confidence_interval.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
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   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import scipy.stats as stats\n",
    "import numpy as np\n",
    "import random\n",
    "import warnings\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set(rc={'figure.figsize':(13, 7.5)})\n",
    "sns.set_context('talk')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('submission.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Patient_Week</th>\n",
       "      <th>FVC</th>\n",
       "      <th>Confidence</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ID00419637202311204720264_-12</td>\n",
       "      <td>9818</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ID00421637202311550012437_-12</td>\n",
       "      <td>9881</td>\n",
       "      <td>100</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>9825</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ID00423637202312137826377_-12</td>\n",
       "      <td>9835</td>\n",
       "      <td>100</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
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       "      <td>17394</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Patient_Week    FVC  Confidence\n",
       "0  ID00419637202311204720264_-12   9818         100\n",
       "1  ID00421637202311550012437_-12   9881         100\n",
       "2  ID00422637202311677017371_-12   9825         100\n",
       "3  ID00423637202312137826377_-12   9835         100\n",
       "4  ID00426637202313170790466_-12  17394         100"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "m = df['FVC'].mean()\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
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       "3023.9858316937116"
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     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "s = df['FVC'].std()\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = len(df)\n",
    "conf = .95\n",
    "alpha = 1 - conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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     "data": {
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       "730"
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     "execution_count": 14,
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   "source": [
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats\n",
    "\n",
    "z_critical = stats.norm.ppf(q=0.975)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "z_interval = stats.norm.interval(alpha=conf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.959963984540054, (-1.959963984540054, 1.959963984540054))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z_critical, z_interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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     "execution_count": 18,
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   ],
   "source": [
    "std_err = s/np.sqrt(n)\n",
    "std_err"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "ci_lower = m - z_critical * std_err\n",
    "ci_upper = m + z_critical * std_err"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
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     "data": {
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     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ci_lower, ci_upper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0725415216073885"
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     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "(m - ci_lower) / s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "(m - ci_upper) / s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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