DS_Lecture2_solutions.ipynb

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   "source": [
    "# Sampling Distributions"
   ]
  },
  {
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Overview**\n",
    "\n",
    "1. Taking Samples\n",
    "    * Variation of samples \n",
    "    * The $1/\\sqrt{n}$ law\n",
    "2. Distributions\n",
    "    * densities\n",
    "    * ecdfs\n",
    "3. Parametric (\"analytic\") versus nonparametric (\"hacker statistics\")\n",
    "    * Confidence Intervals\n",
    "    * Testing\n",
    "4. Resampling\n",
    "    * Permutations\n",
    "    * Bootstrap"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "**Importing libraries**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from numpy import random \n",
    "random.seed(42) #What is this for ???"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------\n",
    "\n",
    "**Importing the Birthweights Dataframe**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sex</th>\n",
       "      <th>dbirwt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>male</td>\n",
       "      <td>2551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>male</td>\n",
       "      <td>2778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>female</td>\n",
       "      <td>2976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>female</td>\n",
       "      <td>3345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>female</td>\n",
       "      <td>3175</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "      sex  dbirwt\n",
       "0    male    2551\n",
       "1    male    2778\n",
       "2  female    2976\n",
       "3  female    3345\n",
       "4  female    3175"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"https://raw.githubusercontent.com/markusloecher/DataScience-HWR/main/data/BirthWeights.csv\")\n",
    "#df = pd.read_csv('../data/BirthWeights.csv')[[\"sex\", \"dbirwt\"]]\n",
    "df = df[[\"sex\", \"dbirwt\"]]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dbirwt</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sex</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>female</th>\n",
       "      <td>3419.186742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>male</th>\n",
       "      <td>3507.089865</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "             dbirwt\n",
       "sex                \n",
       "female  3419.186742\n",
       "male    3507.089865"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df.groupby(\"sex\").mean()\n"
   ]
  },
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   "source": [
    "---------\n",
    "\n",
    "## Operator Overloading\n",
    "\n",
    "The [] operator is overloaded. This means, that depending on the inputs, pandas will do something completely different. Here are the rules for the different objects you pass to just the indexing operator.\n",
    "\n",
    "* string — return a column as a Series\n",
    "* list of strings — return all those columns as a DataFrame\n",
    "* a slice — select rows (can do both label and integer location — confusing!)\n",
    "* a sequence of booleans — select all rows where True\n",
    "\n",
    "In summary, primarily just the indexing operator selects columns, but if you pass it a sequence of booleans it will select all rows that are `True`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sex</th>\n",
       "      <th>dbirwt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>male</td>\n",
       "      <td>2551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>male</td>\n",
       "      <td>2778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>female</td>\n",
       "      <td>2976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>female</td>\n",
       "      <td>3345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>female</td>\n",
       "      <td>3175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4995</th>\n",
       "      <td>male</td>\n",
       "      <td>4405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4996</th>\n",
       "      <td>male</td>\n",
       "      <td>2764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4997</th>\n",
       "      <td>female</td>\n",
       "      <td>2776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4998</th>\n",
       "      <td>female</td>\n",
       "      <td>3615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4999</th>\n",
       "      <td>male</td>\n",
       "      <td>3379</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4909 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         sex  dbirwt\n",
       "0       male    2551\n",
       "1       male    2778\n",
       "2     female    2976\n",
       "3     female    3345\n",
       "4     female    3175\n",
       "...      ...     ...\n",
       "4995    male    4405\n",
       "4996    male    2764\n",
       "4997  female    2776\n",
       "4998  female    3615\n",
       "4999    male    3379\n",
       "\n",
       "[4909 rows x 2 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "df = df[(df[ \"dbirwt\"] < 6000) & (df[ \"dbirwt\"] > 2000)] # 2000 < birthweight < 6000\n",
    "df#.head()"
   ]
  },
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   "metadata": {},
   "source": [
    "---------\n",
    "\n",
    "**Boxplot of weight vs. sex**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dbirwt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>4909.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3480.557344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>529.280103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2012.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3146.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>3486.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3827.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>5981.000000</td>\n",
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      "text/plain": [
       "            dbirwt\n",
       "count  4909.000000\n",
       "mean   3480.557344\n",
       "std     529.280103\n",
       "min    2012.000000\n",
       "25%    3146.000000\n",
       "50%    3486.000000\n",
       "75%    3827.000000\n",
       "max    5981.000000"
      ]
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   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp=df.boxplot( \"dbirwt\",\"sex\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------\n",
    "\n",
    "**We notice a small difference in the average weight, which is more clearly visible when we plot overlaying densities for male/female**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        dbirwt\n",
      "sex           \n",
      "female  3427.0\n",
      "male    3533.0 \n",
      "\n",
      "mean:  dbirwt    3480.0\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "bwghtBySex = np.round(df[[\"dbirwt\",\"sex\"]].groupby(\"sex\")[[\"dbirwt\"]].mean())\n",
    "\n",
    "print(bwghtBySex, '\\n')\n",
    "print('mean: ',bwghtBySex.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp=df[[\"dbirwt\",\"sex\"]].groupby(\"sex\")[\"dbirwt\"].plot(kind='density', legend=True)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----------\n",
    "\n",
    "## A/B Testing\n",
    "\n",
    "Let us hypothesize that one wanted to classify babies into male/female solely based on their weight. What would its accuracy be if we applied the following simple rule:\n",
    "\n",
    "if dbirwt > 3480 y = male else y = female\n",
    "\n",
    "This would be the equivalent of testing for global warming by measuring the temperature on **one** day. We all know that it took a long time (= many samples) to reliably detect a small difference like 0.5 degrees buried in the noise. Let us apply the same idea here. Maybe we can build a high-accuracy classifier if we weighed enough babies separately for each sex."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------\n",
    "\n",
    "**Confusion Matrix for simple classifier**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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>sex</th>\n",
       "      <th>female</th>\n",
       "      <th>male</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>predMale</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>1331</td>\n",
       "      <td>1105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>1100</td>\n",
       "      <td>1373</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "sex       female  male\n",
       "predMale              \n",
       "False       1331  1105\n",
       "True        1100  1373"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"predMale\"] = (df[\"dbirwt\"] > 3480)\n",
    "ConfMat = pd.crosstab(df[\"predMale\"], df[\"sex\"])\n",
    "ConfMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of lame classifier: 0.551\n"
     ]
    }
   ],
   "source": [
    "N = np.sum(ConfMat.values)\n",
    "acc1 = np.round( (ConfMat.values[0,0]+ConfMat.values[1,1]) / N, 3)\n",
    "\n",
    "#Acc0 = (1331+1373)/5000\n",
    "print(\"Accuracy of lame classifier:\", acc1)\n",
    "#Think about the baseline accuracy"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------\n",
    "\n",
    "## Distributions"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mean Density Comparison Function\n",
    "\n",
    "**Write a function which:**\n",
    "\n",
    "1. draws repeated (e.g. M=500) random samples of size n (e.g. 40, 640) from each sex from the data\n",
    "2. Computes the stdevs for the sample means of each sex separately\n",
    "3. Repeats the above density plot for the sample mean distributions\n",
    "4. computes the confusion matrix/accuracy of a classifier that applies the rule $\\bar{x} > 3480$.\n",
    "\n",
    "`Hint:\n",
    "np.random.choice(df[\"dbirwt\"],2)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "def mean_density_comparison(df_cleaned, M=500, n=10):\n",
    "    \n",
    "    #Generate a sex iteration array\n",
    "    sex_iter = ['male', 'female']\n",
    "    \n",
    "    #Create an empty DataFrame with 'sex' and 'dbirwt' column\n",
    "    columns = ['sex', 'dbirwt']\n",
    "    df_new = pd.DataFrame(columns=columns)\n",
    "    \n",
    "    #Create an empty array to store the standard deviation of the differnt sex 'male' = std_dev[0], 'female' = std_dev[1]\n",
    "    std_dev = np.empty(2)\n",
    "    \n",
    "    #Iterate over sex and create a specific data subset\n",
    "    for ind,v in enumerate(sex_iter):\n",
    "        subset = df_cleaned[df_cleaned.sex == v]\n",
    "        \n",
    "        #create M random sample means of n samples and add it to df_new\n",
    "        for i in range(M):\n",
    "            rand_samples = np.random.choice(subset.dbirwt, n)\n",
    "            x = np.mean(rand_samples)#sample mean per sex\n",
    "            df_new.loc[len(df_new)+1] = [v, x]\n",
    "        \n",
    "        #plot male and female data and calculate the standard deviation of the data\n",
    "        plot_data = df_new[df_new.sex == v]\n",
    "        std_dev[ind] = np.std(plot_data['dbirwt'])  \n",
    "        \n",
    "        plot_data.dbirwt.plot.density()\n",
    "        plt.xlabel('dbirwt')\n",
    "        plt.legend(sex_iter)\n",
    "\t\t#plt.grid()\n",
    "\t\t#plt.title(\"n=\" + str(n))\n",
    "\t\t\n",
    "    #return the sample mean data\n",
    "    return df_new\n",
    " \n",
    "        "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------\n",
    "\n",
    "**Testing the Function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "SM10 = mean_density_comparison(df, M=500, n=10)\n",
    "SM640 = mean_density_comparison(df, M=500, n=640)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>sex</th>\n",
       "      <th>female</th>\n",
       "      <th>male</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>predMale</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>320</td>\n",
       "      <td>182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>180</td>\n",
       "      <td>318</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "sex       female  male\n",
       "predMale              \n",
       "False        320   182\n",
       "True         180   318"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SM10[\"predMale\"] = (SM10[\"dbirwt\"] > 3480)\n",
    "ConfMat10 = pd.crosstab(SM10[\"predMale\"], SM10[\"sex\"])\n",
    "ConfMat10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>sex</th>\n",
       "      <th>female</th>\n",
       "      <th>male</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>predMale</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>498</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>2</td>\n",
       "      <td>500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "sex       female  male\n",
       "predMale              \n",
       "False        498     0\n",
       "True           2   500"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SM640[\"predMale\"] = (SM640[\"dbirwt\"] > 3480)\n",
    "ConfMat640 = pd.crosstab(SM640[\"predMale\"], SM640[\"sex\"])\n",
    "ConfMat640"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=640, means: sex\n",
      "female    3427.276397\n",
      "male      3533.081803\n",
      "Name: dbirwt, dtype: float64\n",
      "\n",
      "n=640, SESMs: sex\n",
      "female    20.937106\n",
      "male      19.819436\n",
      "Name: dbirwt, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "grouped640 = SM640[\"dbirwt\"].groupby(SM640[\"sex\"])\n",
    "\n",
    "print(\"n=640, means:\", grouped640.mean())\n",
    "print()\n",
    "print(\"n=640, SESMs:\", grouped640.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "SM40 = mean_density_comparison(df, M=500, n=40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=40, means: sex\n",
      "female    3423.30740\n",
      "male      3527.34015\n",
      "Name: dbirwt, dtype: float64\n",
      "\n",
      "n=40, SESMs: sex\n",
      "female    82.787145\n",
      "male      84.921927\n",
      "Name: dbirwt, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "grouped40 = SM40[\"dbirwt\"].groupby(SM40[\"sex\"])\n",
    "\n",
    "print(\"n=40, means:\", grouped40.mean())\n",
    "print()\n",
    "print(\"n=40, SESMs:\", grouped40.std())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How much smaller is $\\sigma_{\\bar{x},640}$ than $\\sigma_{\\bar{x},40}$ ?\n",
    "Compare that factor to the ratio of the sample sizes $640/40 = 16$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------\n",
    "\n",
    "### Empirical Cumulative Distribution Function"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The density -like a histogram- has a few complications that include the arbitrary choice of bin width (kernel width for density) and the loss of information. Welcome to the *empirical cumulative distribution function* **ecdf**"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**ECDF Function**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ecdf(data):\n",
    "    \"\"\"Compute ECDF for a one-dimensional array of measurements.\"\"\"\n",
    "\n",
    "    # Number of data points: n\n",
    "    n = len(data)\n",
    "\n",
    "    # x-data for the ECDF: x\n",
    "    x = np.sort(data)\n",
    "\n",
    "    # y-data for the ECDF: y\n",
    "    y = np.arange(1, n+1) / n\n",
    "\n",
    "    return x, y"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "**ECDF Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute ECDF for sample size 40: m_40, f_40\n",
    "male40 = SM40[SM40.sex == \"male\"][\"dbirwt\"]\n",
    "female40 = SM40[SM40.sex == \"female\"][\"dbirwt\"]\n",
    "\n",
    "mx_40, my_40 = ecdf(male40)\n",
    "fx_40, fy_40 = ecdf(female40)\n",
    "\n",
    "# Plot all ECDFs on the same plot\n",
    "fig, ax = plt.subplots()\n",
    "_ = ax.plot(mx_40, my_40, marker = '.', linestyle = 'none')\n",
    "_ = ax.plot(fx_40, fy_40, marker = '.', linestyle = 'none')\n",
    "\n",
    "# Make nice margins\n",
    "plt.margins(0.02)\n",
    "\n",
    "# Annotate the plot\n",
    "plt.legend(('male', 'female'), loc='lower right')\n",
    "_ = plt.xlabel('birth weight(g)')\n",
    "_ = plt.ylabel('ECDF')\n",
    "\n",
    "# Display the plot\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------------------------------------------------------\n",
    "\n",
    "- What is the relationship to quantiles/percentiles ?\n",
    "- Find the IQR !\n",
    "- Sketch the densities just from the ecdf."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------\n",
    "\n",
    "### Checking Normality of sample mean distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute mean and standard deviation: mu, sigma\n",
    "mu = np.mean(male40)\n",
    "sigma = np.std(male40)\n",
    "\n",
    "# Sample out of a normal distribution with this mu and sigma: samples\n",
    "samples = np.random.normal(mu, sigma, 10000)\n",
    "\n",
    "# Get the CDF of the samples and of the data\n",
    "x_theor, y_theor = ecdf(samples)\n",
    "\n",
    "# Plot the CDFs and show the plot\n",
    "_ = plt.plot(mx_40, my_40, marker='.', linestyle='none')\n",
    "_ = plt.plot(x_theor, y_theor)\n",
    "\n",
    "plt.margins(0.02)\n",
    "_ = plt.xlabel('birth weight (g)')\n",
    "_ = plt.ylabel('CDF')\n",
    "_ = plt.title('CDF of Birthweight')\n",
    "\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Tasks**\n",
    "1. Find the \"5% tails\" which are just the (0.05, 0.95) quantiles \n",
    "2. Read up on theoretical quantiles: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm\n",
    "3. stone age: get the \"5% tails\" from a normal table.\n",
    "4. How many stdevs do you need to cover the 90% sample interval ?\n",
    "5. Can you replace the \"empirical theoretical cdf\" from above with the exact line without sampling 10000 random numbers from a normal distribution ?\n",
    "\n",
    "--------------------------------------------------------------\n",
    "\n",
    "Let us recap what we observed when sampling from a \"population\": The *sample mean distribution* gets narrower with increasing sample size n, SESM =$\\sigma_{\\bar{x}} = \\sigma/\\sqrt{n}$.\n",
    "Take a look at this [interactive applet](http://onlinestatbook.com/stat_sim/sampling_dist/) for further understanding.\n",
    "\n",
    "How is this useful ? And how is it relevant because in reality we would only have **one sample**, not hundreds !\n",
    "\n",
    "**Small Tasks**\n",
    "\n",
    "1. Choose one random sample of size n=40 from the male babies and compute $\\bar{x}$, $\\hat{\\sigma}$. Assume all that is known to you, are these two *summary statistics*. In particular, we do **not know** the true mean $\\mu$!\n",
    "2. Argue intuitively with the ecdf plot about plausible values of $\\mu$.\n",
    "3. More precisely: what interval around $\\bar{x}$ would contain $\\mu$ with 90% probability ?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Hacker Statistic\n",
    "\n",
    "The ability to draw new samples from a population with a known mean is a luxury that we usually do not have. Is there any way to \"fake\" new samples using just the one \"lousy\" sample we have at hand ? \n",
    "This might sound like an impossible feat analogously to \"pulling yourself up by your own **bootstraps**\"!\n",
    "\n",
    "[BootstrapIlustration](https://github.com/markusloecher/DataScience-HWR/blob/main/figures/DC_bootstrap_animated.gif)\n",
    "\n",
    "But that is exactly what we will try now:\n",
    "\n",
    "**Tasks**\n",
    "1. Look up the help for [np.random.choice()](https://docs.scipy.org/doc/numpy15.0/reference/generated/numpy.random.choice.html)\n",
    "<br>\n",
    "2. Draw repeated samples of size n=40 from the sample above.\n",
    "3. Compute the mean of each sample and store it an array.\n",
    "4. Plot the histogram\n",
    "5. Compute the stdev of this distribution and compare to the SEM.\n",
    "<br>\n",
    "6. Write a function that computes *bootstrap replicates* of the mean from a sample.\n",
    "7. Generalize this function to accept any summary statistic, not just the mean."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "2. Draw repeated samples of size n=40 from the sample above.\n",
    "3. Compute the mean of each sample and store it an array.\n",
    "4. Plot the histogram\n",
    "5. Compute the stdev of this distribution and compare to the SEM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_bs_reps_mean(data, size=100):\n",
    "    \"\"\"Draw bootstrap replicates.\"\"\"\n",
    "\n",
    "    # Initialize array of replicates: bs_replicates\n",
    "    bs_replicates = np.empty(size)\n",
    "\n",
    "    # Generate replicates\n",
    "    for i in range(size):\n",
    "        bs_replicates[i] = np.mean(np.random.choice(data, size=len(data)))\n",
    "\n",
    "    return bs_replicates"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "4. Plot the histogram\n",
    "5. Compute the stdev of this distribution and compare to the SEM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "STDEV: 21.66460863574146\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = df[\"dbirwt\"][0:400]\n",
    "\n",
    "data = draw_bs_reps_mean(data=samples, size=40)\n",
    "plt.hist(x=data);\n",
    "print(f\"STDEV: {np.std(data)}\")\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "6. Write a function that computes *bootstrap replicates* of the mean from a sample.\n",
    "7. Generalize this function to accept any summary statistic, not just the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bootstrap_replicate_1d(data, func):\n",
    "    return func(np.random.choice(data, size=len(data)))\n",
    "\n",
    "def draw_bs_reps(data, func = np.mean, size=100):\n",
    "    \"\"\"Draw bootstrap replicates.\"\"\"\n",
    "\n",
    "    # Initialize array of replicates: bs_replicates\n",
    "    bs_replicates = np.empty(size)\n",
    "\n",
    "    # Generate replicates\n",
    "    for i in range(size):\n",
    "        bs_replicates[i] = bootstrap_replicate_1d(data, func)\n",
    "\n",
    "    return bs_replicates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3798, 3515, 2919, 4110, 3769, 2636, 4172, 3118, 2636, 3600, 3260,\n",
       "       2948, 2749, 3713, 3486, 4280, 4253, 2998, 2863, 3260, 3273, 4409,\n",
       "       3345, 4139, 2352, 3572, 4053, 3515, 3572, 3968, 3260, 4689, 3781,\n",
       "       2948, 2494, 2948, 3430, 2296, 3969, 3883])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subset = df[df.sex == \"male\"]\n",
    "rand_samples_40 = np.random.choice(subset.dbirwt, 40)\n",
    "xBar = np.mean(rand_samples_40)\n",
    "rand_samples_40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Take 1,000 bootstrap replicates of the mean: bs_replicates\n",
    "bs_replicates = draw_bs_reps(rand_samples_40, np.mean, size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3536.425, 3361.85 , 3587.775, 3257.925, 3533.35 , 3520.325,\n",
       "       3520.275, 3314.375, 3389.275, 3520.75 ])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bs_replicates[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fx_40, fy_40 = ecdf(bs_replicates)\n",
    "\n",
    "# Plot  ECDF\n",
    "_ = plt.plot(fx_40, fy_40, marker = '.', linestyle = 'none')\n",
    "\n",
    "# Make nice margins\n",
    "plt.margins(0.02)\n",
    "\n",
    "# Annotate the plot\n",
    "_ = plt.xlabel('resampled averages of birth weight(g)')\n",
    "_ = plt.ylabel('ECDF')\n",
    "\n",
    "# Display the plot\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
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   "language": "python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  "varInspector": {
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   "kernels_config": {
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