Hypothesis testing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[nan 30. 55. 12. 47. 11. 78. 11. 17. 20. 32. 29. 22. 14. 58. 27. 30. 31.\n",
      " 25. 47.]\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import ttest_1samp\n",
    "import numpy as np\n",
    "\n",
    "ages = np.genfromtxt(\"f:/machine learning/ages.csv\")\n",
    "print(ages)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nan\n"
     ]
    }
   ],
   "source": [
    "ages_mean = np.mean(ages)\n",
    "print(ages_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n",
      "p-value nan\n",
      "we are accepting null hypothesis\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import ttest_1samp\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "df = pd.read_csv('F:/machine learning/ages.csv')\n",
    "df.mean()\n",
    "print(ages_mean)\n",
    "tset, pval = ttest_1samp(ages, 30)\n",
    "print(\"p-value\",pval)\n",
    "if pval < 0.05:    # alpha value is 0.05 or 5%\n",
    "   print(\" we are rejecting null hypothesis\")\n",
    "else:\n",
    "  print(\"we are accepting null hypothesis\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import ttest_1samp\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "df = pd.read_csv('F:/machine learning/ages.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average age:  10.00    31.368421\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(\"Average age: \", df.mean(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standard deviation:  10.00    18.151249\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(\"Standard deviation: \", df.std(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t=-2.262, df=198, cv=1.653, p=0.025\n",
      "Reject the null hypothesis that the means are equal.\n",
      "Reject the null hypothesis that the means are equal.\n"
     ]
    }
   ],
   "source": [
    "# t-test for independent samples\n",
    "from math import sqrt\n",
    "from numpy.random import seed\n",
    "from numpy.random import randn\n",
    "from numpy import mean\n",
    "from scipy.stats import sem\n",
    "from scipy.stats import t\n",
    "import pandas as pd\n",
    "df = pd.read_csv('F:/machine learning/ages.csv')\n",
    "\n",
    "# function for calculating the t-test for two independent samples\n",
    "def independent_ttest(data1, data2, alpha):\n",
    "\t# calculate means\n",
    "\tmean1, mean2 = mean(data1), mean(data2)\n",
    "\t# calculate standard errors\n",
    "\tse1, se2 = sem(data1), sem(data2)\n",
    "\t# standard error on the difference between the samples\n",
    "\tsed = sqrt(se1**2.0 + se2**2.0)\n",
    "\t# calculate the t statistic\n",
    "\tt_stat = (mean1 - mean2) / sed\n",
    "\t# degrees of freedom\n",
    "\tdf = len(data1) + len(data2) - 2\n",
    "\t# calculate the critical value\n",
    "\tcv = t.ppf(1.0 - alpha, df)\n",
    "\t# calculate the p-value\n",
    "\tp = (1.0 - t.cdf(abs(t_stat), df)) * 2.0\n",
    "\t# return everything\n",
    "\treturn t_stat, df, cv, p\n",
    "\n",
    "# seed the random number generator\n",
    "seed(1)\n",
    "# generate two independent samples\n",
    "data1 = 5 * randn(100) + 50\n",
    "data2 = 5 * randn(100) + 51\n",
    "# calculate the t test\n",
    "alpha = 0.05\n",
    "t_stat, df, cv, p = independent_ttest(data1, data2, alpha)\n",
    "print('t=%.3f, df=%d, cv=%.3f, p=%.3f' % (t_stat, df, cv, p))\n",
    "# interpret via critical value\n",
    "if abs(t_stat) <= cv:\n",
    "\tprint('Accept null hypothesis that the means are equal.')\n",
    "else:\n",
    "\tprint('Reject the null hypothesis that the means are equal.')\n",
    "# interpret via p-value\n",
    "if p > alpha:\n",
    "\tprint('Accept null hypothesis that the means are equal.')\n",
    "else:\n",
    "\tprint('Reject the null hypothesis that the means are equal.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "One-sample Z test for data3 | p-value value = : 0.5966020076763254\n",
      "accept null hypothesis\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from scipy import stats\n",
    "from statsmodels.stats import weightstats as stests\n",
    "import pandas as pd\n",
    "df = pd.read_csv('F:/machine learning/ages.csv')\n",
    "ztest ,pval = stests.ztest(df['data3'], x2=None, value=30)\n",
    "print(\"One-sample Z test for data3 | p-value value = :\",float(pval))\n",
    "if pval<0.05:\n",
    "    print(\"reject null hypothesis\")\n",
    "else:\n",
    "    print(\"accept null hypothesis\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Two-sample Z test for data3 and data4 |p-value = : 0.7817871889601071\n",
      "accept null hypothesis\n"
     ]
    }
   ],
   "source": [
    "ztest ,pval1 = stests.ztest(df['data3'], x2=df['data4'], value=0,alternative='two-sided')\n",
    "print(\"Two-sample Z test for data3 and data4 |p-value = :\", float(pval1))\n",
    "if pval<0.05:\n",
    "    print(\"reject null hypothesis\")\n",
    "else:\n",
    "    print(\"accept null hypothesis\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overall model F( 3, 16) =  4.112, p =  0.0243\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(Fert)</th>\n",
       "      <td>69.192</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.766000</td>\n",
       "      <td>0.028847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(Water)</th>\n",
       "      <td>63.368</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.280667</td>\n",
       "      <td>0.035386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C(Fert):C(Water)</th>\n",
       "      <td>15.488</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.290667</td>\n",
       "      <td>0.272656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>192.000</td>\n",
       "      <td>16.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   sum_sq    df         F    PR(>F)\n",
       "C(Fert)            69.192   1.0  5.766000  0.028847\n",
       "C(Water)           63.368   1.0  5.280667  0.035386\n",
       "C(Fert):C(Water)   15.488   1.0  1.290667  0.272656\n",
       "Residual          192.000  16.0       NaN       NaN"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "df_anova2 = pd.read_csv(\"https://raw.githubusercontent.com/Opensourcefordatascience/Data-sets/master/crop_yield.csv\")\n",
    "model = ols('Yield ~ C(Fert)*C(Water)', df_anova2).fit()\n",
    "print(f\"Overall model F({model.df_model: .0f},{model.df_resid: .0f}) = {model.fvalue: .3f}, p = {model.f_pvalue: .4f}\")\n",
    "res = sm.stats.anova_lm(model, typ= 2)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "contingency_table :-\n",
      " data6  0.0  1.0\n",
      "data5          \n",
      "0.0      3    3\n",
      "1.0      5    4\n",
      "Observed Values :-\n",
      " [[3 3]\n",
      " [5 4]]\n",
      "Expected Values :-\n",
      " [[3.2 2.8]\n",
      " [4.8 4.2]]\n",
      "Degree of Freedom:- 1\n",
      "chi-square statistic:- 0.04464285714285722\n",
      "critical_value: 3.841458820694124\n",
      "p-value: 0.8326621063505324\n",
      "Significance level:  0.05\n",
      "Degree of Freedom:  1\n",
      "chi-square statistic: 0.04464285714285722\n",
      "critical_value: 3.841458820694124\n",
      "p-value: 0.8326621063505324\n",
      "Retain H0,There is no relationship between 2 categorical variables\n",
      "Retain H0,There is no relationship between 2 categorical variables\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('F:/machine learning/ages.csv')\n",
    "contingency_table=pd.crosstab(df[\"data5\"],df[\"data6\"])\n",
    "print('contingency_table :-\\n',contingency_table)\n",
    "#Observed Values\n",
    "Observed_Values = contingency_table.values \n",
    "print(\"Observed Values :-\\n\",Observed_Values)\n",
    "b=stats.chi2_contingency(contingency_table)\n",
    "Expected_Values = b[3]\n",
    "print(\"Expected Values :-\\n\",Expected_Values)\n",
    "no_of_rows=len(contingency_table.iloc[0:2,0])\n",
    "no_of_columns=len(contingency_table.iloc[0,0:2])\n",
    "ddof=(no_of_rows-1)*(no_of_columns-1)\n",
    "print(\"Degree of Freedom:-\",ddof)\n",
    "alpha = 0.05\n",
    "from scipy.stats import chi2\n",
    "chi_square=sum([(o-e)**2./e for o,e in zip(Observed_Values,Expected_Values)])\n",
    "chi_square_statistic=chi_square[0]+chi_square[1]\n",
    "print(\"chi-square statistic:-\",chi_square_statistic)\n",
    "critical_value=chi2.ppf(q=1-alpha,df=ddof)\n",
    "print('critical_value:',critical_value)\n",
    "#p-value\n",
    "p_value=1-chi2.cdf(x=chi_square_statistic,df=ddof)\n",
    "print('p-value:',p_value)\n",
    "print('Significance level: ',alpha)\n",
    "print('Degree of Freedom: ',ddof)\n",
    "print('chi-square statistic:',chi_square_statistic)\n",
    "print('critical_value:',critical_value)\n",
    "print('p-value:',p_value)\n",
    "if chi_square_statistic>=critical_value:\n",
    "    print(\"Reject H0,There is a relationship between 2 categorical variables\")\n",
    "else:\n",
    "    print(\"Retain H0,There is no relationship between 2 categorical variables\")\n",
    "    \n",
    "if p_value<=alpha:\n",
    "    print(\"Reject H0,There is a relationship between 2 categorical variables\")\n",
    "else:\n",
    "    print(\"Retain H0,There is no relationship between 2 categorical variables\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "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>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                5.1               3.5                1.4               0.2\n",
       "1                4.9               3.0                1.4               0.2\n",
       "2                4.7               3.2                1.3               0.2\n",
       "3                4.6               3.1                1.5               0.2\n",
       "4                5.0               3.6                1.4               0.2"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "import pandas as pd\n",
    "from pandas import Series,DataFrame\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "# Load the iris datasets\n",
    "iris = datasets.load_iris()\n",
    "iris_df=DataFrame(iris.data)\n",
    "iris_df.columns=iris.feature_names\n",
    "iris_df.head()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get names of each feature for later\n",
    "names = iris_df.get('target_names')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sepal length (cm)    5.843333\n",
      "sepal width (cm)     3.057333\n",
      "petal length (cm)    3.758000\n",
      "petal width (cm)     1.199333\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# What is the overall mean?\n",
    "print(iris_df.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "import researchpy as rp\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "    \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Loading data\n",
    "df = pd.read_csv(\"https://raw.githubusercontent.com/Opensourcefordatascience/Data-sets/master/difficile.csv\")\n",
    "df.drop('person', axis= 1, inplace= True)\n",
    "\n",
    "# Recoding value from numeric to string\n",
    "df['dose'].replace({1: 'placebo', 2: 'low', 3: 'high'}, inplace= True)\n",
    "    \n",
    "# Gettin summary statistics\n",
    "rp.summary_cont(df['libido'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n"
     ]
    },
    {
     "data": {
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       "<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",
       "      <th>0</th>\n",
       "      <td>libido</td>\n",
       "      <td>15.0</td>\n",
       "      <td>3.466667</td>\n",
       "      <td>1.76743</td>\n",
       "      <td>0.456349</td>\n",
       "      <td>2.487896</td>\n",
       "      <td>4.445437</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Variable     N      Mean       SD        SE  95% Conf.  Interval\n",
       "0   libido  15.0  3.466667  1.76743  0.456349   2.487896  4.445437"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "import researchpy as rp\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "    \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Loading data\n",
    "df = pd.read_csv(\"https://raw.githubusercontent.com/Opensourcefordatascience/Data-sets/master/difficile.csv\")\n",
    "df.drop('person', axis= 1, inplace= True)\n",
    "\n",
    "# Recoding value from numeric to string\n",
    "df['dose'].replace({1: 'placebo', 2: 'low', 3: 'high'}, inplace= True)\n",
    "    \n",
    "# Gettin summary statistics\n",
    "rp.summary_cont(df['libido'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n"
     ]
    },
    {
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       "<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>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",
       "    <tr>\n",
       "      <th>dose</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>high</th>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.581139</td>\n",
       "      <td>0.707107</td>\n",
       "      <td>3.450484</td>\n",
       "      <td>6.549516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>low</th>\n",
       "      <td>5</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.303840</td>\n",
       "      <td>0.583095</td>\n",
       "      <td>1.922236</td>\n",
       "      <td>4.477764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>placebo</th>\n",
       "      <td>5</td>\n",
       "      <td>2.2</td>\n",
       "      <td>1.303840</td>\n",
       "      <td>0.583095</td>\n",
       "      <td>0.922236</td>\n",
       "      <td>3.477764</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         N  Mean        SD        SE  95% Conf.  Interval\n",
       "dose                                                     \n",
       "high     5   5.0  1.581139  0.707107   3.450484  6.549516\n",
       "low      5   3.2  1.303840  0.583095   1.922236  4.477764\n",
       "placebo  5   2.2  1.303840  0.583095   0.922236  3.477764"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rp.summary_cont(df['libido'].groupby(df['dose']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=5.11864406779661, pvalue=0.024694289538222603)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.f_oneway(df['libido'][df['dose'] == 'high'], \n",
    "             df['libido'][df['dose'] == 'low'],\n",
    "             df['libido'][df['dose'] == 'placebo'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Owner\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1416: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=15\n",
      "  \"anyway, n=%i\" % int(n))\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>libido</td>      <th>  R-squared:         </th> <td>   0.460</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.370</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   5.119</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 27 Jul 2019</td> <th>  Prob (F-statistic):</th>  <td>0.0247</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:12:21</td>     <th>  Log-Likelihood:    </th> <td> -24.683</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    15</td>      <th>  AIC:               </th> <td>   55.37</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    12</td>      <th>  BIC:               </th> <td>   57.49</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "           <td></td>             <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>          <td>    5.0000</td> <td>    0.627</td> <td>    7.972</td> <td> 0.000</td> <td>    3.634</td> <td>    6.366</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(dose)[T.low]</th>     <td>   -1.8000</td> <td>    0.887</td> <td>   -2.029</td> <td> 0.065</td> <td>   -3.732</td> <td>    0.132</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(dose)[T.placebo]</th> <td>   -2.8000</td> <td>    0.887</td> <td>   -3.157</td> <td> 0.008</td> <td>   -4.732</td> <td>   -0.868</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.517</td> <th>  Durbin-Watson:     </th> <td>   2.408</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.284</td> <th>  Jarque-Bera (JB):  </th> <td>   1.108</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.195</td> <th>  Prob(JB):          </th> <td>   0.575</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 1.727</td> <th>  Cond. No.          </th> <td>    3.73</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                 libido   R-squared:                       0.460\n",
       "Model:                            OLS   Adj. R-squared:                  0.370\n",
       "Method:                 Least Squares   F-statistic:                     5.119\n",
       "Date:                Sat, 27 Jul 2019   Prob (F-statistic):             0.0247\n",
       "Time:                        23:12:21   Log-Likelihood:                -24.683\n",
       "No. Observations:                  15   AIC:                             55.37\n",
       "Df Residuals:                      12   BIC:                             57.49\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "======================================================================================\n",
       "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
       "--------------------------------------------------------------------------------------\n",
       "Intercept              5.0000      0.627      7.972      0.000       3.634       6.366\n",
       "C(dose)[T.low]        -1.8000      0.887     -2.029      0.065      -3.732       0.132\n",
       "C(dose)[T.placebo]    -2.8000      0.887     -3.157      0.008      -4.732      -0.868\n",
       "==============================================================================\n",
       "Omnibus:                        2.517   Durbin-Watson:                   2.408\n",
       "Prob(Omnibus):                  0.284   Jarque-Bera (JB):                1.108\n",
       "Skew:                           0.195   Prob(JB):                        0.575\n",
       "Kurtosis:                       1.727   Cond. No.                         3.73\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = ols('libido ~ C(dose)', data=df).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(dose)</th>\n",
       "      <td>20.133333</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.118644</td>\n",
       "      <td>0.024694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>23.600000</td>\n",
       "      <td>12.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             sum_sq    df         F    PR(>F)\n",
       "C(dose)   20.133333   2.0  5.118644  0.024694\n",
       "Residual  23.600000  12.0       NaN       NaN"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aov_table = sm.stats.anova_lm(results, typ=2)\n",
    "aov_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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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>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "      <th>eta_sq</th>\n",
       "      <th>omega_sq</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>C(dose)</th>\n",
       "      <td>20.133333</td>\n",
       "      <td>2.0</td>\n",
       "      <td>10.066667</td>\n",
       "      <td>5.118644</td>\n",
       "      <td>0.024694</td>\n",
       "      <td>0.460366</td>\n",
       "      <td>0.354486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>23.600000</td>\n",
       "      <td>12.0</td>\n",
       "      <td>1.966667</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             sum_sq    df    mean_sq         F    PR(>F)    eta_sq  omega_sq\n",
       "C(dose)   20.133333   2.0  10.066667  5.118644  0.024694  0.460366  0.354486\n",
       "Residual  23.600000  12.0   1.966667       NaN       NaN       NaN       NaN"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def anova_table(aov):\n",
    "    aov['mean_sq'] = aov[:]['sum_sq']/aov[:]['df']\n",
    "    \n",
    "    aov['eta_sq'] = aov[:-1]['sum_sq']/sum(aov['sum_sq'])\n",
    "    \n",
    "    aov['omega_sq'] = (aov[:-1]['sum_sq']-(aov[:-1]['df']*aov['mean_sq'][-1]))/(sum(aov['sum_sq'])+aov['mean_sq'][-1])\n",
    "    \n",
    "    cols = ['sum_sq', 'df', 'mean_sq', 'F', 'PR(>F)', 'eta_sq', 'omega_sq']\n",
    "    aov = aov[cols]\n",
    "    return aov\n",
    "\n",
    "anova_table(aov_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'jb': 1.1080275776425257,\n",
       " 'jbpv': 0.574638696944554,\n",
       " 'skew': 0.19458085550134038,\n",
       " 'kurtosis': 1.726659006032749,\n",
       " 'omni': 2.517358660775963,\n",
       " 'omnipv': 0.2840288872319991,\n",
       " 'condno': 3.7320508075688767,\n",
       " 'mineigval': 1.3397459621556138}"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.diagn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=0.11764705882352934, pvalue=0.8900225182757423)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.levene(df['libido'][df['dose'] == 'placebo'],\n",
    "             df['libido'][df['dose'] == 'low'],\n",
    "             df['libido'][df['dose'] == 'high'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.916691780090332, 0.1714704930782318)"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.shapiro(results.resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multiple Comparison of Means - Tukey HSD,FWER=0.05\n",
      "==============================================\n",
      "group1  group2 meandiff  lower   upper  reject\n",
      "----------------------------------------------\n",
      " high    low     -1.8   -4.1651  0.5651 False \n",
      " high  placebo   -2.8   -5.1651 -0.4349  True \n",
      " low   placebo   -1.0   -3.3651  1.3651 False \n",
      "----------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.multicomp import pairwise_tukeyhsd\n",
    "from statsmodels.stats.multicomp import MultiComparison\n",
    "\n",
    "mc = MultiComparison(df['libido'], df['dose'])\n",
    "mc_results = mc.tukeyhsd()\n",
    "print(mc_results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=1.963961012123931, pvalue=0.08513507177899203)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(df['libido'][df['dose'] == 'high'], df['libido'][df['dose'] == 'low'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=1.2126781251816647, pvalue=0.2598450452137845)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(df['libido'][df['dose'] == 'low'], df['libido'][df['dose'] == 'placebo'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=3.0550504633038926, pvalue=0.015700141250047695)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(df['libido'][df['dose'] == 'high'], df['libido'][df['dose'] == 'placebo'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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