Illustration with Python Confidence Interval.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# use gamma distribution\n",
    "shape, scale = 2.0, 2.0  # mean=4, std=2*sqrt(2)\n",
    "s = np.random.gamma(shape, scale, 1000000)\n",
    "mu = shape*scale # mean and standard deviation\n",
    "sigma = scale*np.sqrt(shape)\n",
    "\n",
    "# create sample mean distribution\n",
    "meansample = []\n",
    "# sample size\n",
    "samplesize = 500\n",
    "for j in range(0,50000):\n",
    "    # sampling 500 sample from population\n",
    "    rc = random.choices(s, k=samplesize)\n",
    "    # collect mean of each sample\n",
    "    meansample.append(sum(rc)/len(rc))\n",
    "\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.hist(meansample, 200, density=True, color='lightblue')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set mean and 95% probability\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.hist(meansample, 200, density=True, color='lightblue')\n",
    "plt.plot([mu,mu],[0, 3.2], 'k-', lw=4, color='green')\n",
    "plt.plot([mu-(1.96*sigma/np.sqrt(samplesize)),mu-(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=2, color='navy')\n",
    "plt.plot([mu+(1.96*sigma/np.sqrt(samplesize)),mu+(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=2, color='navy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# suppose that we sample 500 data that has a mean as 3.85\n",
    "\n",
    "# Xbar mean = 3.85, sigma = sigma/np.sqrt(samplesize)\n",
    "m, ss = 3.85, sigma/np.sqrt(samplesize) # mean and standard deviation\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.hist(meansample, 200, density=True, color='lightblue')\n",
    "plt.plot([mu,mu],[0, 3.2], 'k-', lw=4, color='green')\n",
    "plt.plot([mu-(1.96*sigma/np.sqrt(samplesize)),mu-(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=2, color='navy')\n",
    "plt.plot([mu+(1.96*sigma/np.sqrt(samplesize)),mu+(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=2, color='navy')\n",
    "plt.plot([m,m],[0, 3.2], 'k-', lw=2, color='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create an interval around sample mean that we got\n",
    "plt.figure(figsize=(20,10))\n",
    "\n",
    "plt.hist(meansample, 200, density=True, color='lightblue')\n",
    "plt.plot([mu,mu],[0, 3.2], 'k-', lw=4, color='green')\n",
    "# plt.plot([mu-(1.96*sigma/np.sqrt(samplesize)),mu-(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=1, color='navy')\n",
    "# plt.plot([mu+(1.96*sigma/np.sqrt(samplesize)),mu+(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=1, color='navy')\n",
    "plt.plot([m,m],[0, 3.2], 'k-', lw=4, color='black')\n",
    "plt.plot([m-(1.96*ss),m-(1.96*ss)],[0, 3.2], 'k-', lw=2, color='red')\n",
    "plt.plot([m+(1.96*ss),m+(1.96*ss)],[0, 3.2], 'k-', lw=2, color='red')\n",
    "# Create a Rectangle patch\n",
    "plt.gca().add_patch(plt.Rectangle((m-(1.96*ss), 0),2*(1.96*ss),3.21, fill=True, linewidth=3, fc=(1,1,0,0.3)))\n",
    "plt.xlim(3.43, 4.67) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the interval we create cover the population mean because it is within 95% range from population mean\n",
    "plt.figure(figsize=(20,10))\n",
    "\n",
    "plt.hist(meansample, 200, density=True, color='lightblue')\n",
    "plt.plot([mu,mu],[0, 3.2], 'k-', lw=4, color='green')\n",
    "plt.plot([mu-(1.96*sigma/np.sqrt(samplesize)),mu-(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=1, color='navy')\n",
    "plt.plot([mu+(1.96*sigma/np.sqrt(samplesize)),mu+(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=1, color='navy')\n",
    "plt.plot([m,m],[0, 3.2], 'k-', lw=4, color='black')\n",
    "plt.plot([m-(1.96*ss),m-(1.96*ss)],[0, 3.2], 'k-', lw=2, color='red')\n",
    "plt.plot([m+(1.96*ss),m+(1.96*ss)],[0, 3.2], 'k-', lw=2, color='red')\n",
    "# Create a Rectangle patch\n",
    "plt.gca().add_patch(plt.Rectangle((m-(1.96*ss), 0),2*(1.96*ss),3.21, fill=True, linewidth=3, fc=(1,1,0,0.3)))\n",
    "plt.xlim(3.43, 4.67) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if the interval is not within 95% range from population mean the interval will not cover the true population mean\n",
    "plt.figure(figsize=(20,10))\n",
    "m = 3.72\n",
    "plt.hist(meansample, 200, density=True, color='lightblue')\n",
    "plt.plot([mu,mu],[0, 3.2], 'k-', lw=4, color='green')\n",
    "plt.plot([mu-(1.96*sigma/np.sqrt(samplesize)),mu-(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=1, color='navy')\n",
    "plt.plot([mu+(1.96*sigma/np.sqrt(samplesize)),mu+(1.96*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=1, color='navy')\n",
    "plt.plot([m,m],[0, 3.2], 'k-', lw=4, color='black')\n",
    "plt.plot([m-(1.96*ss),m-(1.96*ss)],[0, 3.2], 'k-', lw=2, color='red')\n",
    "plt.plot([m+(1.96*ss),m+(1.96*ss)],[0, 3.2], 'k-', lw=2, color='red')\n",
    "# Create a Rectangle patch\n",
    "plt.gca().add_patch(plt.Rectangle((m-(1.96*ss), 0),2*(1.96*ss),3.21, fill=True, linewidth=3, fc=(1,1,0,0.3)))\n",
    "plt.xlim(3.43, 4.67) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# use 90% instead of 95%\n",
    "plt.figure(figsize=(20,10))\n",
    "m = 3.72\n",
    "plt.hist(meansample, 200, density=True, color='lightblue')\n",
    "plt.plot([mu,mu],[0, 3.2], 'k-', lw=4, color='green')\n",
    "plt.plot([mu-(1.645*sigma/np.sqrt(samplesize)),mu-(1.645*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=1, color='navy')\n",
    "plt.plot([mu+(1.645*sigma/np.sqrt(samplesize)),mu+(1.645*sigma/np.sqrt(samplesize))],[0, 3.2], 'k-', lw=1, color='navy')\n",
    "plt.plot([m,m],[0, 3.2], 'k-', lw=4, color='black')\n",
    "plt.plot([m-(1.645*ss),m-(1.645*ss)],[0, 3.2], 'k-', lw=2, color='red')\n",
    "plt.plot([m+(1.645*ss),m+(1.645*ss)],[0, 3.2], 'k-', lw=2, color='red')\n",
    "# Create a Rectangle patch\n",
    "plt.gca().add_patch(plt.Rectangle((m-(1.645*ss), 0),2*(1.645*ss),3.21, fill=True, linewidth=3, fc=(1,1,0,0.3)))\n",
    "plt.xlim(3.43, 4.67) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of interval that cover the expected values: 95\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simulate 100 interval with 5,000 sample size\n",
    "mu = shape*scale # mean and standard deviation\n",
    "sigma = scale*np.sqrt(shape)\n",
    "intervallist = []\n",
    "k = 1.96\n",
    "# sample size\n",
    "samplesize = 5000\n",
    "# start count\n",
    "c = 0\n",
    "for i in range(0,100):\n",
    "    # sample 100 sample\n",
    "    rs = random.choices(s, k=samplesize)\n",
    "    # calculate mean\n",
    "    mean = np.mean(rs)\n",
    "    upbound = mean + k*sigma/np.sqrt(samplesize)\n",
    "    lowbound = mean - k*sigma/np.sqrt(samplesize)\n",
    "    # collect difference between sample mean and mu\n",
    "    intervallist.append([lowbound,mean,upbound])\n",
    "    if upbound >= mu and lowbound <= mu:\n",
    "        c += 1\n",
    "        \n",
    "print(\"number of interval that cover the expected values:\", c)\n",
    "# set figure size.\n",
    "plt.figure(figsize=(20,10))\n",
    "# plot box plots of each sample mean.\n",
    "plt.boxplot(intervallist)\n",
    "plt.plot([1, 100],[mu,mu], 'k-', lw=2, color='red')\n",
    "# show plot.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of interval that cover the expected values: 96\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simulate 100 interval with 20,000 sample size\n",
    "intervallist = []\n",
    "# sample size\n",
    "samplesize = 20000\n",
    "# start count\n",
    "c = 0\n",
    "for i in range(0,100):\n",
    "    # sample 100 sample\n",
    "    rs = random.choices(s, k=samplesize)\n",
    "    # calculate mean\n",
    "    mean = np.mean(rs)\n",
    "    upbound = mean + k*sigma/np.sqrt(samplesize)\n",
    "    lowbound = mean - k*sigma/np.sqrt(samplesize)\n",
    "    # collect difference between sample mean and mu\n",
    "    intervallist.append([lowbound,mean,upbound])\n",
    "    if upbound >= mu and lowbound <= mu:\n",
    "        c += 1\n",
    "        \n",
    "print(\"number of interval that cover the expected values:\", c)\n",
    "# set figure size.\n",
    "plt.figure(figsize=(20,10))\n",
    "# plot box plots of each sample mean.\n",
    "plt.boxplot(intervallist)\n",
    "plt.plot([1, 100],[mu,mu], 'k-', lw=2, color='red')\n",
    "# show plot.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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