0012 Exploring the Central Limit Theorem.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "import seaborn as sns\n",
      "from scipy import stats\n",
      "from __future__ import division\n",
      "\n",
      "# turn of data table rendering\n",
      "pd.set_option('display.notebook_repr_html', False)\n",
      "\n",
      "sns.set_palette(['#00A99D', '#F5CA0C', '#B6129F', '#76620C', '#095C57'])\n",
      "np.version.full_version"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "'1.9.1'"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Data\n",
      "We take as our population a tetrahedral (four sided) die."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# One throw leads to one of four outcomes\n",
      "data = np.array([1.0, 2.0, 3.0, 4.0])\n",
      "data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "array([ 1.,  2.,  3.,  4.])"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Our data has a perfect uniform distribution\n",
      "p=sns.barplot(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x4054198>"
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     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the population mean\n",
      "population_mu = data.mean()\n",
      "population_mu"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "2.5"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the standard deviation of the population\n",
      "population_sigma = data.std(ddof=0)\n",
      "population_sigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "1.1180339887498949"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Illustration of the Central Limit Theorem\n",
      "The Central Limit Theorem (CLT) states, if we take the mean of a large number of independent samples, the sampling distribution will aproximate a normal distribution, regardless of the shape of the underlying distribution. Let's illustrate this by sampling the mean of two throws ($n=2$) with the tetrahedral die."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's find out the number of possible outcomes with a sample size 2\n",
      "possible_outcomes = 4**2\n",
      "possible_outcomes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "16"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create a dataframe with the mean of all possible outcomes\n",
      "mean_outcome_matrix = pd.DataFrame(index=data, dtype='float64', columns=data )\n",
      "\n",
      "for x in data:\n",
      "    for y in data:\n",
      "        mean_outcome_matrix[x][y] = np.mean([x,y])\n",
      "\n",
      "# Below you see a heatmap of the mean of all possible outcomes\n",
      "p=sns.heatmap(mean_outcome_matrix, annot=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eNYDxl5xNn4P259nfP8djP/1VGmGWnCnX/W/m/scv+MqVX0w7lK6jBOb0vg2s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\nklQ2THqSpLLx/wGnlGhKsY48MQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x17f01160>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Now get the mean of all possible mean outcomes\n",
      "sample_mean = mean_outcome_matrix.mean().mean()\n",
      "sample_mean"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "2.5"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Note the mean of all possible mean outcomes \n",
      "# is exactly the same as the population mean!\n",
      "population_mu == sample_mean"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Below a plot the sampling distribution of all possible mean outcomes\n",
      "# Note that it's perfectly normal\n",
      "diff_val_count = mean_outcome_matrix.stack().value_counts().count()\n",
      "p=sns.distplot(mean_outcome_matrix.stack(), bins=diff_val_count)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2bf/qmBOLTOFL+3YAcEPTWlz6rFjm2HuWrOJ/2vfx9QPPcnltI/ma91zm0JRl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\niIgYpjIWERExTGUsIiJi2P8HCYX/FCb4OJAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x17eebac8>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Standard Error\n",
      "The standard deviation of the sampling distribution is called the standard Error (SE)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the standard error (SE) of all possible mean outcomes\n",
      "mean_outcomes_SE = mean_outcome_matrix.stack().std(ddof=0)\n",
      "mean_outcomes_SE"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "0.79056941504209488"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# If we now calculate the ratio of sigma to SE\n",
      "# we see it is the square root of 2\n",
      "ratio_sigma_SE = population_sigma / mean_outcomes_SE\n",
      "ratio_sigma_SE"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "1.4142135623730949"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# So if we square this ratio we get... our sample size (approximately)\n",
      "ratio_sigma_SE ** 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "1.9999999999999996"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This means that sigma $\\sigma$ divided by the standard error $SE$ is the square root of our sample size $n$:\n",
      "\n",
      "$$\\frac{\\sigma}{SE}= \\sqrt{n}$$\n",
      "\n",
      "Also means we can calculate the Standard Error as follows:\n",
      "\n",
      "$$SE=\\frac{\\sigma}{\\sqrt{n}}$$\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Increasing the sample size\n",
      "When we take a larger sample to calculate the sampling mean, the resulting distribution will become more normal and skinny. Also, the mean of the sampling distribution will match up more with the population mean. This effect is illustrated in the example below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's simulate a population of a 1000 throws with a weighted \n",
      "# tetrahedral die (with a 40% chance of throwing a 4)\n",
      "# The result is a negatively skewed distribution\n",
      "non_normal_data = np.random.choice(data, 1000, p=[0.10, .20, .30, .4])\n",
      "p=sns.barplot(non_normal_data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QS5JUMUMuSVLFDLkkSRUz5JIkVcyQS5JUMUMuSVLFDLkkSRUz5JIkVcyQS5JUMUMuSVLF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\nSJAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x185de278>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Check out the mean of the non normal distribution\n",
      "non_normal_data.mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "3.0110000000000001"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# In this example we plot four sampling distributions of different\n",
      "# sizes to show the effect of the increasing sample size.\n",
      "# Note thst the distribution is getting more normal and skinny\n",
      "# with an increased sample size.\n",
      "f, (ax1, ax2) = plt.subplots(2, 2, sharex=True)\n",
      "axes = [ax1[0], ax1[1], ax2[0], ax2[1]]\n",
      "ax = 0\n",
      "\n",
      "for sample_size in [2,5,20,100]:\n",
      "    sampling_distribution = []\n",
      "    for i in range(100):\n",
      "        mean_sample = np.random.choice(non_normal_data, sample_size).mean()\n",
      "        sampling_distribution.append(mean_sample)\n",
      "\n",
      "    p=sns.distplot(sampling_distribution, ax=axes[ax], \n",
      "                   axlabel=str(sample_size) + ' samples, $\\\\bar{x}=$' + \n",
      "                   str(np.mean(sampling_distribution)))\n",
      "    ax += 1  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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e0RCfWLaeKvl0mVKjw8kb6xbzl94jPOPt57TKunyHVGiO7r5QSm0lvvviQpiw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\nW3Y+S7T92JTy1pFBWgNBTmzr8PRa+ZGfOfa6VW6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       "text": [
        "<matplotlib.figure.Figure at 0x17c739e8>"
       ]
      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}