4a_brainsize.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# HW1 | Task 4a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Данные: http://lib.stat.cmu.edu/DASL/Stories/BrainSizeandIntelligence.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_table('data/brainsize.tsv', sep='\\t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>FSIQ</th>\n",
       "      <th>VIQ</th>\n",
       "      <th>PIQ</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Height</th>\n",
       "      <th>MRI_Count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>FSIQ</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.946639</td>\n",
       "      <td>0.934125</td>\n",
       "      <td>-0.049590</td>\n",
       "      <td>-0.084175</td>\n",
       "      <td>0.515625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>VIQ</th>\n",
       "      <td>0.946639</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.778135</td>\n",
       "      <td>-0.071988</td>\n",
       "      <td>-0.069610</td>\n",
       "      <td>0.479138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PIQ</th>\n",
       "      <td>0.934125</td>\n",
       "      <td>0.778135</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.002461</td>\n",
       "      <td>-0.075462</td>\n",
       "      <td>0.541535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Weight</th>\n",
       "      <td>-0.049590</td>\n",
       "      <td>-0.071988</td>\n",
       "      <td>0.002461</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.690199</td>\n",
       "      <td>0.018493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Height</th>\n",
       "      <td>-0.084175</td>\n",
       "      <td>-0.069610</td>\n",
       "      <td>-0.075462</td>\n",
       "      <td>0.690199</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.141882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MRI_Count</th>\n",
       "      <td>0.515625</td>\n",
       "      <td>0.479138</td>\n",
       "      <td>0.541535</td>\n",
       "      <td>0.018493</td>\n",
       "      <td>-0.141882</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               FSIQ       VIQ       PIQ    Weight    Height  MRI_Count\n",
       "FSIQ       1.000000  0.946639  0.934125 -0.049590 -0.084175   0.515625\n",
       "VIQ        0.946639  1.000000  0.778135 -0.071988 -0.069610   0.479138\n",
       "PIQ        0.934125  0.778135  1.000000  0.002461 -0.075462   0.541535\n",
       "Weight    -0.049590 -0.071988  0.002461  1.000000  0.690199   0.018493\n",
       "Height    -0.084175 -0.069610 -0.075462  0.690199  1.000000  -0.141882\n",
       "MRI_Count  0.515625  0.479138  0.541535  0.018493 -0.141882   1.000000"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Признаки **FSIQ**, **VIQ** и **PIQ** сильно коррелированы между собой. В описании указано, что основной характеристикой интеллекта является признак **FSIQ**, поэтому проверять на корреляцию с размером мозга **MRI_Count** будем именно его."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Отнормируем размеры мозга на общие размеры тела (рост), чтобы избавиться от такой очевидной зависимости. Потребуется заполнить один пропуск - сделаем это по среднему значению."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.fillna(df.mean(), inplace=True)\n",
    "df['MRI_Count'] /= df['Height']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В описании датасета сказано, что он содержит неоднородность - среди испытуемых можно выделить две группы (IQ <= 103, IQ >= 130). Избавимся от неё, потому что неоднородности зачастую приводят к совершенно неверным выводам. Дополнительно выделим из обеих групп мужчин и женщин."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_low = df[df['FSIQ'] <= 103]\n",
    "df_high = df[df['FSIQ'] >= 130]\n",
    "\n",
    "df_low_male = df_low[df_low['Gender'] == 'Male']\n",
    "df_low_female = df_low[df_low['Gender'] == 'Female']\n",
    "df_high_male = df_high[df_high['Gender'] == 'Male']\n",
    "df_high_female = df_high[df_high['Gender'] == 'Female']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Изучим распределение интересующих нас переменных - **FSIQ** и **MRI_Count**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "# строит гистограммы и проверяет нормальность заданных признаков\n",
    "def check_variables(data, vars):\n",
    "    for var in vars:\n",
    "        print(var)\n",
    "        print('='*len(var))\n",
    "        print('Normality test p-value:', stats.shapiro(data[var])[0])\n",
    "        sns.distplot(data[var])\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сначала в первой группе (IQ <= 103)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FSIQ\n",
      "====\n",
      "Normality test p-value: 0.946094810962677\n"
     ]
    },
    {
     "data": {
      "image/png": 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PVwJvqKo67/EAiMgkYBpwxMd9mgC0s6iGjk5l/qTRbpdiuhERLshO4QuLJlFe18xvNx2m1kIh6PQbCE6f/13ABmAv8LSq7hGRe0XkaqfZo0CSiBQA3wG6biO9ANgpIjuAF4BvqGplX/sczAMzI9O2o1WMj49kQkKU26WYXpw7Po4vnZ9JTVMbv91USE2ThUIwEfWji0i5ubmal5fndhlB54nNxwZlP6U1TfzyjQKunDWe821m0xHt6MkGHnv/CHGRYdx+0WSiwwc+hvWmhRMHoTJzNkRkm6rm9tfOOnHNsNl+tJpQEWanJbhdiunHpKQYblmcQVVjK3/68BjttjpbULBAMMOivbOTj46f4pzxo2wRHD+RmRzDynlpHDnZwLPbi/Cn3gRzduwn0wyL/SfqaGztINcuJvuV2ekJVDe2sjG/jAnxUSydanf6BTI7QzDDYtvRakZFesgaM8rtUswZumhqCtMnxLEx/wRHbERzQLNAMEOurrmNA2V1zE23GTb9kYhw/bw0RkeHs3brMepbbO6jQGWBYIbcR8dO0anY2AM/FhkWyuoFE2ls7eB5u54QsCwQzJBSVbYdq2ZiYrStmeznJiREcen0cew7UcdHx0+5XY4ZAhYIZkiV1DRTUdfC3Il2q2kgOH9KEpMSo/nbxyXU2qC1gGOBYIbUx8dPESrCzAm2KlogCBHh+vlpdHQqL3xUbF1HAcYCwQyZTlU+Lq4he2ws0Tb2IGAkx0bwuXPHsr+sjr2ltW6XYwaRBYIZMkdPNlLT1GYjkwPQ4inJjI2L4G+7SmmzUcwBwwLBDJmdx08RFiqca+seBJzQEOGqWRM41djG2wdsnZJAYYFghkR7Zye7ims4d3wc4R77NgtEk1NimZUWzzsHKqhqaHW7HDMI7CfVDImC8nqa2jqYY91FAe3yGeMRgVfzT7hdihkEFghmSOw8foqosFCyxsa6XYoZQvFRYZw/JZmdRTWUnGpyuxwzQBYIZtC1tneSX1rLjNR4PCH2LRbolmanEBUWyoY9dpbg7+yn1Qy6vSdqaetQZqfZ2INgEBUeysXTUjhYXs+hinq3yzED4FMgiMhyEdkvIgUicncvr0eIyFPO65tFJMPZ/jkR2SYiu5x/P9PtPW85+9zhfIwZrIMy7tp5/BRxkR4ykmPcLsUMk0WTk4iPCmPjnhM2WM2P9RsIIhIKPARcDuQAq0Ukp0ez24BqVc0CHgDuc7ZXAlep6kzgVuCPPd53s6rOcT7KB3AcZoRobG3nYFk9s9ISCBGb2TRYhIWGcPG0FI5XN1FgZwl+y5czhAVAgaoWqmorsBZY0aPNCuBx5/GzwDIREVX9SFVLnO17gEgRsRnOAtie4lo6VG0wWhCaP3E0cZEe3txnf9v5K18CIRU43u15kbOt1zaq2g7UAEk92lwPfKSqLd22/d7pLvqhiP05GQh2Fp0iKSacCQmRbpdihpknNISlU1M4crKRwko7S/BHvgRCb7+oe3YSnraNiEzH2410e7fXb3a6ki50Pr7Y6ycXWSMieSKSV1FhIyJHsrrmNg5XNjArLQHL9+B0XkYisREe3rCzBL/kSyAUAendnqcBJX21EREPEA9UOc/TgBeAW1T1UNcbVLXY+bcOeAJv19TfUdWHVTVXVXNTUmw915FsT0ktCsxMtbuLglVYaAgXZidTWNHAsapGt8sxZ8iXQNgKZItIpoiEA6uAdT3arMN70RhgJfCGqqqIJAAvAd9X1fe6GouIR0SSncdhwJXA7oEdinHb7uIakmMjGBtnl4mC2YKMRCLDQnj3oJ3R+5t+A8G5JnAXsAHYCzytqntE5F4Rudpp9iiQJCIFwHeArltT7wKygB/2uL00AtggIh8DO4Bi4JHBPDAzvOpb2jlc2cDM1DjrLgpyEWGhLMxMYk9Jrc1x5Gd8mqReVdcD63tsu6fb42bghl7e92Pgx33sdr7vZZqRbk9JDQrMsO4iAyyenMS7Byt5r6CSq2ZPcLsc4yMbqWwGxa7iGpJjwxkXZ3cXGYiLCmN2egJ5R6tobG13uxzjIwsEM2D1Le0crmhgRmq8dReZT1yQlUxbh7LlcJXbpRgfWSCYAevqLrK7i0x34+IjyUqJZfPhKjo6bToLf2CBYAZsd3ENSTHWXWT+3uIpSdQ0tdnay37CAsEMSH1LO4UVDcy07iLTi2njRpEQHcYHhSfdLsX4wALBDEi+MxjN7i4yvQkRYVFmEocrG9h3ws4SRjoLBDMgXd1F4+Otu8j0LnfSaDwhwh8+OOp2KaYfFgjmrDW0tFNYWW/dRea0oiM8zE5P4IXtxdQ1t7ldjjkNCwRz1vJLaulU6y4y/VuQkUhTWwfrdvacBs2MJBYI5qztKrHuIuObtNFRnDNuFGu3HO+/sXGNBYI5Kw0t7RRW1NtgNOMTEWHVeensKq5hd3GN2+WYPlggmLOSX+rtLrLBaMZX185NI9wTwlNb7SxhpLJAMGdld3ENidZdZM5AfHQYV8wYx192FNPU2uF2OaYXFgjmjDW2tHOowu4uMmdu1YKJ1DW3s35XqdulmF5YIJgz1tVdZHcXmTO1MDORzOQY1m495nYpphcWCOaM7XK6iyZYd5E5QyLCjeels/VINQXl9W6XY3qwQDBnpKu7aMYE6y4yZ+f6eWl4QoSn7CxhxPEpEERkuYjsF5ECEbm7l9cjROQp5/XNIpLhbP+ciGwTkV3Ov5/p9p75zvYCEfmF2G8Xv/DJ3UVp1l1kzk7KqAg+lzOW57YX09re6XY5ppt+A0FEQoGHgMuBHGC1iOT0aHYbUK2qWcADwH3O9krgKlWdCdwK/LHbe34FrAGynY/lAzgOM0ysu8gMhhvPS6eqoZVX88vcLsV048sZwgKgQFULVbUVWAus6NFmBfC48/hZYJmIiKp+pKpdY9X3AJHO2cR4IE5VP1BVBf4AXDPgozFDqrHVuovM4LgwO4XUhCi7uDzC+BIIqUD3kSRFzrZe26hqO1ADJPVocz3wkaq2OO2L+tknACKyRkTyRCSvoqLCh3LNUOmau8gGo5mBCg0Rrp+XynsFlZyoaXa7HOPwJRB6+1Ow53p4p20jItPxdiPdfgb79G5UfVhVc1U1NyUlxYdyzVDZXVLD6OgwJiRYd5EZuGvnpdGp8OKOYrdLMQ5fAqEISO/2PA3oOWXhJ21ExAPEA1XO8zTgBeAWVT3UrX1aP/s0I0hjazsF5TYYzQyezOQY5k8azXPbi/D2HBu3+RIIW4FsEckUkXBgFbCuR5t1eC8aA6wE3lBVFZEE4CXg+6r6XldjVS0F6kRkkXN30S3AiwM8FjOE9tpgNDMErpuXyoGyevaU2GpqI0G/geBcE7gL2ADsBZ5W1T0icq+IXO00exRIEpEC4DtA162pdwFZwA9FZIfzMcZ57evAb4EC4BDw8mAdlBl8u4q93UWpCVFul2ICyJUzJxAeGsJz24v6b2yGnMeXRqq6HljfY9s93R43Azf08r4fAz/uY595wIwzKda4o6m1g4LyepZkJVt3kRlU8dFhfDZnDOt2lPCDK84lLNTGyrrJ/vdNv/JLa+zuIjNkrpubxsmGVt45YHcRus0CwfTLuovMULpoWgqJMeE8v93uNnKbBYI5rZrGNg6VN9jKaGbIhIWGcPXsCby6t4yaxja3ywlqFgjmtDbmn6BD1bqLzJC6fl4are2dvGTrJLjKAsGc1vpdpdZdZIbcjNQ4ssfE2t1GLrNAMH2qaWrj3YJKm7vIDDkR4bp5aWw7Ws2Ryga3ywlaFgimT6/ml9HWoTYYzQyLa+emIgLPf2QXl91igWD6tH5XKakJUaSNtu4iM/TGxUdyQVYyz28vorPTprJwgwWC6VVNUxubDlZwxcxx1l1khs1181Ipqm4i72i126UEJQsE06vXnO6iK2aOd7sUE0Qumz6O6PBQnreLy66wQDC9esnpLpqTnuB2KSaIRId7uHzGeF76uJTmtg63ywk6Fgjm71h3kXHT9fNSqWtpZ6MtrznsLBDM39mw5wRtHco/zJrgdikmCC2anMSE+Eie22bdRsPNAsH8nXU7SpiUFM3sNLvd1Ay/kBDhmrmpbDpYQXmdLa85nCwQzKeU1zXz/qFKrp49wbqLjGuu61pe8yNbSHE4WSCYT3np41I6FVbMse4i456sMbHMTk+w5TWHmU+BICLLRWS/iBSIyN29vB4hIk85r28WkQxne5KIvCki9SLyYI/3vOXss+dKasZFL+4oIWd8HFljRrldiglyK+elsu9EHfmltrzmcOk3EEQkFHgIuBzIAVaLSE6PZrcB1aqaBTwA3OdsbwZ+CHy3j93frKpznI/yszkAM3iOnWxkx/FTXG1nB2YEuGr2BMJChee22VQWw8WXM4QFQIGqFqpqK7AWWNGjzQrgcefxs8AyERFVbVDVd/EGgxnh1u30/uBdNdsCwbgvITqcZeeMZd3OYto6Ot0uJyj4EgipwPFuz4ucbb22UdV2oAZI8mHfv3e6i34odgXTVarKiztKWJCRaFNdmxHj+vlpVNbb8prDxZdA6O0Xdc+rPL606elmVZ0JXOh8fLHXTy6yRkTyRCSvosK+KYbKvhN1HCyv5yrrLjIjyMXO8pq2TsLw8CUQioD0bs/TgJ73gn3SRkQ8QDxQdbqdqmqx828d8ATerqne2j2sqrmqmpuSkuJDueZsvLijBE+I8A82d5EZQbqW13wtv9yW1xwGvgTCViBbRDJFJBxYBazr0WYdcKvzeCXwhp7mXjER8YhIsvM4DLgS2H2mxZvB0dmp/HVnCRdkJ5MYE+52OcZ8ysr5abR2dPLXj21MwlDrNxCcawJ3ARuAvcDTqrpHRO4VkaudZo8CSSJSAHwH+OTWVBE5AtwPfElEipw7lCKADSLyMbADKAYeGbzDMmdi+7Fqik812dgDMyJNnxDHtLGjrNtoGHh8aaSq64H1Pbbd0+1xM3BDH+/N6GO3830r0Qy1F3eUEBkWwudyxrldijF/x7u8Zir/7+V9FFbUMzkl1u2SApaNVA5ybR2dvLSrlGXnjiU2wqe/D4wZdtfOTSVE4PntNiZhKFkgBLk39pVT1dDK9fN63klszMgxJi6SC7NTeOGjYltecwhZIAS5Z/KKSBkVwdJsu4PLjGzXzUul+FQTHx4+6XYpAcsCIYhV1LXw5v5yrpubiifUvhXMyHbZ9HGMivDYVBZDyH4LBLEXdxTT0anckJvmdinG9CsyLJR/mDWel3eX0tja7nY5AckCIUipKs/kFTEnPcFmNjV+47p5aTS2dvDK7hNulxKQLBCC1O7iWvaX1dnZgfEr52WMZmJitN1tNEQsEILUM9uOE+EJ4UpbN9n4ka4xCe8dqqT4VJPb5QQcC4Qg1NzWwYs7Srhs+jjio8LcLseYM7Jyvves9umtx/tpac6UBUIQen1vOTVNbdZdZPxS2uholman8HTecdptnYRBZYEQhJ7Zdpzx8ZGcPyXZ7VKMOSurF0yktKaZt22dhEFlgRBkTtQ0886BCq6fl0ZoiK1JZPzTsnPHkDIqgie3HHO7lIBigRBkXviomE79n35YY/xRWGgIN8xP44195ZyosRV6B4sFQhDp7FSezjvOgoxEMpJj3C7HmAFZdd5EOhWezrOLy4PFAiGIvH/oJIcrG7hp4US3SzFmwCYmRXNhdjJPbT1Oh014NygsEILInzcfZXR0GMtn2LoHJjCsOm8ixaea2HTQLi4PBguEIFFW28zG/DI+n5tOZFio2+UYMyg+lzOWpJhwu7g8SHwKBBFZLiL7RaRARO7u5fUIEXnKeX2ziGQ425NE5E0RqReRB3u8Z76I7HLe8wsRsVtehlDXafXqBdZdZAJHuCeElblpvLa3nPJau7g8UP0GgoiEAg8BlwM5wGpnXeTubgOqVTULeAC4z9neDPwQ+G4vu/4VsAbIdj6Wn80BmP51dCprtxzjwuxku5hsAs6q8ybS0ak8s83WXB4oX84QFgAFqlqoqq3AWmBFjzYrgMedx88Cy0REVLVBVd/FGwyfEJHxQJyqfqCqCvwBuGYgB2L69mp+GSU1zdxsF5NNAMpMjmHx5CSe3HLMLi4PkC+BkAp0v6+ryNnWaxtVbQdqgKR+9tk9znvbpxkkv3/vMKmSo1RgAAASZUlEQVQJUXz23LFul2LMkPjCokkUVTfx5r5yt0vxa74EQm99+z1j2Jc2Z9VeRNaISJ6I5FVU2J0EZyq/pJbNh6u4ZfEkWxXNBKxLp49lXFwkj39wxO1S/JovvyGKgPRuz9OAkr7aiIgHiAeq+tln96Gyve0TAFV9WFVzVTU3JcXW/T1Tj71/mKiwUFadZ91FJnCFhYbwxcWT2HSwkoLyOrfL8Vu+BMJWIFtEMkUkHFgFrOvRZh1wq/N4JfCGc22gV6paCtSJyCLn7qJbgBfPuHpzWifrW/jLjhKunZdKfLRNc20C26rz0gn3hPD4+0fdLsVv9RsIzjWBu4ANwF7gaVXdIyL3isjVTrNHgSQRKQC+A3xya6qIHAHuB74kIkXd7lD6OvBboAA4BLw8OIdkujyx+Rit7Z18+fwMt0sxZsglxUZw1awJPLe9iNrmNrfL8UseXxqp6npgfY9t93R73Azc0Md7M/rYngfM8LVQc2aa2zp4/IMjLJ2aQvZYWzPZBIcvL8ngue1FPLXlOF9bOtntcvyOXWUMUM9tL6KyvpU7LrIfChM8ZqTGs2hyIr9/7zBttnjOGbNACEAdncoj7xQyOy2exZNPd/evMYFnzdLJlNQ0s35Xqdul+B0LhAC0Yc8Jjpxs5PaLpmAzgphgc/HUMWSNieU3bxdymntbTC8sEAKMqvKbtw+RkRTNZdNtVlMTfEJChK9dmEl+aS3vHzrpdjl+xQIhwLx9oIKdRTXcftEUWyLTBK0Vc1JJjo3g128fcrsUv2KBEEBUlZ+/fpDUhCiun2dLZJrgFRkWym0XZLLpYCU7jp9yuxy/YYEQQN45WMlHx07xjUumEO6xL60Jbl9cPIn4qDAefKPA7VL8hv3WCBCqys9fO8CE+EhumJ/e/xuMCXCxER6+siST1/aWkV9S63Y5fsECIUC8c7CS7cdO8Y1LsuzswBjHl5ZkMCrCw0Nv2lmCL+w3RwDo7FTue3kf6YlR3JBr1w6M6RIfFcYt509i/e5S9p2ws4T+WCAEgL9+XEJ+aS3fvXQaER5bL9mY7r524WRiwz38dMMBt0sZ8SwQ/FxLewf/tWE/OePjuGrWBLfLMWbESYgOZ83Syby2t4ztx6rdLmdEs0Dwc09sPkZRdRN3X34OITbuwJhefeWCTJJjw/mvV/bb6OXTsEDwY9UNrfz89YNckJXMhdnJbpdjzIgVE+Hhzkuy+KDwJJsOVrpdzohlgeDHfrpxP3XN7dxzVY7NWWRMP25aOJG00VH8x/q9tNtMqL2yQPBTu4treGLLMW5ZPImptt6BMf2K8ITygyvOZd+JOtZuPe52OSOSBYIfUlV+tG4PidHhfPuzU90uxxi/cfmMcSzITOT+Vw9Q02SrqvXkUyCIyHIR2S8iBSJydy+vR4jIU87rm0Uko9tr33e27xeRy7ptPyIiu0Rkh4jkDcbBBIunth4n72g1/2f5NOKjbK1kY3wlItxzZQ7Vja388vWDbpcz4vQbCCISCjwEXA7kAKu7rYvc5TagWlWzgAeA+5z35gCrgOnAcuC/nf11uURV56hq7oCPJEiU1Tbz7+v3smhyIp/PtSkqjDlTM1LjuTE3nd+/f4S9pTZYrTtfzhAWAAWqWqiqrcBaYEWPNiuAx53HzwLLxHuVcwWwVlVbVPUwUODsz5wFVeVf/rKb1vZO/vO6WXYh2Ziz9L3l55AQFcbdz++io9NuQ+3iSyCkAt2vwBQ523pto6rtQA2Q1M97FdgoIttEZE1fn1xE1ohInojkVVRU+FBu4Prbx6W8ml/Gdz43lYzkGLfLMcZvjY4J556rcth5/BR/+vCo2+WMGL4EQm9/hvaM1L7anO69S1R1Ht6uqDtFZGlvn1xVH1bVXFXNTUlJ8aHcwFRyqol/fmEXs9MTuO2CTLfLMcbvXT17AkunpvCTV/ZRfKrJ7XJGBF8CoQjo3lmdBpT01UZEPEA8UHW696pq17/lwAtYV1KfOjqVf3xqBx2dys9vnIMn1G4OM2agRIR/v2YGAN99eied1nXkUyBsBbJFJFNEwvFeJF7Xo8064Fbn8UrgDfWOD18HrHLuQsoEsoEtIhIjIqMARCQGuBTYPfDDCUy/fvsQmw9X8aOrp1tXkTGDKD0xmn+9ajofFJ7k0XcPu12O6zz9NVDVdhG5C9gAhAK/U9U9InIvkKeq64BHgT+KSAHeM4NVznv3iMjTQD7QDtypqh0iMhZ4wbko6gGeUNVXhuD4/N77BZXc/+oBrpw1npXzbWprYwbbDblpvL6vjP/asJ8lWcnkTIhzuyTXiD9N9JSbm6t5ecEzZKGoupGrH3yPxJhw/nLnEmIj+s3vIfHE5mOufF4TWG5aONHtEvpU1dDKZT97h1GRHl68cwmjIgNrfI+IbPPl9n7rjB6hmts6uONP22hr7+ThL853LQyMCQaJMeH8cvVcjp5s5H8H8fUEC4QRqKNT+eaTH7GnpJYHbpzD5JRYt0syJuAtmpzED644l435Zfzq7UNul+MKC4QRRlW558XdbMwv454rc/hszli3SzImaHxlSQZXzZ7ATzfu55XdpW6XM+wsEEaYn712kD9vPsbtF03my0tsvIExw0lE+Mn1s5iTnsA31+5g65Eqt0saVhYII8jPXjvAz18/yPXz0vjeZee4XY4xQSkqPJRHbz2PtIQovvp4HgfK6twuadhYIIwAqsr9G/fzs9cOsnJ+Gj9ZOcuWwzTGRYkx4Tz+lQWEe0K46ZEP2X8iOELBAsFl7R2d/OCF3fzijQI+n5vGT66fRaiFgTGuS0+MZu2aRYSIsPqRD4NiZlQLBBfVt7Rz2+N5PLnlGF+/eAr/eZ2dGRgzkkxJieWp2xcTHhrCjb/5gA8OnXS7pCFlgeCS/SfquPrBd3m3oJL/uHYm31t+joWBMSNQZnIMz9yxmLFxkdzyu808u63I7ZKGjAXCMFNVns47zoqH3qW2qZ0/3rZgRI/gNMZ4u4+e/fr5LMhM5LvP7OSeF3fT3NbhdlmDzoa/DqPSmiZ+8Pwu3txfweLJSfx89RzGjIp0uyxjjA/io8J47MsLuO/lffz23cNsOVzFgzfNJWvMKLdLGzR2hjAMWts7+e2mQi69/x0+LKziX6/K4U9fXWhhYIyfCQsN4V+uzOF3X8qlrLaZK37+Lj977QAt7YFxtmBnCEOoo1NZv6uUn27cz9GTjVw0NYV7V0xnUpJNYW2MP/vMOWPZ+I8Xce/f8vnZawdZt7OE7y0/h0tzxvr10rYWCEOgua2Dv+4s4VdvH6KwooHsMbE89uXzuHjaGLdLM8YMkpRREfxy9Vyun5fKvX/L5/Y/bmNOegLfWpbNRVNT/PImEQuEQXSgrI5n8o7zzLYiTjW2ce74OB66aR7LZ4yzsQXGBKiLp43hgqxknt9ezM9eO8CXH9tK1phYbj0/g6tnTSA+2n+m0rZAGIDOTmVXcQ1v7a9g/a5S9pfVERoiXJozli8smsT5U5L8+vTRGOMbT2gInz8vnWvmprJ+VymPbCrkh3/Zzf/9Wz6fPXcMy2eM5+JpKcSN8HUWfAoEEVkO/Bzvimm/VdX/7PF6BPAHYD5wErhRVY84r30fuA3oAL6pqht82edIVNPUxsGyOnYW1bD1cBVbj1RxsqEVEZg/cTT3rpjO5TPGkzIqwu1SjTEuCPeEcM3cVFbMmcDu4lqe217EX3eWsH7XCTwhwryJo1k0OZHcjETOHR834n5X9BsIIhIKPAR8DigCtorIOlXN79bsNqBaVbNEZBVwH3CjiOTgXU5zOjABeE1Epjrv6W+fw669o5PK+lZO1DZzoqaZ8rpmiqqb2H+ijgNldZTWNH/SNm10FBdNTeHCqckszU4hKXZkfWGNMe4REWamxTMzLZ4fXpnDjuPVvJpfzgeHKnnwzQK61t9JignnnPGjmDY2jskpMYyLi2RsXCRj4yJIio0Y9q5mX84QFgAFqloIICJrgRV410nusgL4kfP4WeBB8faVrADWqmoLcNhZc3mB066/fQ6af3pmJ0XVTSjer4IqKNDU2kFDSzv1Le00tLTT2NZBzxVFwz0hZKXEsmhyElPHjmLauFhyxsczLt5uGTXG9C80RJg/KZH5kxIBqGtu4+OiGvadqGP/iVr2najjiS1HaW7r/NT7QsQ79mFUZBijIj08c8diosOHtpffl72nAse7PS8CFvbVRlXbRaQGSHK2f9jjvanO4/72OWjaO5X2zk4EASdwBUiKDWdiUjSx4R5iIjzERnoYMyqCcXGRjIuPZExcBMkxEX55t4AxZmQaFRnGkqxklmQlf7Kto1OpqGuhrLbZ+1HXQllNM6eaWqlrbqeuuZ1IT+iQ1+ZLIPT227DngqN9telre28D4npdxFRE1gBrnKf1IrK/jzr9XTJQ6XYRQ8iOz78N+PhuHqRChsiI//r9/ssDevskXxr5EghFQHq352lASR9tikTEA8QDVf28t799AqCqDwMP+1CnXxORPFXNdbuOoWLH59/s+IKDL1NXbAWyRSRTRMLxXiRe16PNOuBW5/FK4A1VVWf7KhGJEJFMIBvY4uM+jTHGDKN+zxCcawJ3ARvw3iL6O1XdIyL3Anmqug54FPijc9G4Cu8veJx2T+O9WNwO3KmqHQC97XPwD88YY4yvRHveVmNcISJrnO6xgGTH59/s+IKDBYIxxhjApr82xhjjsEBwgYhME5Ed3T5qReTbIpIoIq+KyEHn39Fu13o2ROQfRWSPiOwWkSdFJNK5gWCzc2xPOTcT+CUR+ZZzbHtE5NvONr/+2onI70SkXER2d9vW6zGJ1y9EpEBEPhaRee5V7ps+ju8G52vYKSK5Pdp/3zm+/SJy2fBX7A4LBBeo6n5VnaOqc/DO/9QIvADcDbyuqtnA685zvyIiqcA3gVxVnYH3poGu6UwecI6tGu90J35HRGYAX8M74n42cKWIZOP/X7vHgOU9tvV1TJfjvWMwG+8YoV8NU40D8Rh/f3y7geuAd7pv7DHlznLgv50pfAKeBYL7lgGHVPUo3uk7Hne2Pw5c41pVA+MBopwxKdFAKfAZvNOagH8f27nAh6raqKrtwNvAtfj5105V38F7h2B3fR3TCuAP6vUhkCAi44en0rPT2/Gp6l5V7W2g6ydT7qjqYaD7lDsBzQLBfauAJ53HY1W1FMD51+9W1FHVYuCnwDG8QVADbANOOb9A4dNTmPib3cBSEUkSkWjgCryDLP3+a9eLvo6pt+ls/PXr2ZtAP74+WSC4yOlHvxp4xu1aBovTz7wCyMQ7w20M3i6Gnvzy9jZV3Yu3++tV4BVgJ94xNsHEl+ls/FmgH1+fLBDcdTmwXVXLnOdlXafezr/lrlV29j4LHFbVClVtA54HzsfbrdA1ELLPqUr8gao+qqrzVHUp3m6IgwTG166nvo7Jl+ls/FmgH1+fLBDctZr/6S6CT08Bcivw4rBXNHDHgEUiEu1Mgb4M70j1N/FOawL+e2wAiMgY59+JeC9KPklgfO166uuY1gG3OHcbLQJqurqWAkRfU+4EPBuY5hKn//k4MFlVa5xtScDTwES8v1hvUNWeF/pGPBH5N+BGvF0pHwFfxdsHuxZIdLZ9wVknw++IyCa807u3Ad9R1df9/WsnIk8CF+Od9bMM+FfgL/RyTE7QP4j3DpxG4MuqmudG3b7q4/iqgF8CKcApYIeqXua0/2fgK3i/h7+tqi+7UPaws0AwxhgDWJeRMcYYhwWCMcYYwALBGGOMwwLBGGMMYIFgjDHGYYFgzGmISEePmWkznDEWfxaRXc6sp++KSKzTvr7be6eLyBsickBEDonIv4mI/cyZEavfJTSNCXJNzqy0nxCR7wNlqjrTeT4N75iE7m2i8A5w+rqqbnTGnTwHfAt4YFgqN+YM2V8rxpy58UBx1xNnOvOeg+xuAt5T1Y1Om0bgLuCfhq1KY86QBYIxpxfVrbvoBWfb74DvicgHIvJjZz2EnqbjneX1E6p6yNlfwhDXbMxZsS4jY07v77qMVHWHiEwGLsU7md9WEVnszITaReh9hszeZtI0ZkSwQDDmLKhqPd6ZXJ8XkU686yJ0D4Q9wNLu73FCpFJVTw1bocacAesyMuYMiciSbusLhwM5wNEezf4MXCAin3XaRQG/wDupmjEjkgWCMWduCvC2iOzCO3NrHt47iD6hqk14Fz/6ZxE5AFTivcj85+Eu1hhf2WynxgwDEbkGuB+4xFk/25gRxwLBGGMMYF1GxhhjHBYIxhhjAAsEY4wxDgsEY4wxgAWCMcYYhwWCMcYYwALBGGOM4/8Dx4ZWSJHpj6YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20e61f9c080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MRI_Count\n",
      "=========\n",
      "Normality test p-value: 0.9918928742408752\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20e620a57f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_variables(df_low, ['FSIQ', 'MRI_Count'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Затем - во второй (IQ >= 130)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FSIQ\n",
      "====\n",
      "Normality test p-value: 0.9272173643112183\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20e620f74a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MRI_Count\n",
      "=========\n",
      "Normality test p-value: 0.9863025546073914\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20e62162ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "check_variables(df_high, ['FSIQ', 'MRI_Count'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Таким образом, все исследуемые переменные можно с высокой степенью уверенности считать нормальными и использовать для анализа корреляций $r$-тест Пирсона."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Перейдём к анализу корреляций."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "def corr_test(df):\n",
    "    x = df['FSIQ']\n",
    "    y = df['MRI_Count']\n",
    "    r, p = stats.pearsonr(x, y)\n",
    "    print('Correlation:', r)\n",
    "    print('p-value:', p)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Смешанный половой состав, IQ <= 103"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation: -0.1671773216981077\n",
      "p-value: 0.481132706952653\n",
      "\n"
     ]
    }
   ],
   "source": [
    "corr_test(df_low)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нет свидетельств в пользу коррелированности переменных."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Смешанный половой состав, IQ >= 130"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation: -0.014036891060796955\n",
      "p-value: 0.9531628659973005\n",
      "\n"
     ]
    }
   ],
   "source": [
    "corr_test(df_high)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нет свидетельств в пользу коррелированности переменных."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Мужчины, IQ <= 103"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation: -0.24610923096092446\n",
      "p-value: 0.49307666286291385\n",
      "\n"
     ]
    }
   ],
   "source": [
    "corr_test(df_low_male)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нет свидетельств в пользу коррелированности переменных."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Мужчины, IQ >= 130"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation: 0.06814284790020832\n",
      "p-value: 0.8516277577662514\n",
      "\n"
     ]
    }
   ],
   "source": [
    "corr_test(df_high_male)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нет свидетельств в пользу коррелированности переменных."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Женщины, IQ <= 103"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation: 0.048212422034780295\n",
      "p-value: 0.8947801311480204\n",
      "\n"
     ]
    }
   ],
   "source": [
    "corr_test(df_low_female)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нет свидетельств в пользу коррелированности переменных."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Женщины, IQ >= 130"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation: 0.13304744274131822\n",
      "p-value: 0.714056134150054\n",
      "\n"
     ]
    }
   ],
   "source": [
    "corr_test(df_high_female)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нет свидетельств в пользу коррелированности переменных."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Вывод\n",
    "\n",
    "Ни в одной из изученных групп не было обнаружено статистически значимых корреляций между размером мозга и интеллектом."
   ]
  }
 ],
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