Assignment_4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q1.\n",
    "    a. Please download the data from \"http://archive.ics.uci.edu/ml/datasets/Liver+Disorders\"\n",
    "    b. Get to know about the features\n",
    "        i. given data set has 6 attributes and 1 output varaible\n",
    "    c. Find me the two most corelated feature out of 6 attributes with the output varaible\n",
    "    d. Prove that the features are correlated with output varaible using null hypothsis test\n",
    "        i.hint: consider 100 random samples from the data set and find out the correlation, repeat it for 50 times"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "1. Title: BUPA liver disorders\n",
    "\n",
    "2. Source information:\n",
    "   -- http://archive.ics.uci.edu/ml/datasets/Liver+Disorders\n",
    "   -- Creators: BUPA Medical Research Ltd.\n",
    "   -- Donor: Richard S. Forsyth\n",
    "   -- Date: 5/15/1990\n",
    "\n",
    "3. Past usage: \n",
    "   -- None known other than what is shown in the PC/BEAGLE User's Guide\n",
    "      (written by Richard S. Forsyth).\n",
    "\n",
    "4. Number of instances: 345\n",
    "\n",
    "5. Number of attributes: 7 overall\n",
    "\n",
    "6. Attribute information:\n",
    "   1. mcv\tmean corpuscular volume\n",
    "   2. alkphos\talkaline phosphotase\n",
    "   3. sgpt\talamine aminotransferase\n",
    "   4. sgot \taspartate aminotransferase\n",
    "   5. gammagt\tgamma-glutamyl transpeptidase\n",
    "   6. drinks\tnumber of half-pint equivalents of alcoholic beverages drunk per day\n",
    "   7. selector  field used to split data into two sets\n",
    "\n",
    "7. Relevent Information\n",
    "The first 5 variables are all blood tests which are thought to be sensitive to liver disorders that might arise from excessive alcohol consumption. Each line in the data file constitutes the record of a single male individual.\n",
    "\n",
    "8. Missing values: none"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   mcv  alhphos  sgpt  sgot  gammagt  drinks  selector\n",
      "0   85       92    45    27       31     0.0         1\n",
      "1   85       64    59    32       23     0.0         2\n",
      "2   86       54    33    16       54     0.0         2\n",
      "3   91       78    34    24       36     0.0         2\n",
      "4   87       70    12    28       10     0.0         2\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as sp\n",
    "from random import * \n",
    "from __future__ import division\n",
    "\n",
    "h=['mcv','alhphos','sgpt','sgot','gammagt','drinks','selector']\n",
    "data= pd.read_csv(\"dataLiver.csv\",names=h)\n",
    "\n",
    "print data.head() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mcv</th>\n",
       "      <th>alhphos</th>\n",
       "      <th>sgpt</th>\n",
       "      <th>sgot</th>\n",
       "      <th>gammagt</th>\n",
       "      <th>drinks</th>\n",
       "      <th>selector</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>345.000000</td>\n",
       "      <td>345.000000</td>\n",
       "      <td>345.000000</td>\n",
       "      <td>345.000000</td>\n",
       "      <td>345.000000</td>\n",
       "      <td>345.000000</td>\n",
       "      <td>345.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>90.159420</td>\n",
       "      <td>69.869565</td>\n",
       "      <td>30.405797</td>\n",
       "      <td>24.643478</td>\n",
       "      <td>38.284058</td>\n",
       "      <td>3.455072</td>\n",
       "      <td>1.579710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.448096</td>\n",
       "      <td>18.347670</td>\n",
       "      <td>19.512309</td>\n",
       "      <td>10.064494</td>\n",
       "      <td>39.254616</td>\n",
       "      <td>3.337835</td>\n",
       "      <td>0.494322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>65.000000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>87.000000</td>\n",
       "      <td>57.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>90.000000</td>\n",
       "      <td>67.000000</td>\n",
       "      <td>26.000000</td>\n",
       "      <td>23.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>93.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>34.000000</td>\n",
       "      <td>27.000000</td>\n",
       "      <td>46.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>103.000000</td>\n",
       "      <td>138.000000</td>\n",
       "      <td>155.000000</td>\n",
       "      <td>82.000000</td>\n",
       "      <td>297.000000</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              mcv     alhphos        sgpt        sgot     gammagt      drinks  \\\n",
       "count  345.000000  345.000000  345.000000  345.000000  345.000000  345.000000   \n",
       "mean    90.159420   69.869565   30.405797   24.643478   38.284058    3.455072   \n",
       "std      4.448096   18.347670   19.512309   10.064494   39.254616    3.337835   \n",
       "min     65.000000   23.000000    4.000000    5.000000    5.000000    0.000000   \n",
       "25%     87.000000   57.000000   19.000000   19.000000   15.000000    0.500000   \n",
       "50%     90.000000   67.000000   26.000000   23.000000   25.000000    3.000000   \n",
       "75%     93.000000   80.000000   34.000000   27.000000   46.000000    6.000000   \n",
       "max    103.000000  138.000000  155.000000   82.000000  297.000000   20.000000   \n",
       "\n",
       "         selector  \n",
       "count  345.000000  \n",
       "mean     1.579710  \n",
       "std      0.494322  \n",
       "min      1.000000  \n",
       "25%      1.000000  \n",
       "50%      2.000000  \n",
       "75%      2.000000  \n",
       "max      2.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2    200\n",
       "1    145\n",
       "Name: selector, dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['selector'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculating the Spearman's Rank Correlation Coefficient between the different features and the output variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SpearmanrResult(correlation=-0.10246626896937111, pvalue=0.057259266268041349)\n"
     ]
    }
   ],
   "source": [
    "print sp.spearmanr(data['mcv'],data['selector'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=-0.12222686443646685, pvalue=0.023174635184627524)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.spearmanr(data['alhphos'],data['selector'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=-0.13467770721374014, pvalue=0.012284455216342641)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.spearmanr(data['sgpt'],data['selector'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=0.14463984221647871, pvalue=0.007124242098003857)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.spearmanr(data['sgot'],data['selector'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=0.21961129022957107, pvalue=3.8779315464892418e-05)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.spearmanr(data['gammagt'],data['selector'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=0.038725467248969442, pvalue=0.47340364292085135)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.spearmanr(data['drinks'],data['selector'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The features 'gammagt' and 'sgot' are the most correlated to the output variable 'selector'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.18\n"
     ]
    }
   ],
   "source": [
    "#Null Hypothesis: gammagt and selector are not correlated\n",
    "p=0\n",
    "for i in range(50):\n",
    "    sg=[]\n",
    "    ss=[]\n",
    "    for j in range(100):\n",
    "        x=randint(0,344)\n",
    "        sg.append(data.loc[x,'gammagt'])\n",
    "        ss.append(data.loc[x,'selector'])\n",
    "        \n",
    "    if sp.spearmanr(sg,ss).correlation<0.10:\n",
    "        p+=1\n",
    "\n",
    "print p/50\n",
    "        \n",
    "        \n",
    "#Since, p=0.04<0.05 I reject the null hypothesis with 95% confidence\n",
    "# and conclude that gammagt and selector are correlated.\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24\n"
     ]
    }
   ],
   "source": [
    "#Null Hypothesis: sgot and selector are not correlated\n",
    "p=0\n",
    "for i in range(50):\n",
    "    sg=[]\n",
    "    ss=[]\n",
    "    for j in range(100):\n",
    "        x=randint(0,344)\n",
    "        sg.append(data.loc[x,'sgot'])\n",
    "        ss.append(data.loc[x,'selector'])\n",
    "        \n",
    "    if sp.spearmanr(sg,ss).correlation<0.08:\n",
    "        p+=1\n",
    "\n",
    "print p/50\n",
    "\n",
    "#Since p is high I fail to reject the null hypothesis that sgot and selector are not correlated"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q2.\n",
    "    a. Simulate the coin tossing by writing a function wich gives the output \"head\" with 50% chance and \"tail\" with 50% chance\n",
    "    b. call the same function 250 times, find out the number tests which gave the output \"head\"\n",
    "    c. based on the result conclude that the coin is baised or not\n",
    "    d. prove your conclusion with the help of null hypothisis test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "126\n"
     ]
    }
   ],
   "source": [
    "def toss():\n",
    "    x=random()\n",
    "    if(x<0.5):\n",
    "        return \"H\"\n",
    "    else:\n",
    "        return \"T\"\n",
    "def expt():\n",
    "    l=[]\n",
    "    count_heads=0\n",
    "    for i in range(250) :\n",
    "        x=toss()\n",
    "        if x==\"H\":\n",
    "            l.append(\"H\")\n",
    "            count_heads+=1\n",
    "        else:\n",
    "            l.append(\"T\")\n",
    "    return count_heads,l\n",
    "\n",
    "C,l=expt()\n",
    "\n",
    "print C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.61\n"
     ]
    }
   ],
   "source": [
    "#Given that the value of one experiment resulted in 115 heads out of 250 coin tosses instead of approx. 125, \n",
    "#I hypothesize that the coin is biased.  \n",
    "\n",
    "#Null Hypothesis:- The coin is biased\n",
    "#Alternate Hypothesis:- The coin is unbiased\n",
    "\n",
    "# To test this a sample of 50 values is taken from the array containing the result of the 250 coin tosses. If the no. of heads\n",
    "#is not between 23 to 27 the coin is assumed to be biased. This experiment is repeated for 100 times and the probability \n",
    "# of the number of biased coins is tested. \n",
    "\n",
    "p=0\n",
    "for i in range(100):\n",
    "    s=sample(l,50)\n",
    "    ch=0\n",
    "    for x in s:\n",
    "        if x==\"H\":\n",
    "            ch+=1\n",
    "    if ch not in range(23,26):\n",
    "        p+=1\n",
    "\n",
    "p=p/100\n",
    "print p\n",
    "\n",
    "#Since 55 out of the 100 random samples showed that the coin is biased, \n",
    "#I fail to reject the null hypothesis and conclude that the coin is biased."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "def generate_data():\n",
    "    X = np.linspace(-10,10, 500)\n",
    "    Y = [(4 / 3 ** 2) * (x - 3) ** 2 for x in X]\n",
    "    return X, Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre>\n",
    "Q3. \n",
    "    a. call the function genarate_data() to get two vectors, \"X, Y = genarate_data()\"\n",
    "    b. find out the trasofrmation of given vectors which will help us to find the correlation between X, Y with the help of techniques that are discussed in the class (Pearson Product Moment Correlation, Spearman rank Order Correlation)\n",
    "        hint: use the techniques that are discussed in the class while solving \"X^2 + Y^2 =a^2 (circle data)\"\n",
    "    </pre>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe0AAAFlCAYAAADGV7BOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbcf9f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X,Y=generate_data()\n",
    "plt.scatter(X,Y)\n",
    "plt.title('Scatter plot')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SpearmanrResult(correlation=-0.65553142212568849, pvalue=1.0024014496100716e-62)\n",
      "(-0.75729314730485919, 3.3483974622873407e-94)\n"
     ]
    }
   ],
   "source": [
    "print sp.spearmanr(X,Y)\n",
    "print sp.pearsonr(X,Y)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}