, можно ли использовать там Манна-Уитни? Если да, то это даст возможность нивелировать влияние выбросов в этих гипотезах и сделать больше прокрасов.\n",
1347
    "\n",
1348
    "1. Сравнение средних: $H_0: \\mathbb{E}A = \\mathbb{E}B$. \n",
1349
    "2. Сравнение медиан: $H_0: \\text{median}\\ A = \\text{median}\\ B$. \n",
1350
    "3. Смещения выборок между собой: $H_0: \\mathbb{P}(A < B) = \\dfrac{1}{2}$. То есть вероятность, что в одной выборке значения будут лежать левее или правее второго распределения равна 0.5.\n",
1351
    "\n",
1352
    "\n",
1353
    "Для проверки рассмотрим 2 симметричных распределения для которых все три гипотзы выполняются:\n",
1354
    "- U[−1, 1] — равномерное распределение от −1 до 1\n",
1355
    "- U[−100, 100] — равномерное распределение от −100 до 100\n",
1356
    "\n",
1357
    "Про эти два распределения мы знаем, что у них равны средние и медианы, и что они симметричны относительно 0. Кроме того, вероятность, что сгенерированное значение в первой выборке будет больше значения во второй выборке, равна $\\dfrac{1}{2}$. Или, если сформулировать математически, $\\mathbb{P}(T > C) = \\dfrac{1}{2}$, где T и C — выборки теста и контроля.\n",
1358
    "\n",
1359
    "Работает ли здесь корректно Манн-Уитни? Для этого мы запустим эксперимент 1000 раз и посмотрим на количество отвержений нулевой гипотезы у критерия.\n"
1360
   ]
1361
  },
1362
  {
1363
   "cell_type": "code",
1364
   "execution_count": 31,
1365
   "metadata": {},
1366
   "outputs": [
1367
    {
1368
     "data": {
1369
      "application/vnd.jupyter.widget-view+json": {
1370
       "model_id": "f89a73e9a342456391309779d6dfaaf3",
1371
       "version_major": 2,
1372
       "version_minor": 0
1373
      },
1374
      "text/plain": [
1375
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
1376
      ]
1377
     },
1378
     "metadata": {},
1379
     "output_type": "display_data"
1380
    },
1381
    {
1382
     "name": "stdout",
1383
     "output_type": "stream",
1384
     "text": [
1385
      "Mann-whitneyu significance level: 0.099, (0.082, 0.1191)\n",
1386
      "T-test significance level: 0.056, (0.0434, 0.072)\n"
1387
     ]
1388
    }
1389
   ],
1390
   "source": [
1391
    "numpy.random.seed(8)\n",
1392
    "# Заводим счетчики количества отвергнутых гипотез для Манна-Уитни и для t-test\n",
1393
    "mann_bad_cnt = 0\n",
1394
    "ttest_bad_cnt = 0\n",
1395
    " \n",
1396
    "# Прогоняем критерии 1000 раз\n",
1397
    "sz = 1000\n",
1398
    "for i in tqdm_notebook(range(sz)):\n",
1399
    "    # Генерируем распределение\n",
1400
    "    test = uniform(loc=-1, scale=2).rvs(1000) # U[-1, 1]\n",
1401
    "    control = uniform(loc=-100, scale=200).rvs(1000) # U[-100, 100]\n",
1402
    "     \n",
1403
    "    # Считаем p-value\n",
1404
    "    mann_pvalue = mannwhitneyu(control, test, alternative='two-sided').pvalue\n",
1405
    "    ttest_pvalue = ttest_ind(control, test, alternative='two-sided').pvalue\n",
1406
    "     \n",
1407
    "    # Отвергаем критерий на уровне 5%\n",
1408
    "    if mann_pvalue < 0.05:\n",
1409
    "        mann_bad_cnt += 1\n",
1410
    " \n",
1411
    "    if ttest_pvalue < 0.05:\n",
1412
    "        ttest_bad_cnt += 1\n",
1413
    "\n",
1414
    "# Строим доверительный интервал для уровня значимости критерия (или для FPR критерия)\n",
1415
    "left_mann_level, right_mann_level = proportion_confint(count = mann_bad_cnt, nobs = sz, alpha=0.05, method='wilson')\n",
1416
    "left_ttest_level, right_ttest_level = proportion_confint(count = ttest_bad_cnt, nobs = sz, alpha=0.05, method='wilson')\n",
1417
    "# Выводим результаты\n",
1418
    "print(f\"Mann-whitneyu significance level: {round(mann_bad_cnt / sz, 4)}, ({round(left_mann_level, 4)}, {round(right_mann_level, 4)})\")\n",
1419
    "print(f\"T-test significance level: {round(ttest_bad_cnt / sz, 4)}, ({round(left_ttest_level, 4)}, {round(right_ttest_level, 4)})\")"
1420
   ]
1421
  },
1422
  {
1423
   "cell_type": "markdown",
1424
   "metadata": {},
1425
   "source": [
1426
    "Мы видим, что Манн-Уитни ошибся в 2 раза больше, чем должен был! При этом пример валиден: t-test работает нормально.\n",
1427
    "\n",
1428
    "А значит Манн-Уитни НЕ проверяет сравнение средних, смещения медиан и смещения выборок $\\mathbb{P}(A < B) = \\dfrac{1}{2}$!\n",
1429
    "\n",
1430
    "Мы посмотрели 1 пример. В нем ошибка 1 рода была всего 10% вместо 5%: иногда это может быть не страшно. Но правда ли, что это наихудший возможный случай? Особенно интересно ответить на этот вопрос на более практических примерах: например в AB-тестах. Ведь это наиболее популярная задача на практике у аналитиков.\n",
1431
    "\n",
1432
    "-----\n",
1433
    "\n",
1434
    "Давайте разберем новый кейс на примере выдачи скидки. Мы выдали скидки. Количество платящих пользователей увеличилось, но ARPPU (Average revenue per paying user) упал. Наша ключевая метрика здесь — выручка. Мы хотим понять: начнём ли мы больше зарабатывать со скидками. Или выросло ли ARPU (Average revenue per user) или математическое ожидание выручки? \n",
1435
    "\n",
1436
    "Сразу зафиксируем проверяемую гипотезу о равенстве средних: $H_0$ — средний чек не изменился vs. $H_1$ — средний чек вырос среди всех пользователей.\n",
1437
    "\n",
1438
    "Искусственно просимулируем эксперимент, который мог бы произойти в реальности. Пусть распределение ненулевой части метрики подчиняется экспоненциальному распределению (это люди, которые платят на сайте). Для выручки это хорошее приближение.\n",
1439
    "\n"
1440
   ]
1441
  },
1442
  {
1443
   "cell_type": "code",
1444
   "execution_count": 32,
1445
   "metadata": {},
1446
   "outputs": [
1447
    {
1448
     "data": {
1449
      "image/png": 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\n",
1450
      "text/plain": [
1451
       "<Figure size 720x360 with 1 Axes>"
1452
      ]
1453
     },
1454
     "metadata": {
1455
      "needs_background": "dark"
1456
     },
1457
     "output_type": "display_data"
1458
    }
1459
   ],
1460
   "source": [
1461
    "pyplot.figure(figsize=(10, 5))\n",
1462
    "pyplot.title(\"Визуализация возможных ARPPU\", fontsize=12)\n",
1463
    "pyplot.hist(expon(loc=0, scale=6).rvs(1000), bins='auto')\n",
1464
    "pyplot.show()"
1465
   ]
1466
  },
1467
  {
1468
   "cell_type": "markdown",
1469
   "metadata": {},
1470
   "source": [
1471
    "1. Пусть нашими скидками мы увеличили число платящих пользователей на 5%.\n",
1472
    "    - Изначально в контроле было 50% нулей. Половина пользователей ничего не покупали на сайте.\n",
1473
    "    - В тесте стало 55% платящих пользователей.\n",
1474
    "\n",
1475
    "2. Раньше пользователь в среднем платил 7 рублей, а сейчас из-за скидки он платит 6 ₽, скидка была примерно 15%. Тогда математическое ожидание выручки в контроле было 3.5 ₽ (7 * 0.5), а в тесте — 3.3 ₽ (6 * 0.55).\n",
1476
    "\n",
1477
    "То есть платящих пользователей стало больше, а средний чек упал. Давайте снова запустим Монте-Карло 1000 раз и проверим, что здесь покажут T-test с Манном-Уитни, используя односторонние критерии.\n",
1478
    "\n",
1479
    "Демонстрация результатов:"
1480
   ]
1481
  },
1482
  {
1483
   "cell_type": "code",
1484
   "execution_count": 33,
1485
   "metadata": {},
1486
   "outputs": [
1487
    {
1488
     "data": {
1489
      "application/vnd.jupyter.widget-view+json": {
1490
       "model_id": "9271819fd5d34a74a455fab53d7ad70d",
1491
       "version_major": 2,
1492
       "version_minor": 0
1493
      },
1494
      "text/plain": [
1495
       "  0%|          | 0/10000 [00:00<?, ?it/s]"
1496
      ]
1497
     },
1498
     "metadata": {},
1499
     "output_type": "display_data"
1500
    },
1501
    {
1502
     "name": "stdout",
1503
     "output_type": "stream",
1504
     "text": [
1505
      "Mann-whitneyu GREATER FPR: 0.8427, (0.8354, 0.8497)\n",
1506
      "T-test GREATER FPR: 0.0002, (0.0001, 0.0007)\n"
1507
     ]
1508
    }
1509
   ],
1510
   "source": [
1511
    "numpy.random.seed(8)\n",
1512
    "# Заводим счетчики количества отвергнутых гипотез для Манна-Уитни и для t-test\n",
1513
    "mann_bad_cnt = 0\n",
1514
    "ttest_bad_cnt = 0\n",
1515
    "sz = 10000\n",
1516
    " \n",
1517
    "for i in tqdm_notebook(range(sz)):\n",
1518
    "    test_zero_array = bernoulli(p=0.55).rvs(5000)\n",
1519
    "    control_zero_array = bernoulli(p=0.5).rvs(5000)\n",
1520
    "    test = expon(loc=0, scale=6).rvs(5000) * test_zero_array # ET = 3.3\n",
1521
    "    control = expon(loc=0, scale=7).rvs(5000) * control_zero_array # EC = 3.5\n",
1522
    "     \n",
1523
    "    # Проверяем гипотезу\n",
1524
    "    mann_pvalue = mannwhitneyu(test, control, alternative='greater').pvalue\n",
1525
    "    ttest_pvalue = ttest_ind(test, control, alternative='greater').pvalue\n",
1526
    "    if mann_pvalue < 0.05:\n",
1527
    "        mann_bad_cnt += 1\n",
1528
    " \n",
1529
    "    if ttest_pvalue < 0.05:\n",
1530
    "        ttest_bad_cnt += 1\n",
1531
    "\n",
1532
    "# Строим доверительный интервал\n",
1533
    "left_mann_fpr, right_mann_fpr = proportion_confint(count = mann_bad_cnt, nobs = sz, alpha=0.05, method='wilson')\n",
1534
    "left_ttest_fpr, right_ttest_fpr = proportion_confint(count = ttest_bad_cnt, nobs = sz, alpha=0.05, method='wilson')\n",
1535
    "# Выводим результаты\n",
1536
    "print(f\"Mann-whitneyu GREATER FPR: {round(mann_bad_cnt / sz, 4)}, ({round(left_mann_fpr, 4)}, {round(right_mann_fpr, 4)})\")\n",
1537
    "print(f\"T-test GREATER FPR: {round(ttest_bad_cnt / sz, 4)}, ({round(left_ttest_fpr, 4)}, {round(right_ttest_fpr, 4)})\")"
1538
   ]
1539
  },
1540
  {
1541
   "cell_type": "markdown",
1542
   "metadata": {},
1543
   "source": [
1544
    "Мы знаем, что мат. ожидание в тесте МЕНЬШЕ, чем в контроле: скидки в текущем примере ВРЕДНЫ. Но Манн-Уитни показал бы в 84% случаев, что скидки полезны! И мы бы раскатили изменение! А должен был обманывать лишь в 5% случаев. В этот раз ошибка была не 10% как в случае выше, а 84%!\n",
1545
    "\n",
1546
    "При этом T-test нас обманул < 1% случаев, что соответствует нашему FPR."
1547
   ]
1548
  },
1549
  {
1550
   "cell_type": "markdown",
1551
   "metadata": {},
1552
   "source": [
1553
    "## Итог\n",
1554
    "\n",
1555
    "На текущей лекции мы вывели с вами критерий однородности Манна-Уитни. Какие выводы мы извлекли из текущей лекции:\n",
1556
    "\n",
1557
    "- **Не пытайтесь применить критерий, который проверяет одну нулевую гипотезу, для решения других задач, для которых он не предназначен!** Этот совет вам может помочь не только в текущием примере с Манном-Уитни, но и в других задачах.\n",
1558
    "- Манн-Уитни проверяет только гипотезу $H_0: F = G$. Лучше всего он работает в ситуации, когда вы проверяете смещения выборок. Если у вас измениллась дисперсия у одной из выборок, то он это плохо детектирует.\n",
1559
    "    - Очень аккуратно проверяйте применимость односторонней гипотезы Манна-Уитни: она подходит далеко не для всех задач и в очень редких кейсах имеет понятную интерпретацию для бизнеса.\n",
1560
    "- Манн-Уитни не применим для гипотезы равенства средних! Почему мы отдельно акцентируем внимание на эту тему? Это заблуждение настолько часто приводит к неправильным выводам в реальном бизнесе, что мы в Авито написали специальную [статью, чтобы предостеречь других аналитиков](https://habr.com/ru/companies/avito/articles/709596/).\n",
1561
    "\n",
1562
    "Исходя из этих аргументов в Авито мы не используем этот критерий на практике."
1563
   ]
1564
  }
1565
 ],
1566
 "metadata": {
1567
  "kernelspec": {
1568
   "display_name": "Python 3",
1569
   "language": "python",
1570
   "name": "python3"
1571
  },
1572
  "language_info": {
1573
   "codemirror_mode": {
1574
    "name": "ipython",
1575
    "version": 3
1576
   },
1577
   "file_extension": ".py",
1578
   "mimetype": "text/x-python",
1579
   "name": "python",
1580
   "nbconvert_exporter": "python",
1581
   "pygments_lexer": "ipython3",
1582
   "version": "3.8.6"
1583
  }
1584
 },
1585
 "nbformat": 4,
1586
 "nbformat_minor": 5
1587
}
1588

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