t-test_Significance-Statistics-Assignment-3-NU.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## In this assignment we will test the hypothesis that the economic growth of the German Stock market was the same during 2 equal periods of times,\n",
    "- We test the null hypothesis using t table\n",
    "- We use a significance level of 5%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. Load the data: \n"
     ]
    }
   ],
   "source": [
    "print(\"1. Load the data: \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dax=pd.read_csv('EUstock.csv')['DAX']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "930.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(dax)/2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2. Split the data into 2 halves: \n"
     ]
    }
   ],
   "source": [
    "print(\"2. Split the data into 2 halves: \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "half_1=dax.loc[:len(dax)/2-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "half_2=dax.loc[len(dax)/2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "930"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(half_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "930"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(half_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3. Claculate mean and std of 1st half: \n"
     ]
    }
   ],
   "source": [
    "print(\"3. Claculate mean and std of 1st half: \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean:  1822.8727419354855\n"
     ]
    }
   ],
   "source": [
    "print(\"mean: \", half_1.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard d:  241.15169373506328\n"
     ]
    }
   ],
   "source": [
    "print(\"standard d: \",half_1.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4. Claculate mean and std of 2nd half: \n"
     ]
    }
   ],
   "source": [
    "print(\"4. Claculate mean and std of 2nd half: \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean:  3238.441021505378\n"
     ]
    }
   ],
   "source": [
    "print(\"mean: \", half_2.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard d:  1137.3952192152863\n"
     ]
    }
   ],
   "source": [
    "print(\"standard d: \",half_2.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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95VnP2uMst6WUrOnyrlUTv2gYChERkboifYOzbDsEzvl32fmmTvB0ju861reGrEknZ7yu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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4ae7bec2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5))\n",
    "plt.ylim(0,6350)\n",
    "plt.plot((half_1))\n",
    "plt.plot((half_2))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We can see, by just drawing, that of course they are not the same, \n",
    "- however let's make things more quantified"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5. q is a random variable, representing the difference between the 2 samples: \n"
     ]
    }
   ],
   "source": [
    "print(\"5. q is a random variable, representing the difference between the 2 samples: \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1415.5682795698926\n"
     ]
    }
   ],
   "source": [
    "q=half_1.mean()-half_2.mean()\n",
    "print(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6. Calculate the variance of q, (the difference): \n"
     ]
    }
   ],
   "source": [
    "print(\"6. Calculate the variance of q, (the difference): \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q variance:  1452.00908819\n",
      "i.e. Standard error for the difference of means:  38.1052370179\n"
     ]
    }
   ],
   "source": [
    "\n",
    "qvar=np.array(half_1).var()/(len(half_1))+np.array(half_2).var()/(len(half_2))\n",
    "print(\"q variance: \",qvar)\n",
    "print(\"i.e. Standard error for the difference of means: \" , qvar**0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We can draw a gaussian distribution of q, where the center mean is q (as calculated above) and standard deviation as calculated in this step's standard error.\n"
     ]
    }
   ],
   "source": [
    "print(\"We can draw a gaussian distribution of q, where the center mean is q (as calculated above) and standard deviation as calculated in this step's standard error.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jsolMlhBMVPrjtnISYmP48AVjBm2dKYlxXH/BGJ7bdYIOu+GdiUCWEEzU6ejs4s87jnH1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\nxhjjsoRgjDEGsIRgjDHG9f8BCQNtyRbK5iQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4adfdce7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-1600,-1200)\n",
    "y = stats.norm.pdf(x, loc=q, scale=qvar**0.5)    \n",
    "plt.plot(x,y)\n",
    "plt.title(\"Distributoin of difference of means/q\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7. With significance level of 5%, test the Hypothesis that m1=m2 \n",
      "We don't know the population standard deviation since those are 2 samples, so I use t test as below.\n"
     ]
    }
   ],
   "source": [
    "print(\"7. With significance level of 5%, test the Hypothesis that m1=m2 \")\n",
    "print(\"We don't know the population standard deviation since those are 2 samples, so I use t test as below.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha=0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-37.1489167986\n"
     ]
    }
   ],
   "source": [
    "t_value=(q)/((qvar)**0.5) \n",
    "# the difference in means divided by the standard deviation of the means \n",
    "print(t_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tcritical_from_table=1.962 # alpha 0.05 2 tailed test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checkingt from the stats package: \n"
     ]
    }
   ],
   "source": [
    "print(\"Checkingt from the stats package: \")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.9625208332\n"
     ]
    }
   ],
   "source": [
    "print(stats.t.ppf((1-alpha/2), len(half_1)-1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### I try to visualize the pdf and q "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yRAV56fUTeGrsDm2ESEgR6fUNAgAAAADgONXtaU6rptoxEypLlJ9rqttDiITU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\niIiIiIiISFrqRBIRERERERERkbT+Hwn5qhvWDvaqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4adfc17278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,5))\n",
    "x = np.linspace(-200,200)\n",
    "y = stats.norm.pdf(x, loc=0, scale=qvar**0.5)    \n",
    "plt.plot(x,y)\n",
    "plt.scatter([(1.962*(qvar**0.5)),(-1.962*(qvar**0.5))],[0,0],c='y')\n",
    "plt.annotate('critical value', xy=(-(1.962*(qvar**0.5)), 0),xytext=((-1.962*(qvar**0.5))-100, 0.002),\n",
    "            arrowprops=dict(facecolor='black', shrink=0.05))\n",
    "plt.scatter([(q)],[0],c='g')\n",
    "plt.annotate('q', xy=(q,0),xytext=(q+10, 0.002),\n",
    "            arrowprops=dict(facecolor='black', shrink=0.05))\n",
    "plt.title(\"normalized distribution vs q(the difference of means)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pvalue is almost 0...\n"
     ]
    }
   ],
   "source": [
    "print (\"Pvalue is almost 0...\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-37.128938890874657, pvalue=3.3756087351451227e-226)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(half_1,half_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Since t<<tcritical from the table(-1.962 & 1.962), we reject the null hypothesis"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}