statistic_notes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ÖRNEK TEORİSİ - ÖRNEKLEM DAĞILIMI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bir popülasyon içerisinden popülasyonu temsil ettiği düşünülen alt küme seçme işlemi örneklemdir. Olasılıksal ve olasılıksal olmayan olarak ikiye ayrılır. Birden fazla örneklem çektiğimizde örneklemlerin dağılımı konusu önem taşımaktadır."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:20.853197Z",
     "start_time": "2020-06-13T16:00:20.686642Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "20 ile 50 yaş arasında 20000 kişiden oluşan bir popülasyonumuz olduğunu düşünelim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:20.861175Z",
     "start_time": "2020-06-13T16:00:20.856189Z"
    }
   },
   "outputs": [],
   "source": [
    "populasyon=np.random.randint(20,50,20000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:20.885112Z",
     "start_time": "2020-06-13T16:00:20.864167Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([21, 41, 41, 40, 39, 31, 33, 43, 25, 45, 31, 41, 45, 24, 35, 23, 20,\n",
       "       48, 34, 33])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "populasyon[:20]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Popülasyon içerisinden 1000 gözlem seçerek örneklem oluşturalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:20.893090Z",
     "start_time": "2020-06-13T16:00:20.888102Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(12345)\n",
    "orneklem=np.random.choice(populasyon,size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:20.905058Z",
     "start_time": "2020-06-13T16:00:20.896082Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Popülasyon Ortalaması: 34.4385 \n",
      "Örneklem Ortalaması: 34.489\n"
     ]
    }
   ],
   "source": [
    "print(\"Popülasyon Ortalaması:\",populasyon.mean(),\"\\nÖrneklem Ortalaması:\",orneklem.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Şimdi farklı örneklemler çekerek bu örneklemlerin ortalamalarını inceleyelim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:20.919021Z",
     "start_time": "2020-06-13T16:00:20.907052Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(10)\n",
    "orneklem1=np.random.choice(populasyon,1000)\n",
    "orneklem2=np.random.choice(populasyon,1000)\n",
    "orneklem3=np.random.choice(populasyon,1000)\n",
    "orneklem4=np.random.choice(populasyon,1000)\n",
    "orneklem5=np.random.choice(populasyon,1000)\n",
    "orneklem6=np.random.choice(populasyon,1000)\n",
    "orneklem7=np.random.choice(populasyon,1000)\n",
    "orneklem8=np.random.choice(populasyon,1000)\n",
    "orneklem9=np.random.choice(populasyon,1000)\n",
    "orneklem10=np.random.choice(populasyon,1000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:20.928003Z",
     "start_time": "2020-06-13T16:00:20.921014Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5 Örneklemin Ortalaması 34.563599999999994\n"
     ]
    }
   ],
   "source": [
    "print(\"5 Örneklemin Ortalaması\",(orneklem1.mean() + orneklem2.mean() + orneklem3.mean() + orneklem4.mean() + orneklem5.mean())/5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:20.940961Z",
     "start_time": "2020-06-13T16:00:20.932983Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tüm Örneklemlerin Ortalaması : 34.5198\n"
     ]
    }
   ],
   "source": [
    "print(\"Tüm Örneklemlerin Ortalaması :\",(orneklem1.mean() + orneklem2.mean() + orneklem3.mean() + orneklem4.mean() + orneklem5.mean() \n",
    "+ orneklem6.mean() + orneklem7.mean() + orneklem8.mean() + orneklem9.mean() + orneklem10.mean())/10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Daha fazla örneklem çekilip ortalaması alındığında örneklemlerin ortalamasının popülasyonun ortalamasına daha yakın olması beklenir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BETİMSEL İSTATİSTİKLER"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* **Ortalama** : Orta konumu tek bir sayı ile ifade eder.\n",
    "* **Medyan** :Bir anakütle ya da örneklem veri serisini küçükten büyüğe doğru sıraladığımızda, seriyi ortadan ikiye ayıran değerdir.\n",
    "* **Mod** : Bir veri kümesi içinde en sık görülen değerdir.\n",
    "* **Kartiller** : Bir seriyi dört eşit parçaya bölen değerlerdir.\n",
    "* **Değişim Aralığı** : Gözlem değerleri küçükten büyüğe doğru sıralanarak bir dizi oluşturulduğunda, en büyük değerle en küçük değer arasındaki fark\n",
    "* **Standart Sapma** :  Bir anakütle, bir örneklem, bir olasılık dağılımı veya bir rassal değişken, veri değerlerinin yayılımının özetlenmesi için kullanılan bir ölçüdür.\n",
    "* **Kovaryans**: İki değişken arasındaki ilişkinin değişkenliğiyle ilgilenir.\n",
    "* **Korelasyon**: İki değişken arasındaki ikişkiyi,anlamlı olup olmadığını,ilişkinin şiddetini ve yönünü ifade eder.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:19:42.975710Z",
     "start_time": "2020-06-14T11:19:42.816138Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "    }\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>age</th>\n",
       "      <th>workclass</th>\n",
       "      <th>fnlwgt</th>\n",
       "      <th>education</th>\n",
       "      <th>educational-num</th>\n",
       "      <th>marital-status</th>\n",
       "      <th>occupation</th>\n",
       "      <th>relationship</th>\n",
       "      <th>race</th>\n",
       "      <th>gender</th>\n",
       "      <th>capital-gain</th>\n",
       "      <th>capital-loss</th>\n",
       "      <th>hours-per-week</th>\n",
       "      <th>native-country</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>25</td>\n",
       "      <td>Private</td>\n",
       "      <td>226802</td>\n",
       "      <td>11th</td>\n",
       "      <td>7</td>\n",
       "      <td>Never-married</td>\n",
       "      <td>Machine-op-inspct</td>\n",
       "      <td>Own-child</td>\n",
       "      <td>Black</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>38</td>\n",
       "      <td>Private</td>\n",
       "      <td>89814</td>\n",
       "      <td>HS-grad</td>\n",
       "      <td>9</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Farming-fishing</td>\n",
       "      <td>Husband</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>50</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>28</td>\n",
       "      <td>Local-gov</td>\n",
       "      <td>336951</td>\n",
       "      <td>Assoc-acdm</td>\n",
       "      <td>12</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Protective-serv</td>\n",
       "      <td>Husband</td>\n",
       "      <td>White</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&gt;50K</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>44</td>\n",
       "      <td>Private</td>\n",
       "      <td>160323</td>\n",
       "      <td>Some-college</td>\n",
       "      <td>10</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>Machine-op-inspct</td>\n",
       "      <td>Husband</td>\n",
       "      <td>Black</td>\n",
       "      <td>Male</td>\n",
       "      <td>7688</td>\n",
       "      <td>0</td>\n",
       "      <td>40</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&gt;50K</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>18</td>\n",
       "      <td>?</td>\n",
       "      <td>103497</td>\n",
       "      <td>Some-college</td>\n",
       "      <td>10</td>\n",
       "      <td>Never-married</td>\n",
       "      <td>?</td>\n",
       "      <td>Own-child</td>\n",
       "      <td>White</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "      <td>United-States</td>\n",
       "      <td>&lt;=50K</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  workclass  fnlwgt     education  educational-num      marital-status  \\\n",
       "0   25    Private  226802          11th                7       Never-married   \n",
       "1   38    Private   89814       HS-grad                9  Married-civ-spouse   \n",
       "2   28  Local-gov  336951    Assoc-acdm               12  Married-civ-spouse   \n",
       "3   44    Private  160323  Some-college               10  Married-civ-spouse   \n",
       "4   18          ?  103497  Some-college               10       Never-married   \n",
       "\n",
       "          occupation relationship   race  gender  capital-gain  capital-loss  \\\n",
       "0  Machine-op-inspct    Own-child  Black    Male             0             0   \n",
       "1    Farming-fishing      Husband  White    Male             0             0   \n",
       "2    Protective-serv      Husband  White    Male             0             0   \n",
       "3  Machine-op-inspct      Husband  Black    Male          7688             0   \n",
       "4                  ?    Own-child  White  Female             0             0   \n",
       "\n",
       "   hours-per-week native-country income  \n",
       "0              40  United-States  <=50K  \n",
       "1              50  United-States  <=50K  \n",
       "2              40  United-States   >50K  \n",
       "3              40  United-States   >50K  \n",
       "4              30  United-States  <=50K  "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data=pd.read_csv(\"adult.csv\")\n",
    "df=data.copy()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.045507Z",
     "start_time": "2020-06-13T16:00:22.001625Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "    }\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>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>age</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>38.643585</td>\n",
       "      <td>13.710510</td>\n",
       "      <td>17.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>90.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>fnlwgt</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>189664.134597</td>\n",
       "      <td>105604.025423</td>\n",
       "      <td>12285.0</td>\n",
       "      <td>117550.5</td>\n",
       "      <td>178144.5</td>\n",
       "      <td>237642.0</td>\n",
       "      <td>1490400.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>educational-num</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>10.078089</td>\n",
       "      <td>2.570973</td>\n",
       "      <td>1.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>16.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>capital-gain</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>1079.067626</td>\n",
       "      <td>7452.019058</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>99999.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>capital-loss</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>87.502314</td>\n",
       "      <td>403.004552</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4356.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>hours-per-week</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>40.422382</td>\n",
       "      <td>12.391444</td>\n",
       "      <td>1.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>99.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   count           mean            std      min       25%  \\\n",
       "age              48842.0      38.643585      13.710510     17.0      28.0   \n",
       "fnlwgt           48842.0  189664.134597  105604.025423  12285.0  117550.5   \n",
       "educational-num  48842.0      10.078089       2.570973      1.0       9.0   \n",
       "capital-gain     48842.0    1079.067626    7452.019058      0.0       0.0   \n",
       "capital-loss     48842.0      87.502314     403.004552      0.0       0.0   \n",
       "hours-per-week   48842.0      40.422382      12.391444      1.0      40.0   \n",
       "\n",
       "                      50%       75%        max  \n",
       "age                  37.0      48.0       90.0  \n",
       "fnlwgt           178144.5  237642.0  1490400.0  \n",
       "educational-num      10.0      12.0       16.0  \n",
       "capital-gain          0.0       0.0    99999.0  \n",
       "capital-loss          0.0       0.0     4356.0  \n",
       "hours-per-week       40.0      45.0       99.0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe().T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.464413Z",
     "start_time": "2020-06-13T16:00:22.047502Z"
    }
   },
   "outputs": [],
   "source": [
    "#!pip install researchpy\n",
    "import researchpy as rp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.520238Z",
     "start_time": "2020-06-13T16:00:22.467402Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n"
     ]
    },
    {
     "data": {
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       "\n",
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       "        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>Variable</th>\n",
       "      <th>N</th>\n",
       "      <th>Mean</th>\n",
       "      <th>SD</th>\n",
       "      <th>SE</th>\n",
       "      <th>95% Conf.</th>\n",
       "      <th>Interval</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>age</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>38.643585</td>\n",
       "      <td>13.710510</td>\n",
       "      <td>0.062038</td>\n",
       "      <td>38.521990</td>\n",
       "      <td>38.765180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>fnlwgt</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>189664.134597</td>\n",
       "      <td>105604.025423</td>\n",
       "      <td>477.841377</td>\n",
       "      <td>188727.559498</td>\n",
       "      <td>190600.709697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>capital-gain</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>1079.067626</td>\n",
       "      <td>7452.019058</td>\n",
       "      <td>33.719198</td>\n",
       "      <td>1012.977575</td>\n",
       "      <td>1145.157678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>capital-loss</td>\n",
       "      <td>48842.0</td>\n",
       "      <td>87.502314</td>\n",
       "      <td>403.004552</td>\n",
       "      <td>1.823531</td>\n",
       "      <td>83.928169</td>\n",
       "      <td>91.076458</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Variable        N           Mean             SD          SE  \\\n",
       "0           age  48842.0      38.643585      13.710510    0.062038   \n",
       "1        fnlwgt  48842.0  189664.134597  105604.025423  477.841377   \n",
       "2  capital-gain  48842.0    1079.067626    7452.019058   33.719198   \n",
       "3  capital-loss  48842.0      87.502314     403.004552    1.823531   \n",
       "\n",
       "       95% Conf.       Interval  \n",
       "0      38.521990      38.765180  \n",
       "1  188727.559498  190600.709697  \n",
       "2    1012.977575    1145.157678  \n",
       "3      83.928169      91.076458  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rp.summary_cont(df[[\"age\",\"fnlwgt\",\"capital-gain\",\"capital-loss\"]]) #Sayısal değişkenler için"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**SD** : Standart Sapma ,  **SE** : Standart Hata , **Conf-Interval** : Güven Aralıkları"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.609001Z",
     "start_time": "2020-06-13T16:00:22.523232Z"
    }
   },
   "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>Variable</th>\n",
       "      <th>Outcome</th>\n",
       "      <th>Count</th>\n",
       "      <th>Percent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>marital-status</td>\n",
       "      <td>Married-civ-spouse</td>\n",
       "      <td>22379</td>\n",
       "      <td>45.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td></td>\n",
       "      <td>Never-married</td>\n",
       "      <td>16117</td>\n",
       "      <td>33.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td></td>\n",
       "      <td>Divorced</td>\n",
       "      <td>6633</td>\n",
       "      <td>13.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td></td>\n",
       "      <td>Separated</td>\n",
       "      <td>1530</td>\n",
       "      <td>3.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td></td>\n",
       "      <td>Widowed</td>\n",
       "      <td>1518</td>\n",
       "      <td>3.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td></td>\n",
       "      <td>Married-spouse-absent</td>\n",
       "      <td>628</td>\n",
       "      <td>1.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td></td>\n",
       "      <td>Married-AF-spouse</td>\n",
       "      <td>37</td>\n",
       "      <td>0.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>gender</td>\n",
       "      <td>Male</td>\n",
       "      <td>32650</td>\n",
       "      <td>66.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td></td>\n",
       "      <td>Female</td>\n",
       "      <td>16192</td>\n",
       "      <td>33.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>race</td>\n",
       "      <td>White</td>\n",
       "      <td>41762</td>\n",
       "      <td>85.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td></td>\n",
       "      <td>Black</td>\n",
       "      <td>4685</td>\n",
       "      <td>9.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td></td>\n",
       "      <td>Asian-Pac-Islander</td>\n",
       "      <td>1519</td>\n",
       "      <td>3.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td></td>\n",
       "      <td>Amer-Indian-Eskimo</td>\n",
       "      <td>470</td>\n",
       "      <td>0.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td></td>\n",
       "      <td>Other</td>\n",
       "      <td>406</td>\n",
       "      <td>0.83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Variable                Outcome  Count  Percent\n",
       "0   marital-status     Married-civ-spouse  22379    45.82\n",
       "1                           Never-married  16117    33.00\n",
       "2                                Divorced   6633    13.58\n",
       "3                               Separated   1530     3.13\n",
       "4                                 Widowed   1518     3.11\n",
       "5                   Married-spouse-absent    628     1.29\n",
       "6                       Married-AF-spouse     37     0.08\n",
       "7           gender                   Male  32650    66.85\n",
       "8                                  Female  16192    33.15\n",
       "9             race                  White  41762    85.50\n",
       "10                                  Black   4685     9.59\n",
       "11                     Asian-Pac-Islander   1519     3.11\n",
       "12                     Amer-Indian-Eskimo    470     0.96\n",
       "13                                  Other    406     0.83"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rp.summary_cat(df[[\"marital-status\",\"gender\",\"race\"]]) #kategorik değişkenler için"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.629944Z",
     "start_time": "2020-06-13T16:00:22.611994Z"
    }
   },
   "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>capital-gain</th>\n",
       "      <th>capital-loss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>capital-gain</td>\n",
       "      <td>5.553259e+07</td>\n",
       "      <td>-94422.847037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>capital-loss</td>\n",
       "      <td>-9.442285e+04</td>\n",
       "      <td>162412.669033</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              capital-gain   capital-loss\n",
       "capital-gain  5.553259e+07  -94422.847037\n",
       "capital-loss -9.442285e+04  162412.669033"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"capital-gain\",\"capital-loss\"]].cov() #kovaryans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.652884Z",
     "start_time": "2020-06-13T16:00:22.632937Z"
    }
   },
   "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>capital-gain</th>\n",
       "      <th>capital-loss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>capital-gain</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.031441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>capital-loss</td>\n",
       "      <td>-0.031441</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              capital-gain  capital-loss\n",
       "capital-gain      1.000000     -0.031441\n",
       "capital-loss     -0.031441      1.000000"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"capital-gain\",\"capital-loss\"]].corr() #korelasyon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GÜVEN ARALIKLARI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bir anakütle parametre değerinin tek bir sayı ile kestirimi yapılacağına, bu parametre değerini kapsayabilecek iki sayıdan oluşan bir aralık bulunur. Örneklem büyüklüğü arttıkça güven aralığı daralır. Örneklemden elde edilen varyans,ortalama gibi değerlerden hareketle tahmini sınırlar verir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](guvenn.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Örneğin belli bir yaştaki 1000 hastaya ait kan basıncı değerlerini aldığımızı düşünelim. İlgili popülasyonun ortalama kan basıncının %95 olasılıkla hangi değerler arasında olabileceğini bulalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.661859Z",
     "start_time": "2020-06-13T16:00:22.655875Z"
    }
   },
   "outputs": [],
   "source": [
    "kan_basinci = np.random.randint(10,130, 1000) # 10 ile 130 arasında 1000 gözlem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.677816Z",
     "start_time": "2020-06-13T16:00:22.669838Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "68.467"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kan_basinci.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:40:25.880904Z",
     "start_time": "2020-06-14T10:40:25.537328Z"
    }
   },
   "outputs": [],
   "source": [
    "import statsmodels.stats.api as sms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.934133Z",
     "start_time": "2020-06-13T16:00:22.926152Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Güven Aralıkları : (66.34188141753465, 70.59211858246535)\n"
     ]
    }
   ],
   "source": [
    "print(\"Güven Aralıkları :\",sms.DescrStatsW(kan_basinci).tconfint_mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Popülasyondan alınan kan basıncı değeri istatistiksel olarak %95 güvenilirlikle bulunan değerler arasındadır."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OLASILIK DAĞILIMLARI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Olasılık Dağılımı** : Rassal bir olaya ait değerler ve bu değerlerin gerçekleşme olasılıklarının bir arada ifade edilmesidir.\n",
    "\n",
    "**Olasılık Fonksiyonu** : Bir değişkenin herhangi bir değeri alması olasılığını hesaplayan fonksiyon.\n",
    "\n",
    "**Kesikli (Discrete) Olasılık Dağılımları**: Bernoilli, Binom, Poisson, Geometric, Hypergeometric...\n",
    "\n",
    "**Sürekli (Continious) Olasılık Dağılımları**: Normal, Uniform, Üstel (Exponential), Gamma, Beta..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KESİKLİ OLASILIK DAĞILIMLARI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bernoulli Dağılımı"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Olumlu-olumsuz,başarılı-başarısız,iyi-kötü şeklindeki iki sonucu olan olaylar ile ilgilenildiğinde kullanılır."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](bernoulli.png)  ![title](bernoulli2.png) ![title](bernoulli3.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.943107Z",
     "start_time": "2020-06-13T16:00:22.937123Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import bernoulli"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bir parayı attığımızda tura gelme olasılığını 0,4 olarak belirleyelim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.952085Z",
     "start_time": "2020-06-13T16:00:22.946099Z"
    }
   },
   "outputs": [],
   "source": [
    "p=0.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.965048Z",
     "start_time": "2020-06-13T16:00:22.955075Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bernoulli(p).pmf(k=1)  #pmf - probabilty mass function - olasılık kütle fonksiyonu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:00:22.982005Z",
     "start_time": "2020-06-13T16:00:22.973027Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bernoulli(p).pmf(k=0) #yazı gelme olasılığı"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:10.339304Z",
     "start_time": "2020-06-13T16:02:10.156792Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Bernoulli Dağılımı')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "data_bern = bernoulli.rvs(size=10000,p=0.6)\n",
    "sns.distplot(data_bern,\n",
    "                 kde=False,\n",
    "                 color=\"skyblue\",\n",
    "                 hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "plt.title(\"Bernoulli Dağılımı\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binom Dağılımı"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bir deney n kez tekrarlandığında belli bir olay x defa meydana geliyorsa bu olayın olasılığı\n",
    "binom dağılımı ile bulunur. Deneyler bağımsızdır."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](binom.png) **E(X) = np       Var(X) = np(1-p)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p=0,5 olduğunda dağılım simetrik yapıdadır.p>0,5 ise çarpıklık sola doğru,p<0,5 ise çarpıklık sağa doğru olur."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bir işletmede çalışan işçilerin işe geç kalma oranının %10 olduğunu bildiğimizi varsayalım.Bu işletmede çalışan işçilerden 200 tane rastgele seçtiğimizde 8 tanesinin işe geç kalma olasılığını bulalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:22.386180Z",
     "start_time": "2020-06-13T16:02:22.379210Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0009030369045712714\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "p = 0.10\n",
    "n = 200\n",
    "rv = binom(n, p)\n",
    "print(rv.pmf(8))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:34.132635Z",
     "start_time": "2020-06-13T16:02:33.879313Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Binom Dağılımı')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_binom = binom.rvs(n=10,p=0.8,size=10000)\n",
    "sns.distplot(data_binom,\n",
    "                  kde=False,\n",
    "                  color='skyblue',                  \n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "plt.title(\"Binom Dağılımı\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T09:59:05.740770Z",
     "start_time": "2020-06-13T09:59:05.734778Z"
    }
   },
   "source": [
    "### Poisson Dağılımı"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nadir meydana gelen olayların dağılımını ifade eder. Bağımsız olaylarda kullanılır. Kütle sınırsız olduğunda olayların bağımsızlığına bakılmaksızın bu dağılım kullanılabilir. İş kazaları, nadir görülen hastalıklar, ürün muayenesi gibi alanlarda kullanılır. Binom dağılımının özel bir halidir. Bir olayın nadir olması için rassal deneme sayısı n>50 olmalı ve $\\lambda<5$ olmalı. Bir sürücünün trafik kazası yapması, 20000 kelimeden oluşan bir kitapta hatalı yazını yer alması gibi olaylar nadir olaylardır."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "${\\displaystyle f(x,\\lambda )={\\frac {\\lambda ^{x}e^{-\\lambda }}{x!}}\\,\\!}$,  x = 0,1,2,...,n   $ E(x) =\\lambda $  $   Var(x)=\\lambda $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bir işletmede yılık kişi başına düşen ortalama iş kazası 0,2 olarak bulunmuş olsun.Tesadüfen seçilen bir kişinin hiç kaza geçirmeme,bir kaza geçirme ve en az bir kaza geçirme olasıklarını bulalım"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:36.978483Z",
     "start_time": "2020-06-13T16:02:36.975486Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:37.329118Z",
     "start_time": "2020-06-13T16:02:37.323159Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8187307530779818\n"
     ]
    }
   ],
   "source": [
    "lambda_= 0.2\n",
    "rv = poisson(mu = lambda_)\n",
    "print(rv.pmf(k = 0)) #hiç kaza geçirmeme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:37.873216Z",
     "start_time": "2020-06-13T16:02:37.866269Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1637461506155964\n"
     ]
    }
   ],
   "source": [
    "print(rv.pmf(k=1)) #bir kaza geçirme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:38.275109Z",
     "start_time": "2020-06-13T16:02:38.268142Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.18126924692201818\n"
     ]
    }
   ],
   "source": [
    "print(1-rv.pmf(k=0)) #en az bir kaza geçirme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:51.175867Z",
     "start_time": "2020-06-13T16:02:50.922558Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Poisson Dağılımı')"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_poisson = poisson.rvs(mu=3, size=10000)\n",
    "sns.distplot(data_poisson,\n",
    "                  bins=30,\n",
    "                  kde=False,\n",
    "                  color='skyblue',\n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "plt.title(\"Poisson Dağılımı\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hipergeometrik Dağılım"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Örnek, kütleden yerine koymadan çekildiği takdirde artık bağımsız olay söz konusu olmadığı için binom dağılım uygulanamaz. Bu gibi durumlarda yani deneylerin bağımsız olmadığı durumlarda hipergeometrik dağılım uygulanır."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](hipergeometrik.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bir dernekte 12 si erkek 8 i bayan toplam 20 üye vardır. 5 Kişilik bir komisyon kura ile seçiliyor. Komisyonda 3 erkek bulunma olasılığını bulalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:54.406106Z",
     "start_time": "2020-06-13T16:02:54.404094Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import hypergeom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:54.681944Z",
     "start_time": "2020-06-13T16:02:54.673983Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3973168214654285"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[M, n, N] = [20, 12, 5] # 20 üye, 12 erkek, 5 kişilik komisyon\n",
    "rv = hypergeom(M, n, N)\n",
    "rv.pmf(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T10:24:21.419804Z",
     "start_time": "2020-06-13T10:24:21.413821Z"
    }
   },
   "source": [
    "###  Geometrik Dağılım"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eğer uygun hal x'inci deneyde ilk defa meydana geliyorsa x-1 sayıdaki deneyde uygun olmayan hal meydana gelmiş demektir. Buna göre geometrik dağılım fonksiyonu aşağıdaki gibidir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](geometrik.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bir basketbol oyuncusunun sayı üçlük sayı yapma olasılığı 0,7 olsun. Oyuncunun 6.atışta ilk defa üçlük sayı yapma olasığını bulalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:56.956541Z",
     "start_time": "2020-06-13T16:02:56.951554Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import geom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:57.283831Z",
     "start_time": "2020-06-13T16:02:57.276849Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0017010000000000011"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "geom.pmf(k=6,p=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SÜREKLİ OLASILIK DAĞILIMLARI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal Dağılım"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gauss dağılımı,normal eğri,çan eğrisi gibi adlarla da bilinir.\n",
    "* Dağılım aritmetik ortalama etrafında simetriktir.\n",
    "* Artimetik ortalama,mod ve medyan birbirine eşittir.\n",
    "* Sürekli rassal bir değişkenin yoğunluk fonksiyonu olduğu için eğrinin altında kalan alanın tamamı 1’e eşittir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](normal.png) \n",
    "* $\\mu$  ortalama ya da dağılımın beklenen değeri\n",
    "\n",
    "* ${\\displaystyle \\sigma }$  standart sapma\n",
    "\n",
    "* ${\\displaystyle \\sigma ^{2}}$ varyans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:58.979802Z",
     "start_time": "2020-06-13T16:02:58.975813Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aylık ortalama 70.000 TL'lik satış yaptığımızı düşünelim.Satışlarımız normal dağılıyor.Standart sapma ise 5000 olsun.80.000 TL'den fazla satış yapma olasılığını bulalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:59.526215Z",
     "start_time": "2020-06-13T16:02:59.519232Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02275013194817921"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1-norm.cdf(80, 70, 5) #kmülatif yoğunluk fonksiyonu.Kesikli dağılımdan farklı olarak bir alan tarasması yapıyoruz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:59.717929Z",
     "start_time": "2020-06-13T16:02:59.711944Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9772498680518208"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1-norm.cdf(60, 70, 5) #60'tan fazla olma olasılığı"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:02:59.917395Z",
     "start_time": "2020-06-13T16:02:59.910440Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.054799291699557974"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.cdf(62,70,5) #62'den az olma olasılığı"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:00.126837Z",
     "start_time": "2020-06-13T16:03:00.119855Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02271846070634609"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.cdf(90,70,5)-norm.cdf(80,70,5) #80 ile 90 arasında olma olasılığı"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:11.579801Z",
     "start_time": "2020-06-13T16:03:11.219790Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Normal Dağılım')"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_normal = norm.rvs(size=10000,loc=0,scale=1)\n",
    "sns.distplot(data_normal,\n",
    "                  bins=100,\n",
    "                  kde=True,\n",
    "                  color='skyblue',\n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "plt.title(\"Normal Dağılım\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uniform Dağılım"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "X sürekli değişkeninin tanım aralığındaki olasılıkları eşit ise X'in dağılımı uniform dağılım olarak kabul edilir. Olasılık yoğunluk ve olasılık dağılım fonksiyonları aşağıdaki gibidir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T11:25:32.172887Z",
     "start_time": "2020-06-13T11:25:32.149945Z"
    }
   },
   "source": [
    "![title](uniform.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:14.312873Z",
     "start_time": "2020-06-13T16:03:14.308879Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import uniform\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:20.600992Z",
     "start_time": "2020-06-13T16:03:20.283805Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0, 0.5, 'Frekans'), Text(0.5, 0, 'Uniform Dağılım ')]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_uniform = uniform.rvs(size=10000, loc = 10, scale=20)\n",
    "ax = sns.distplot(data_uniform,\n",
    "                  bins=100,\n",
    "                  kde=True,\n",
    "                  color='skyblue',\n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "ax.set(xlabel='Uniform Dağılım ', ylabel='Frekans')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gamma Dağılımı"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gama dağılımı, sürekli olasılık dağılımlarının iki parametreli bir ailesidir. Ham haliyle nadiren kullanılırken, üstel, ki-kare dağılımları gibi diğer yaygın olarak kullanılan dağılımlar gama dağılımının özel durumlarıdır. Alfa 1 olduğunda üstel(exponential) dağılım elde edilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Olasılık yoğunluk fonksiyonu ![title](gamma.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:25.468347Z",
     "start_time": "2020-06-13T16:03:25.463281Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:25.842365Z",
     "start_time": "2020-06-13T16:03:25.838377Z"
    }
   },
   "outputs": [],
   "source": [
    "data_gamma = gamma.rvs(a=5, size=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:37.998979Z",
     "start_time": "2020-06-13T16:03:37.700741Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Gamma Dağılımı')"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data_gamma,\n",
    "                  kde=True,\n",
    "                  bins=100,\n",
    "                  color='skyblue',\n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "plt.title(\"Gamma Dağılımı\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Üstel Dağılım"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Olayların sürekli ve bağımsız olarak sabit bir ortalama hızda gerçekleştiği bir süreci tanımlar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](ustel.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:41.340431Z",
     "start_time": "2020-06-13T16:03:41.337430Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import expon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:41.657282Z",
     "start_time": "2020-06-13T16:03:41.652270Z"
    }
   },
   "outputs": [],
   "source": [
    "data_expon = expon.rvs(scale=1,loc=0,size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:52.339950Z",
     "start_time": "2020-06-13T16:03:52.031775Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Üstel Dağılım')"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(data_expon,\n",
    "                  kde=True,\n",
    "                  bins=100,\n",
    "                  color='skyblue',\n",
    "                  hist_kws={\"linewidth\": 15,'alpha':1})\n",
    "plt.title(\"Üstel Dağılım\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weibull Dağılımı"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Güvenilirlik analizlerinde kullanılan bir dağılımdır. Alfa 1 olursa dağılım üstel dağılıma dönüşür.Alfa büyüdükçe dağılım normal dağılıma yaklaşır."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](weibull.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:55.547441Z",
     "start_time": "2020-06-13T16:03:55.357946Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  9.,  30.,  85., 146., 221., 230., 173.,  78.,  26.,   2.]),\n",
       " array([0.29023941, 0.41693325, 0.54362709, 0.67032094, 0.79701478,\n",
       "        0.92370862, 1.05040247, 1.17709631, 1.30379015, 1.43048399,\n",
       "        1.55717784]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s = np.random.weibull(5, 1000)\n",
    "plt.hist(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:03:56.205356Z",
     "start_time": "2020-06-13T16:03:55.954002Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "x = np.arange(1,100.)/50.\n",
    "def weib(x,n,a):\n",
    "     return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)\n",
    "count, bins, ignored = plt.hist(np.random.weibull(5.,1000))\n",
    "x = np.arange(1,100.)/50.\n",
    "scale = count.max()/weib(x, 1., 5.).max()\n",
    "plt.plot(x, weib(x, 1., 5.)*scale)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# HİPOTEZ TESTLERİ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uygulamada çoğu zaman örneklem istatistikleri yardımıyla ana kütle parametreleri hakkında bir karara varmaya çalışılmaktadır. Örneğin bir makine üzerinde yapılan bir ayarlamanın kusurlu mamul oranını düşürüp düşürmediği, yeni geliştirilen bir ilacın hastalığın tedavisinde etkin olup olmadığı, Üretim prosesinde yapılan bir değişikliğin mamul kalitesini yükseltip yükseltmediği, makine ayarında yapılan bir değişikliğin varyansı değiştirip değiştirmediği veya geliştirilen bir öğretim sisteminin eskisine göre bir farklılık gösterip göstermediği gibi konularda karar verilmesi gibi. İşletmelerde bu tür kararların verilebilmesi için istatistik karar verme tekniği olarak hipotez testlerinden faydalanılır.\n",
    "\n",
    "H0 hipotezi bir testte öne sürülen ve test edilmek istenen hipotezdir.H1 hipotezi ise alternatif hipotezdir ve H0 hipotezine karşı kurulur.Tek yönlü veya çift yönlü olabilirler.\n",
    "\n",
    "Bir hipotezin tek ya da çift yönlü olduğunu H1 hipotezi belirler. Örneğin,\n",
    "* **H0** : İkinci dönemde kız ve erkeklerin yaş ortalamaları arasında fark yoktur.\n",
    "* **H1** : İkinci dönemde kız ve erkeklerin yaş ortalamaları arasında fark vardır.\n",
    "**Bu şekilde kurulan bir hipotez çift yönlüdür çünkü bir ortalamanın diğerinden büyük ya da küçük olmasının bir önemi yoktur.\n",
    "H0 hipotezini reddederiz ya da reddetmeyiz.H0'ı kabul etmek yorumu doğru değildir.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](hipotez_.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**P Value**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\alpha$ kabul edilebilir hata miktarını ifade eder.  p<0,05 ise H0 hipotezini reddederiz.Bazı durumlarda H0'ı reddetmeyi ya da reddetmemeyi isteyebiliriz. Örneğin,dağılıma uygunluk testi yaptığımızı düşünelim. H0'ı \"Örnek dağılımla teorik dağılım arasında fark yoktur\" şeklinde kurarsak H0'ı reddetmek istemeyiz."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tek Örneklem T Testi\n",
    "\n",
    "Örnek ortalamasına ilişkin test yapmak için kullanılır.Popülasyon ortalaması ile varsayımsal değer arasında anlamlı bir fark olup olmadığını test etmek için kullanılan parametrik bir testtir. Web sitesinde geçirilen süre,bir ilçedeki yaş ortalamasıyla ilgili bir test kurmak istersek bunu kullanabiliriz.Örneğin bir kütlenin yaş ortalamasıyla ilgili aşağıdaki hipotezleri kurabiliriz.\n",
    "\n",
    "**Hipotezler:**\n",
    "\n",
    "<d><i>H</i><sub>0</sub>: <i>μ</i> = <i>40</i></d>   \n",
    "<d><i>H</i><sub>1</sub>: <i>μ</i> ≠ <i>40</i></d><br><br>\n",
    "\n",
    "<d><i>H</i><sub>0</sub>: <i>μ</i> <= <i>40</i></d><br>\n",
    "<d><i>H</i><sub>1</sub>: <i>μ</i> > <i>40</i></d><br><br>\n",
    "\n",
    "<d><i>H</i><sub>0</sub>: <i>μ</i> >= <i>40</i></d><br>\n",
    "<d><i>H</i><sub>1</sub>: <i>μ</i> < <i>40</i></d><br><br>\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "<table></table>\n",
    "\n",
    "**Test İstatistiği:**\n",
    "\n",
    "${\\displaystyle t={\\frac {{\\bar {x}}-\\mu _{0}}{\\frac {s}{\\sqrt {n}}}}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hipotez Testi Adımları**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Hipotezlerin kurulması ve yönlerinin Belirlenmesi\n",
    "* Anlamlılık düzeyi ve tablo değerinin belirlenmesi ( $\\alpha$)\n",
    "* Test istatistiğinin belirlenmesi ve hesaplanması\n",
    "* Hesaplanmış test istatistiği ile $\\alpha$'ya karşılık gelen tablo değerinin karşılaştırılması\n",
    "* Test istatistiği > Tablo değeri ise H0 değeri reddedilir. Sonuçlar yorumlanır."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Anakütle standart sapması biliniyorsa Z istatistiği kullanılır. Anakütle standart sapması bilinmiyorsa ve n>30 ise Z istatistiği kullanılır. Anakütle standart sapması bilinmiyor ve n<30 ise t istatistiği kullanılır. örnek sayısı büyüdükçe t dağılımı normal dağılıma yaklaşır.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Varsayımlar sağlanmıyorsa non-parametric testler kullanılmalı."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Örneğin bir web sitesinde geçiren sürenin gerçekten 190 saniye olup olmadığıyla alakalı şüpheler olsun.Elimizde websitesinde geçirilen ortalama süreler var.Buna göre,\n",
    "\n",
    "* **H0**: Web sitesinde geçirilen süre ortalama 190 saniyedir.\n",
    "* **H1**: Web sitesinde geçirilen süre ortalama 190 saniye değildir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Örnek olması açısından ölçüm değerleri oluşturalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:28:47.287477Z",
     "start_time": "2020-06-13T16:28:47.280495Z"
    }
   },
   "outputs": [],
   "source": [
    "olcum=np.array([15,150,240,125,117,186,100,120,111,185,154,135,146,144,212,\n",
    "                187,183,150,198,25,103,175,73,110,67,132,188,155,188,202,133,\n",
    "               134,45,99,101,156,154,234,153,201,164,153,28,280,130,177,135,\n",
    "               120,188,195,199,186])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:40:45.748449Z",
     "start_time": "2020-06-14T10:40:45.744460Z"
    }
   },
   "outputs": [],
   "source": [
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:28:47.792805Z",
     "start_time": "2020-06-13T16:28:47.785823Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DescribeResult(nobs=52, minmax=(15, 280), mean=146.94230769230768, variance=2949.231900452489, skewness=-0.3704009880734704, kurtosis=0.33125829527445294)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.describe(olcum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ortalama 194 olarak görünüyor. Bu değerin şansa bağlı oluşup oluşmadığını test edelim ama bunun için varsayımları kontrol etmek gerekir.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:36:22.314971Z",
     "start_time": "2020-06-13T16:36:22.137462Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x231dc6bbbc8>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(pd.DataFrame(olcum),color=\"r\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:30:24.675003Z",
     "start_time": "2020-06-13T16:30:24.545283Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ucblkw4aKt1eWvNXmmHzVSu5m1oiQ2Ivc/fHY5mVm1jL2ektgeWz7YqB13OG7A0uSE66IpNSyZXDOOaG9ceVK3howib2+eIXXlnTY5EJoRZ2OFY3Qy5J1ZclbbY7JVZ1uGQPGArPcfUTcS08DfWLf9wGeitvey8y2MrM9gL2BD5MXsogk3fr1cMcdoQTz0ENw1VUweza9nz6Ntd9v+sd4Wdkl0Ui8b9+KR+hK3ulVnZH7r4DewOFm9nHsqwfwV+AoM5sLHBV7jrvPACYBM4EXgH7uXsEfayISuSlTwjS8gwaFbpjp0+Gmm2CbbSosv6xenXgkfvfdKq9kCnPfrByedgUFBV5cXBx1GCL1y5IlcMUVoVexTRu4/XY46aSQlWPy8hJ3sbRtG0bfEi0zm+ruBYle0x2qIvVEWf/5lvYTQ3cazg957VhX9E9u5E+091kUrT2Zoodskx71Hj3UxZK13D3yr65du7qI1MyECe5t27qbhccLL6z4edOm7ltu6f4bXvUZdHAHn8xxvifzPNwz6t6oUdin7Dm4N2my+XknTIjwh5ZNAMVeQV5VWUYkS5Td6blwYehWWbMGfvyxesfuziJu4zJO51H+zZ4M5A6e5fhqHasSTOaqrCyjlZhEskD59UNXrarecVuyjksYyZ+4kQaU8if+wq1czjq2rvZ7awqA7KTkLpKh4kfqDRpUfINQRY7iJe5kAO0o4QlO4hJGsoC8GsehKQCyky6oimSg8rMo1iSxt2EBj3EKL3EMhtOd5zmFJ6pM7I0awZZbbrpNF0+zl5K7SAZKNItiVbbiBwYzhFl04Bhe5GqGsR+f8SLdgZC8mzbd2H9+4YWb9qPfdx+MG6ce9VyhsoxIBqpOnbtRI9h++3BDUZ9mz3LzuoG0+PbfTOI0Rra6jc4ntqblc+FcbdpsvEu0KkrmuUHJXSRDVKfG3rBhuH3/f8n6l5/DwIHwzDPQvj089jKnH3kkp6c/fMkwKsuIZIDq1NibNAlzpZeWwvxZ31NYch107AhvvAG33gqffAJHHpn22CUzKbmLRKjsrtGzz05cY2/YsFz9+yyHJ58MSf0vf4FTToHZs+GPf9z8aqjUayrLiESkfO96IqWl4QuAkhLoMRBeeAH23Rdefx0OOywdoUoW0shdJCLV6Yhp0wb47ruwzN1++4VFNG6/HaZNU2KXSmnkLhKRqjpimjR2Hjzxn9D+Uli8GH73O7j5Zth11/QEKFlNI3eRiFR25+cRLWcyb8+jOPjO06FZM3j77XA1VYldqknJXSQiiRaFbtF4DTN6XM4rK35Oy/9MhVGjoLg4LHsnUgNK7iIR2WRRaJwBzR7ii63a0fG54aEEU1IC/fpVvDCpSCVUcxeJUGEhFO7/GQwYAG++CV27wl1PwAEHRB2aZDmN3EXSqKyvvUED2K/NN8zuPgg6d4bPPoO//x0++ECJXZJCI3eRNCnra/9+bSlnM4FbFl1Bi0XLKTniAvIfGRJm9RJJEo3cRdJk8GDYe+3HvMXBPEAf5pNHNz7k6Hmjldgl6ZTcRdLhq6+4fEF/ptKVfEo4l7EcxLtMpUArHUlKKLmLpFJpKYwdC/n5/IHRjOZC8inhPs7FY//9tNKRpIKSu0iqTJ0KBx0E558P+fm8OKSYK5uM4mt2+t8uWulIUkXJXSTZVq1i7uEXUFrwC778YD4XbTue5rPf4vg/daZx401XQ9JKR5IqSu4itRTf1tisGbRouoEL7R6+ar43e7w+ljsYSDvmMPq/v2Pl6ga4w6pV8P338OCDMH++ErukjpK7SCXiE3heHlx0UXg0g969Ny6u8bNV7/Pc6gMYzYV84vvTiY+5lJF8yw6bnXPt2tA5I5JK6nMXqUD5+dYXLIDRoze+7g7NWMFfuYrzGMd/2I1ePMwjnAFYpedWh4ykWpUjdzMbZ2bLzWx63Lbrzew/ZvZx7KtH3GtXm9k8M5tjZsekKnCRZCpfYmnWrOLVkQAasp5+jKKEfH7HA9zC5bRnNo/Qi6oSO6hDRlKvOiP3+4FRwAPlto909+HxG8ysI9AL2AfYDXjFzPLdPcGKkCKZofwIfdWqyvc/iHe4i3504hNe5kgGcCdzaF/t91OHjKRDlSN3d58CrK7m+XoCE919nbt/AcwDutUhPpGUq86KSAC78CX3cQ7v8Gt2ZjWn8ihH81LCxN6o0caumKZN1SEj6VeXC6r9zezTWNmmrHG3FbAobp/FsW2bMbO+ZlZsZsUrVqyoQxgiNRdfhlmwoPJ9t+AnBjGSEvI5k4cZyjV0YBaPcSpmoQRTPoHfdx+sXBnuYVq5cuP36pCRdKltch8N7AV0ApYCt8W2Jyo2eqITuPsYdy9w94LmzZvXMgyRmisrw5R1ulTmUN7gIzozkkuZuvWvGXbmdO5tO5TvbRvatg0tje5K4JJ5atUt4+7Lyr43s3uBZ2JPFwOt43bdHVhS6+hEkqioKJRgqhqpA7RkCbdxGWcykfmWx5uDnuQ3t53Ib8y4IdWBiiRBrUbuZtYy7unJQFknzdNALzPbysz2APYGPqxbiCJ1Fz9ar8yW/MifmwynhHaczBPcvsN1vD92JoeO6BlqLiJZosqRu5k9DBwGNDOzxcB1wGFm1olQcpkPXADg7jPMbBIwE1gP9FOnjGSC6lw0PavFKxTtPABmz4YTT4SRIxm0557pCVAkyapM7u5+ZoLNYyvZfyigRi/JKJXdNNSahdzR8FJOXv4YbLcXPPMMHHdc+oITSQFNPyD1QqKbhrZkHVczjNnWgRMaPgc33gjTpyuxS05Qcpd6YejQcPNQme48zwzbl2EMpsnJ3dmiZBZcey1svXV0QYokkZK75JSKJvrq3RsaN4bOO37BE5zE8/SgxS4N4MUX4bHHQnO6SA7RxGGS9eJbHM029q7HT/S1Nd/Tb9UtXMVf2WKrhnDDX9n+kktgyy2jC1wkhTRyl6xUNkKPn3oXEt+UdDyTmcE+3MD1PEVPDm42G668UoldcpqSu2SF8rM2nntu5QkdYC/mMZnjmcyJfE9jDudVzmQiHy7ZPW1xi0RFyV0yUkXJvGw1ox9/rPjYxqzlL/yJGezDobzJZQynEx/zOocDmm5X6gfV3CXj1HQK3o2ck3mCkVxCWxYygUIu51a+ZOMN1ZpuV+oLjdwl41R3Ct54+czhBbrzOL/lG3bgEN7k2rYTOPnClrRtq+l2pf7RyF0yTk2WoNuG/3ItQ7iUEXxPY67f6Q7yb7+IKb/TP22p3zRyl4xRVmevahpegEZbOOduO4lZdOAqbmbRwYXs8GUJ16++mLOU2EU0cpfMUL7OXl6jRrD99rB6NRy+60wm7DSAXWe+Bp07w6hH2Ougg9IbsEiG08hdMkJldfb/rWz0+beUXnIZr6z4Obsu/Qjuvhv+9S9QYhfZjEbukhEqqrObwfwvPAzt210Oy5bB+efDsGGhR1JEEtLIXdKmonlfGjQIX4kcveuncOih4TbU3XeH998PLS9K7CKV0shd0qJ8TT1+3heADeWWdNmBrxm2xXX8Ydld8OOOIaGfd17FvwVEZBP6nyIpEz9S79Oner3rWzQo5RzuZ26Ddly44U4aXNAXSkrg//5PiV2kBjRyl5QoP1IvPzJPpDPTGFXan4N4Dw74JYx6Hrp0SW2gIjlKQyFJiZrcZboTq7mbCymmgPwG80JrzNtvK7GL1IGSu6REde4yNUo5n3spIZ++jOGeLfrz2ugSOOcclWBE6kj/gyQpynfC7Lxz4v0aNgztjSfs+i8+b3Eg99KXmXTkuJYfscP9f+P0vjumM2yRnKWau9RK2epHCxeGRL5mzcZpeBcsCHeUbrnlplPzNmkC429byanTroF//AN22QUefJBDCgs5xCyaH0QkRym5S41VZ0ren36Cpk1h223DL4C81huYePgYul0zGL79Fi65BK67LswpICJJp+QuNVbdi6WrV8PKlcB770G/fnD/R3DYYTBqFOyzT6rDFKnXVHOXGqvulLxdWi0LF0cPOgiWL4eJE+G115TYRdJAyV1qrKpl6hqynssa/Y13V7eDhx6CK66A2bPhjDPC1VQRSTkld6lS+U6YHj3CxdF4jRqFGvshTOGzRl0Y/tNAtvxVN/j0U7j55lB8F5G0UXKXSpVdPC1bnHrBAhg/PkwnEL983cMjlrKy+9m8yaF0aPkNPPYYvPgitG8f9Y8gUi9VmdzNbJyZLTez6XHbdjazl81sbuxxp7jXrjazeWY2x8yOSVXgkhrlR+kDB25+8XTtWnjuOZg/H0rX/cT8i0fw22vawaOPhquts2bBKaeoBCMSoeqM3O8HupfbdhXwqrvvDbwae46ZdQR6AfvEjrnbzBomLVqplfIJu6go8faLLtp8lJ6ozRFiF1Vffx06dYLLLoODD4YZM2DIkM1rNiKSdlW2Qrr7FDPLK7e5J3BY7PvxwBvAlbHtE919HfCFmc0DugHvJSdcqalEU+327QvvvBPKK/Hb77mneuuXtmIxoxv/EQ5/BPbYA55+Go4/XiN1kQxS25r7Lu6+FCD22CK2vRWwKG6/xbFtEpFEPelr14bp0ctvryqxN+JHruBmZtOeY396Cq6/PozWTzhBiV0kwyT7JqZE/8MTpgwz6wv0BWhTVW+d1FpFPenVmYK3TNOm0L3hy1y7fADtmcOirj1p/ejIMGoXkYxU25H7MjNrCRB7XB7bvhhoHbff7sCSRCdw9zHuXuDuBc2bN69lGFKVin5vNqzgSkj5AXi7rRcwbc/fMmH50bT/2QZ47jlaFz+pxC6S4Wqb3J8G+sS+7wM8Fbe9l5ltZWZ7AHsDH9YtRKmLoUM3v77ZpEmouyfa/oc/hNbGrfmBW3cYwvTSDrSZ/nw40fTpcOyx6QteRGrP3Sv9Ah4GlgI/EUbm5wFNCV0yc2OPO8ftPxj4NzAHOLaq87s7Xbt2dUmdCRPc27Z1NwuPEyZUvt2ffdZ9r73cwf3UU90XLIgkbhGpHFDsFeRV8+q0R6RYQUGBFxcXRx2GfP45DBoEkydDu3Zw551w1FFRRyUiFTCzqe5ekOg13aEq8P33Yfrdjh3DxF633BKmDVBiF8lamvK3PnMPPeqDBoXbTc88E269FVqpe1Uk22nkXl/NnRtmADvpJNhmm3C36UMPKbGL5Agl9/rmu+/CnU377gvvvgsjR8JHsUU0RCRnqCxTX7iHmRovvRQWLYLevUNtfdddo45MRFJAI/f6YPZsOPpoOO20sJr1W2/BAw8osYvkMCX3XLZmTVgFab/94F//Cq2NxcXw619HHZmIpJjKMrnIHR55JEzFu2QJnHsu3HQTtGhR9bEikhM0cs8106fD4YeHtsZdd4X33oOxY5XYReoZJfdc8e234WJpp07hBqR77oEPP4QDD4w6MhGJgMoy2c4dJkyAyy+H5cvh//4Phg0L8/SKSL2l5J7NPvkE+veHt9+Gbt3gmWegIOE0EyJSz6gsk42+/hoGDIAuXUKb4z/+QVH/98g7tWCzdVJFpH5Scs8mpaUwbhzk58Pdd8OFF0JJCUVbn0ffPzTYZGHrvn2V4EXqMyX3bDF1Khx0EJx3XkjuU6fCqFGw004VrpM6eHA0oYpI9JTcM92qVWF5pF/8IszcOH58uMO0U6f/7VLROqkVbReR3Kfknqk2bIC//z2M0v/xDxg4kEk3ziHvz7+jQUPbpK5e0TqpWndcpP5Scs9EH3wABxwQRuz77gsffURRwUh+P2iHhHX1itZJHTo0mvBFJHpqhcwkK1bAVVeFi6YtW4b51Xv1AjMGn1BxXX3+/PB88OBQimnTJiT2wsK0/wQikiG0hmomWL8+lGCuvRb++9+wMtKf/wzbbfe/XRo0CCP28sxCE42I1D9aQzWTvfNOuPGof3/o2jXcmHTrrZskdlBdXURqRsk9Kl9+CX36hOl3V62CSZPg5ZfDItUJqK4uIjWh5J5u69fD7bdDu3bw8MNw9dXhLtPTTgs1lgoUFsKYMdC2bditbdvwXHV1EUlEF1TT6c03Q/ll+nQ45hj4299Cq2M1FRYqmYtI9Wjkng5LlsBZZ4VFqNesgSeegOefr1FiFxGpCSX3VPrxRxg+PJRgHn88dMDMnAknnVRpCUZEpK5UlkmVV18NJZjZsyQv8PEAAAbaSURBVOH440Odfa+9oo5KROoJjdyTbdEiOP10OPLIMHJ/5hmYPFmJXUTSSsk9WdatC4tQt28fkvlf/gIzZsBxx0UdmYjUQ3Uqy5jZfGANsAFY7+4FZrYz8AiQB8wHTnf3r+oWZoZ74QW4+GKYOxdOPhlGjAgrZoiIRCQZI/ffuHunuFtgrwJedfe9gVdjz3PT/PkhmR97bLhA+sIL4cKpEruIRCwVZZmewPjY9+OBk1LwHtH64YdQdunQAV56KZRjPv009K6LiGSAunbLOPCSmTnwd3cfA+zi7ksB3H2pmbVIdKCZ9QX6ArTJpglSJk8OE3t9/nm4cDp8OLRuHXVUIiKbqOvI/Vfu3gU4FuhnZodU90B3H+PuBe5e0Lx58zqGkQb//ndoaTzxRNhqK3jlFXjkkaQl9qKiUM3RAtcikgx1Su7uviT2uBx4AugGLDOzlgCxx+V1DTJSa9eGm4/22SdMHzB8eJi58YgjkvYWRUVh4Q0tcC0iyVLr5G5m25jZdmXfA0cD04GngT6x3foAT9U1yEi4h2kCOnaEG2+E3/4W5syByy6DRo2S+lZa4FpEkq0uNfddgCcs3Ea/BfCQu79gZv8CJpnZecBC4LS6h5lmJSUwYEC4WLrffmHEfki1K041pgWuRSTZap3c3f1z4OcJtq8CklezSKfvvoMhQ+C226BxY7jjDrjoItgitbM0tGkTSjGJtouI1IbuUIVQgpk0Kdxd+te/hhkcS0rCjUkpTuyghThEJPmU3GfOhKOOgjPOgGbNwrJ3998Pu+ySthC0EIeIJFv9nRVyzRq44YZQetl2W7jrLrjgAmjYMJJwtBCHiCRT/Uvu7mF5uz/+Maxjet55MGwYZEOvvYhINdWv5P7ZZ2GO9SlToKAAnnwSunWLOioRkaSrHzX3b74JUwZ07hym4R0zBt5/X4ldRHJWbo/cS0vhwQfhiitgxYpQUx8yBJo2jToyEZGUyt2R+0cfwcEHwznnwJ57QnExjB6d1sSu+WJEJCq5l9y/+gr69Qs19blzYdy40N7YpUtaw9B8MSISpdxJ7qWlMHYs5OfDPfeEBF9SAr//fRg611JtR9+aL0ZEopQbNffi4pDMP/wQfv1rGDUKfr7ZzAg1Vjb6LkvSZaNvqLonXfPFiEiUsnvkvnJlyLbduoWs+eCDoc0xCYkd6jb6rmheGM0XIyLpkN3JfeFCGD8eLrkkTMd79tnh/v0knr4m2+NpvhgRiVJ2l2W6dAmZNkXzwNRltsayss3gwSHENm1CYtcUAyKSDtk9coeUTvBV19F3YSHMnx+u9c6fr8QuIumT/ck9hTRbo4hkq+wuy6SBZmsUkWyU1SN33QEqIpJY1o7c69KDLiKS67J25K47QEVEKpa1yV13gIqIVCxrk7vuABURqVjWJnfdASoiUrGsTe7qQRcRqVjWdsuAetBFRCqStSN3ERGpmJK7iEgOUnIXEclBSu4iIjlIyV1EJAeZu0cdA2a2AkiwLEZaNANWRvTemUifx+b0mWxKn8fmovpM2rp780QvZERyj5KZFbt7QdRxZAp9HpvTZ7IpfR6by8TPRGUZEZEcpOQuIpKDlNxhTNQBZBh9HpvTZ7IpfR6by7jPpN7X3EVEcpFG7iIiOUjJXUQkB9X75G5mt5rZbDP71MyeMLMdo44pamZ2mpnNMLNSM8uo9q50MrPuZjbHzOaZ2VVRxxM1MxtnZsvNbHrUsWQCM2ttZq+b2azY/5eBUccUr94nd+BlYF933x8oAa6OOJ5MMB04BZgSdSBRMbOGwF3AsUBH4Ewz6xhtVJG7H+gedRAZZD1wmbt3AA4E+mXSv5F6n9zd/SV3Xx97+j6we5TxZAJ3n+Xuc6KOI2LdgHnu/rm7/whMBHpGHFOk3H0KsDrqODKFuy9192mx79cAs4BW0Ua1Ub1P7uWcCzwfdRCSEVoBi+KeLyaD/uNKZjGzPKAz8EG0kWyU1SsxVZeZvQLsmuClwe7+VGyfwYQ/s4rSGVtUqvOZ1HOWYJv6hmUzZrYt8BgwyN2/jTqeMvUiubv7kZW9bmZ9gOOBI7yeNP5X9ZkIi4HWcc93B5ZEFItkKDNrREjsRe7+eNTxxKv3ZRkz6w5cCZzo7mujjkcyxr+Avc1sDzPbEugFPB1xTJJBzMyAscAsdx8RdTzl1fvkDowCtgNeNrOPzeyeqAOKmpmdbGaLgV8Cz5rZi1HHlG6xi+z9gRcJF8omufuMaKOKlpk9DLwHtDOzxWZ2XtQxRexXQG/g8Fju+NjMekQdVBlNPyAikoM0chcRyUFK7iIiOUjJXUQkBym5i4jkICV3EZEcpOQuIpKDlNxFRHLQ/wMtW4vhtgw3eQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pylab\n",
    "stats.probplot(olcum, dist=\"norm\", plot=pylab) #qqplot grafiği sol taraf örnek,alt taraf teorik dağılımı ifade eder\n",
    "pylab.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normallik varsayımını test etmek için Shapiro-Wilks testi yapalım.\n",
    "* H0 :Örnek dağılımı ile teorik normal dağılım arasında istatistiksel olarak anlamlı bir farklılık yoktur.\n",
    "* H1 :Örnek dağılımı ile teorik normal dağılım arasında istatistiksel olarak anlamlı bir farklılık vardır."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:33:04.443997Z",
     "start_time": "2020-06-13T16:33:04.439991Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import shapiro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:33:35.173082Z",
     "start_time": "2020-06-13T16:33:35.169116Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.971328854560852, 0.24038264155387878)"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(olcum) #(test istatistiği, p-value değeri)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p-value 0.24 olduğu için H0'ı reddedemiyoruz.Örnek dağılımı ile teorik normal dağılım arasında istatistiksel olarak anlamlı bir farklılık yoktur. Öyleyse tek örneklem t testini uygulayabiliriz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:41:03.473092Z",
     "start_time": "2020-06-13T16:41:03.467079Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-5.717391877618423, pvalue=5.665357482090354e-07)"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(olcum, popmean = 190)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:43:55.112737Z",
     "start_time": "2020-06-13T16:43:55.107751Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P value değeri : 0.000000567\n"
     ]
    }
   ],
   "source": [
    "print(\"P value değeri : \"f\"{5.665357482090354e-07:.9f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "P value<0,05 olduğundan dolayı H0 hipotezini reddederiz. Web sitede geçirilen ortalama süre 190 değildir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non Parametrik Tek Örneklem T Testi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:55:26.510968Z",
     "start_time": "2020-06-13T16:55:26.507017Z"
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.descriptivestats import sign_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T16:55:37.292570Z",
     "start_time": "2020-06-13T16:55:37.278620Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-17.0, 2.0377698612961117e-06)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sign_test(olcum,190)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bu teste göre p value<0,5 olduğu için H0 reddedilir fakat örnek olması açısından aynı veriyi kullandık,verimizin parametrik testini zaten yapmıştık.O yüzden bu test sonucu dikkate alınmamalıdır. Non parametrik sign test dışında başka birçok test de aynı ihtiyacı karşılayabilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tek Örneklem Oran Testi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oransal bir ifade test edilmek istenirse kullanılabilir. n>30 büyükse bu test kullanılabilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](oransal.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Örneğin bir e-ticaret sitesinde sepete atılan ürünler ve bu sepete atılan ürünlerden kaç tanesinin satın alındığını incelemiş olalım.100 kişi bir ürünü sepete atmış ama 20 tanesi satın almışsa bu durumda dönüşüm oranı 20/100=0,2 olacaktır.Daha önce dönüşüm oranı olarak 0,110 elde edilmiş ve kontrol edilmek isteniyor olsun.\n",
    "\n",
    "H0:  p=0.110\n",
    "\n",
    "H1: p!=0.100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T17:23:03.623810Z",
     "start_time": "2020-06-13T17:23:03.619797Z"
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.proportion import proportions_ztest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-13T17:23:04.326947Z",
     "start_time": "2020-06-13T17:23:04.319964Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.25, 0.02444894531008939)"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proportions_ztest(20, 100, 0.110)  #(başarı sayısı,gözlem sayısı,test edilmek istenen değer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test istatistiği değeri 2.25, p-value ise 0.02 olarak bulundu. Bu durumda H0 hipotezi reddedilir. Dönüşüm oranı 0.110^dan farklıdır.İstatistiksel olarak %95 güvenle bunu ifade etmiş olduk."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bağımsız İki Örneklem T Testi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "İki grubun ortalaması arasında karşılaştırma yapılmak istenirse kullanılabilir. A/B Testi olarak da bilinir. Elimizde  iki farklı ana kütleye ait ortalamalar olduğunu düşünelim. Bu ortalamaların birbirinden farkını elde ettiğimiz örneklemlerle inceleriz. Gerçekte bilmediğimiz ana kütlenin değerlerine ilişkin bir farkın istatistiksel olarak olup olmadığını incelenir.\n",
    "\n",
    "* Örnek sayıları aynı,varyanslar homojen\n",
    "\n",
    "* Örnek sayısı farklı,varyanslar homojen\n",
    "\n",
    "* Örnek sayıları farklı, varyanslar homojen değil\n",
    "\n",
    "Bu üç durumda da farklı formüller kullanılır.Son iki durumda örnek sayıları eşitse de hesaplamalar yapılabilir.\n",
    "\n",
    "**Varsayımlar**\n",
    "\n",
    "* Normallik\n",
    "* Varyans Homojenliği"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:38:19.415009Z",
     "start_time": "2020-06-14T10:38:19.405038Z"
    }
   },
   "outputs": [],
   "source": [
    "A = pd.DataFrame([20,37,24,21,25,30,20,20,29,33,36,23,28,24,25,27,24,27,24,\n",
    "        26,20,16,26,24,30,26,24,20,18,25])\n",
    "\n",
    "B = pd.DataFrame([33,39,37,34,21,26,23,32,29,28,39,18,35,39,32,36,36,34,22,\n",
    "        32,35,31,31,33,33,31,24,33,31,28])\n",
    "\n",
    "\n",
    "A_B = pd.concat([A, B], axis = 1)\n",
    "A_B.columns=[\"A\",\"B\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:38:19.714118Z",
     "start_time": "2020-06-14T10:38:19.706138Z"
    }
   },
   "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>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>37</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>24</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>21</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>25</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    A   B\n",
       "0  20  33\n",
       "1  37  39\n",
       "2  24  37\n",
       "3  21  34\n",
       "4  25  21"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_B.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:38:19.987585Z",
     "start_time": "2020-06-14T10:38:19.976616Z"
    }
   },
   "outputs": [],
   "source": [
    "GRUP_A = np.arange(len(A))\n",
    "GRUP_A = pd.DataFrame(GRUP_A)\n",
    "GRUP_A[:] = \"A\"\n",
    "A = pd.concat([A, GRUP_A], axis = 1)\n",
    "\n",
    "\n",
    "GRUP_B = np.arange(len(B))\n",
    "GRUP_B = pd.DataFrame(GRUP_B)\n",
    "GRUP_B[:] = \"B\"\n",
    "B = pd.concat([B, GRUP_B], axis = 1)\n",
    "\n",
    "\n",
    "AB = pd.concat([A,B])\n",
    "AB.columns = [\"gelir\",\"GRUP\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:38:20.598334Z",
     "start_time": "2020-06-14T10:38:20.590358Z"
    }
   },
   "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>gelir</th>\n",
       "      <th>GRUP</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>30</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>23</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>29</td>\n",
       "      <td>28</td>\n",
       "      <td>B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>20</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>24</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    gelir GRUP\n",
       "5      30    A\n",
       "6      23    B\n",
       "29     28    B\n",
       "6      20    A\n",
       "16     24    A"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AB.sample(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:38:21.134276Z",
     "start_time": "2020-06-14T10:38:20.952728Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x19d6d86be08>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.catplot(x=\"GRUP\",y=\"gelir\",data=AB,kind=\"box\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:47:26.683881Z",
     "start_time": "2020-06-14T10:47:26.678894Z"
    }
   },
   "source": [
    "**H0** : Eski yeni gelirler arasında istatistiksel olarak anlamlı bir fark yoktur.\n",
    "\n",
    "**H1** : Eski yeni gelirler arasında istatistiksel olarak anlamlı bir fark vardır."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:38:26.376276Z",
     "start_time": "2020-06-14T10:38:26.371315Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.951647162437439, 0.18710334599018097)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import shapiro\n",
    "shapiro(A_B.A) # A normallik #H0 reddedilmez"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:38:23.640559Z",
     "start_time": "2020-06-14T10:38:23.635572Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9384799003601074, 0.08278060704469681)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(A_B.B) #B normallik #H0 reddedilmez"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**H0** : Varyanslar homojen.\n",
    "\n",
    "**H1** : Varyanslar homojen değildir."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:40:50.841272Z",
     "start_time": "2020-06-14T10:40:50.826270Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=0.23150684931506824, pvalue=0.6322190341001741)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.levene(A_B.A, A_B.B) #varyans homojenliği için test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "P>0.05 olduğu için H0 reddedilemez ve varyanslar homojendir."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:43:54.973622Z",
     "start_time": "2020-06-14T10:43:54.966641Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-4.567083365467413, pvalue=2.6286107085806983e-05)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(A_B[\"A\"], A_B[\"B\"], equal_var = True) #Bağımsız iki örneklem t testi, equal_var : varsayım testi sağlandı True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p<0,05 olduğu için \"anakütle ortalamaları birbirine eşittir\" diyen H0 hipotezi reddedilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non Parametrik Bağımsız İki Örneklem T Testi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aynı örnekle nonparametrik t testi işlemi gerçekleştirelim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T10:50:13.357117Z",
     "start_time": "2020-06-14T10:50:13.350161Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=184.0, pvalue=4.191188725973341e-05)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(A_B[\"A\"], A_B[\"B\"]) #p<0.05 H0 reddedilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bağımlı İki Örneklem T Testi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bağımlı iki grup ortalaması arasında karşılaştırma yapılmak istenirse kullanılabilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Örneğin bir şirkette eğitim gerçekleştiriliyor ve bu eğitimden önceki ve sonraki durum arasındaki fark test edilmek isteniyor.\n",
    "\n",
    "**Varsayımlar**\n",
    "\n",
    "Normallik (Normale yakın da olsa kabul görebilir.)\n",
    "\n",
    "Varyans Homojenliği\n",
    "\n",
    "**H0**: Eğitimden önceki performans ortalaması ile eğitimden sonraki perdormans ortalaması arasında bir fark yoktur.\n",
    "\n",
    "**H1** : Eğitimden önceki performans ortalaması ile eğitimden sonraki perdormans ortalaması arasında bir fark vardır."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:01:41.674511Z",
     "start_time": "2020-06-14T11:01:41.665517Z"
    }
   },
   "outputs": [],
   "source": [
    "oncesi = pd.DataFrame([123,119,119,116,123,123,121,120,117,118,121,121,123,119,\n",
    "            121,118,124,121,125,115,115,119,118,121,117,117,120,120,\n",
    "            121,117,118,117,123,118,124,121,115,118,125,115])\n",
    "\n",
    "sonrasi = pd.DataFrame([118,127,122,132,129,123,129,132,128,130,128,138,140,130,\n",
    "             134,134,124,140,134,129,129,138,134,124,122,126,133,127,\n",
    "             130,130,130,132,117,130,125,129,133,120,127,123])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:01:41.843828Z",
     "start_time": "2020-06-14T11:01:41.835870Z"
    }
   },
   "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>119</td>\n",
       "    </tr>\n",
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     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
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    "oncesi.head()"
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   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:01:42.031591Z",
     "start_time": "2020-06-14T11:01:42.024611Z"
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   "outputs": [
    {
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     "end_time": "2020-06-14T11:01:42.278197Z",
     "start_time": "2020-06-14T11:01:42.265219Z"
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   "outputs": [],
   "source": [
    "AYRIK = pd.concat([oncesi, sonrasi], axis = 1)\n",
    "AYRIK.columns = [\"ONCESI\",\"SONRASI\"]\n",
    "\n",
    "GRUP_ONCESI = np.arange(len(oncesi))\n",
    "GRUP_ONCESI = pd.DataFrame(GRUP_ONCESI)\n",
    "GRUP_ONCESI[:] = \"ONCESI\"\n",
    "\n",
    "A = pd.concat([oncesi, GRUP_ONCESI], axis = 1)\n",
    "\n",
    "\n",
    "GRUP_SONRASI = np.arange(len(sonrasi))\n",
    "GRUP_SONRASI = pd.DataFrame(GRUP_SONRASI)\n",
    "GRUP_SONRASI[:] = \"SONRASI\"\n",
    "\n",
    "\n",
    "B = pd.concat([sonrasi, GRUP_SONRASI], axis = 1)\n",
    "\n",
    "\n",
    "BIRLIKTE = pd.concat([A,B])\n",
    "BIRLIKTE\n",
    "\n",
    "\n",
    "BIRLIKTE.columns = [\"PERFORMANS\",\"ONCESI_SONRASI\"]"
   ]
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     "start_time": "2020-06-14T11:01:58.423362Z"
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       "   ONCESI  SONRASI\n",
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       "4     123      129"
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     "end_time": "2020-06-14T11:02:11.812699Z",
     "start_time": "2020-06-14T11:02:11.803733Z"
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     "start_time": "2020-06-14T11:02:49.903320Z"
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    {
     "data": {
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       "   PERFORMANS ONCESI_SONRASI\n",
       "0         123         ONCESI\n",
       "1         119         ONCESI\n",
       "2         119         ONCESI\n",
       "3         116         ONCESI\n",
       "4         123         ONCESI"
      ]
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     "execution_count": 58,
     "metadata": {},
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     "start_time": "2020-06-14T11:04:12.729750Z"
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   "outputs": [
    {
     "data": {
      "text/plain": [
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     "execution_count": 60,
     "metadata": {},
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     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.catplot(x=\"ONCESI_SONRASI\",y=\"PERFORMANS\",data=BIRLIKTE,kind=\"box\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:08:06.280769Z",
     "start_time": "2020-06-14T11:08:06.275770Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9543656706809998, 0.10722451657056808)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(AYRIK.ONCESI) #p>0.05 H0 reddedilmez #normallik testi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:08:06.629377Z",
     "start_time": "2020-06-14T11:08:06.623404Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9780089259147644, 0.6159515380859375)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(AYRIK.SONRASI) #p>0.05 H0 reddedilmez"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:08:07.170719Z",
     "start_time": "2020-06-14T11:08:07.162742Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=8.31303288672351, pvalue=0.0050844511807370246)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.levene(AYRIK.ONCESI, AYRIK.SONRASI) #varyans homojenliğini test ettik p<0.05 H0 reddedilir. 2. Varsayım Sağlanmadı."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Varyans homojenliği varsayımı sağlanmadı. Bu durumda aykırı gözlemlerle ilgili düzenlemeye gidilebilir ya da bazı durumlarda dikkate alınmayabilir. Örnek olması açısından varsayımın sağlandığını kabul edip hipotez testini gerçekleştirelim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:13:42.662468Z",
     "start_time": "2020-06-14T11:13:42.656498Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=-9.281533480429937, pvalue=2.0235251764440722e-11)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_rel(AYRIK.ONCESI, AYRIK.SONRASI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p<0,05 olduğu için H0 hipotezi reddedilir. Eğitimden önceki performans ortalaması ile eğitimden sonraki perdormans ortalaması arasında istatistiki olarak % 95 güven aralığında anlamlı bir fark vardır."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonparametrik Bağımlı İki Örneklem T Testi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:18:52.666005Z",
     "start_time": "2020-06-14T11:18:52.660008Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WilcoxonResult(statistic=15.0, pvalue=2.491492033374464e-07)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.wilcoxon(AYRIK.ONCESI, AYRIK.SONRASI) #p<0,05 H0 hipotezi reddedilir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## İki Örneklem Oran Testi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "İki oran arasında karşılaştırma yapmak için kullanılır. n1>30 ve n2>30 olmalı."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:29:22.075465Z",
     "start_time": "2020-06-14T11:29:22.070504Z"
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.stats.proportion import proportions_ztest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "İki web tasarımı olduğunu varsayalım. Yeşil rengin mi yoksa kırmızı rengin mi kullanılması gerektiğine karar verelim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yeşil butonu 1000 kişi görüntülemiş ve 300 tıklama gerçekleşmiş.Kırmızı butonu ise 1100 kişi görüntülemiş ve 250 tıklama gerçekleşmiş.\n",
    "\n",
    "**H0** : p1=p2\n",
    "\n",
    "**H1** : p1!=p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:33:15.407018Z",
     "start_time": "2020-06-14T11:33:15.403037Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "basari_sayisi = np.array([300, 250])\n",
    "gozlem_sayilari = np.array([1000, 1100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T11:34:14.561018Z",
     "start_time": "2020-06-14T11:34:14.555031Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.7857863233209255, 0.0001532232957772221)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proportions_ztest(count = basari_sayisi, nobs = gozlem_sayilari)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p<0.05 olduğu için iki dönüşüm oranı arasında anlamlı bir fark vardır. Yeşil buton tercih edilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Varyans Analizi (ANOVA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Grup ortalamaları ve bunlara bağlı olan işlemleri analiz etmek için kullanılan bir istatistiksel modeller koleksiyonudur. Gruplar arası ortalama hata ya da değişkenliğinin, grup içi ortalama hataya bölünmesiyle F istatistiği olarak ifade edilen değer bulunur.İkiden fazla grup olduğunda kullanılabilir.\n",
    "\n",
    "**Varsayımlar**\n",
    "\n",
    "* Grupların birbirinden bağımsız olması\n",
    "* Normal dağılım\n",
    "* Varyans homojenliği\n",
    "\n",
    "H0 : Grup ortalamaları arasında istatistiksel olarak anlamlı bir fark yoktur.\n",
    "\n",
    "H1 : Grup ortalamaları arasında istatistiksel olarak anlamlı bir fark vardır.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3 farklı kargo şirketine ait elimizde teslim süreleri olduğunu düşünelim. Ortalama sipariş süresi düşük olanın daha hızlı teslim yaptığını söylemek doğru olmaz. Böyle bir genellemenin yapılması doğru değildir. Şimdi örneğimizi yapalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:25:59.072645Z",
     "start_time": "2020-06-14T12:25:59.063643Z"
    }
   },
   "outputs": [],
   "source": [
    "ABC=pd.DataFrame({\"A\":[22,19,18,21,19,30,16,13,24,26,22,20,30,17,24,25,14,16,21,20,29,26,27,13,25,25,32,22,33,38],\n",
    "                  \"B\":[17,21,19,15,19,25,22,33,28,28,24,26,29,13,17,15,13,14,30,25,24,13,38,32,10,12,15,19,30,31],\n",
    "                  \"C\":[18,20,16,14,24,24,28,26,24,23,29,30,16,13,39,32,32,12,18,15,23,32,34,21,20,20,14,14,16,17]})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:27:10.857338Z",
     "start_time": "2020-06-14T12:27:10.851320Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9773266315460205, 0.7509013414382935)"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import shapiro\n",
    "shapiro(ABC.A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:27:19.664178Z",
     "start_time": "2020-06-14T12:27:19.659186Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9559324383735657, 0.2429838329553604)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(ABC.B) #normallik varsayımı"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:27:27.878835Z",
     "start_time": "2020-06-14T12:27:27.871869Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9428073167800903, 0.10826785117387772)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(ABC.C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:28:41.478700Z",
     "start_time": "2020-06-14T12:28:41.471718Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=1.3094952823124166, pvalue=0.27522343223527845)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.levene(ABC.A, ABC.B, ABC.C) #Varyans homojenliği varsayımı # p>0.05 H0 reddedemeyiz. Varyanslar homojendir."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:31:00.790692Z",
     "start_time": "2020-06-14T12:31:00.783714Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=0.16908620390387075, pvalue=0.844712935488465)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import f_oneway\n",
    "f_oneway(ABC.A,ABC.B,ABC.C) # p>0.05 H0 reddedilmez. Grup ortalamaları arasında anlamlı bir fark yoktur."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:34:06.410505Z",
     "start_time": "2020-06-14T12:34:06.402567Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.84471\n"
     ]
    }
   ],
   "source": [
    "print('{:.5f}'.format(f_oneway(ABC.A, ABC.B, ABC.C)[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eğer ortalamalar arasında fark olduğuna kanaat getirmiş olsaydık Tukey testi ile  farkın kaynağını bulmaya çalışabilirdik."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:34:25.225657Z",
     "start_time": "2020-06-14T12:34:25.191749Z"
    }
   },
   "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>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>A</td>\n",
       "      <td>30.0</td>\n",
       "      <td>22.900000</td>\n",
       "      <td>6.127102</td>\n",
       "      <td>13.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>26.0</td>\n",
       "      <td>38.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>B</td>\n",
       "      <td>30.0</td>\n",
       "      <td>21.900000</td>\n",
       "      <td>7.484927</td>\n",
       "      <td>10.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>21.5</td>\n",
       "      <td>28.0</td>\n",
       "      <td>38.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>C</td>\n",
       "      <td>30.0</td>\n",
       "      <td>22.133333</td>\n",
       "      <td>7.219386</td>\n",
       "      <td>12.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>20.5</td>\n",
       "      <td>27.5</td>\n",
       "      <td>39.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   count       mean       std   min   25%   50%   75%   max\n",
       "A   30.0  22.900000  6.127102  13.0  19.0  22.0  26.0  38.0\n",
       "B   30.0  21.900000  7.484927  10.0  15.0  21.5  28.0  38.0\n",
       "C   30.0  22.133333  7.219386  12.0  16.0  20.5  27.5  39.0"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ABC.describe().T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonparametrik Varyans Analizi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:38:25.758531Z",
     "start_time": "2020-06-14T12:38:25.755512Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats import kruskal #kruskal-wallis testi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normallik ve varyans homojenliği varsayımlarının sağlanmadığını varsayalım"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:39:20.301629Z",
     "start_time": "2020-06-14T12:39:20.294659Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KruskalResult(statistic=0.5629391248858203, pvalue=0.7546738857551857)"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kruskal(ABC.A,ABC.B,ABC.C) # p>0.05 H0 hipotezi kabul edilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Korelasyon Analizi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Değişkenler arasındaki ilişki,ilişkinin yönü ve şiddeti ile ilgili bilgiler sağlayan bir yöntemdir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](kore.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1- mükemmel pozitif korelasyon\n",
    "\n",
    "0.9 - yüksek pozitif korelasyon\n",
    "\n",
    "0.5 - düşük pozitif korelasyon\n",
    "\n",
    "-0.5 - düşük negatif korelasyon\n",
    "\n",
    "-0.9 - yüksek negatif korelasyon\n",
    "\n",
    "-1 - mükemmel negatif korelasyon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:51:24.586087Z",
     "start_time": "2020-06-14T12:51:24.550184Z"
    }
   },
   "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>total_bill</th>\n",
       "      <th>tip</th>\n",
       "      <th>sex</th>\n",
       "      <th>smoker</th>\n",
       "      <th>day</th>\n",
       "      <th>time</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>16.99</td>\n",
       "      <td>1.01</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>10.34</td>\n",
       "      <td>1.66</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>21.01</td>\n",
       "      <td>3.50</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>23.68</td>\n",
       "      <td>3.31</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>24.59</td>\n",
       "      <td>3.61</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   total_bill   tip     sex smoker  day    time  size\n",
       "0       16.99  1.01  Female     No  Sun  Dinner     2\n",
       "1       10.34  1.66    Male     No  Sun  Dinner     3\n",
       "2       21.01  3.50    Male     No  Sun  Dinner     3\n",
       "3       23.68  3.31    Male     No  Sun  Dinner     2\n",
       "4       24.59  3.61  Female     No  Sun  Dinner     4"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tips = sns.load_dataset('tips')\n",
    "df = tips.copy()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bahşiş ile ödenen hesap arasında korelasyon olup olmadığını inceleyelim.\n",
    "\n",
    "**H0** : P=0 Değişkenler arasında korelasyon yoktur.\n",
    "\n",
    "**H1** : P!=0 Değişkenler arasında anlamlı bir ilişki vardır."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T12:58:28.740700Z",
     "start_time": "2020-06-14T12:58:28.703799Z"
    }
   },
   "outputs": [],
   "source": [
    "df[\"total_bill\"] = df[\"total_bill\"] - df[\"tip\"] #bahşiş ve vergiler dahildi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:00:13.241317Z",
     "start_time": "2020-06-14T13:00:13.022886Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x19d72675788>"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.relplot(x=\"tip\",y=\"total_bill\",data=df,kind=\"scatter\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:01:37.093645Z",
     "start_time": "2020-06-14T13:01:37.088713Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.897811233997345, 8.20057563521992e-12)"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(df[\"tip\"]) #p<0.05 #normallik varsayımı sağlanmadı"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:01:22.691629Z",
     "start_time": "2020-06-14T13:01:22.685632Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9135652184486389, 1.1060377613780759e-10)"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(df[\"total_bill\"]) #p<0.05 #normallik varsayımı sağlanmadı"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:54:44.217738Z",
     "start_time": "2020-06-14T13:54:44.211757Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5766634471096374"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"tip\"].corr(df[\"total_bill\"]) #normallik varsayımı sağlandığında pearson katsayısı kullanılabilir."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:56:38.754495Z",
     "start_time": "2020-06-14T13:56:38.745473Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.593691939408997"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"tip\"].corr(df[\"total_bill\"],method=\"spearman\") #orta şiddetli pozitif yönlü ilişki"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:03:03.713643Z",
     "start_time": "2020-06-14T13:03:03.709683Z"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.stats.stats import pearsonr #korelasyonun anlamlılığına bakalım."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:03:17.439475Z",
     "start_time": "2020-06-14T13:03:17.429515Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.5766634471096381, 5.018290084948419e-23)"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pearsonr(df[\"tip\"],df[\"total_bill\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p<0.05 Değişkenler arasında anlamlı bir ilişki vardır(pearson'a göre).H0 reddedilir."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonparametrik Korelasyon Analizi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:58:30.675146Z",
     "start_time": "2020-06-14T13:58:30.667153Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=0.593691939408997, pvalue=1.2452285137560276e-24)"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import stats\n",
    "stats.spearmanr(df[\"tip\"],df[\"total_bill\"])  #spearman r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-14T13:58:28.722885Z",
     "start_time": "2020-06-14T13:58:28.706916Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KendalltauResult(correlation=0.4400790074919885, pvalue=7.131027725873721e-24)"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.kendalltau(df[\"tip\"],df[\"total_bill\"]) #kendall tau testi"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
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