0013 Confidence Interval of a Klout Score sample.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 scipy\n",
      "import matplotlib.pyplot as plt\n",
      "import seaborn as sns\n",
      "from scipy import stats\n",
      "import math\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
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    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Data\n",
      "We use a random sample of social media influence scores from the service [Klout.com](http://klout.com/ \"Klout scores\") as presented in Udacity's [Intro to Inferential Statistics](https://www.udacity.com/course/ud201). Of a population of 620+ milion scores we got a sample size $n=1048$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Load the data from a csv file\n",
      "data = pd.read_csv('data/klout-scores.csv', header=None, names=['scores'])\n",
      "data.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "      scores\n",
        "0  25.104179\n",
        "1  60.908747\n",
        "2  23.222238\n",
        "3  51.553491\n",
        "4  22.629690"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot the sample and note the bimodal distribution shape\n",
      "# The first peak are social media consumers, second peak influencers\n",
      "p=sns.distplot(data.scores)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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QG2NfUxFycvxH9wGaaTvjfX5n0VLuOLKfB/uPsccm+b1Fy6kbY4nWoWSKD2+8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\nYgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3c506a0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Sample size\n",
      "n = data.scores.count()\n",
      "\n",
      "# The confidence coefficient\n",
      "confidence_coef = .95\n",
      "\n",
      "# The alpha level\n",
      "alpha = 1. - confidence_coef"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Confidence Interval\n",
      "If we want to estimate a population parameter (mean, proportion, standard deviation) from a sample statistic, we can never be sure of our outcome. But we can give some level of confidence of our prediction; the confidence interval (CI). We use the following symbols to depict parameters and statistics.\n",
      "\n",
      "|   |mean|proportion|std dev|   |\n",
      "|---|:---:|:---:|:---:|---|\n",
      "|population|$\\mu$|$p$|$\\sigma$|parameters|\n",
      "|sample|$\\bar{x}$|$\\hat{p}$|$s$|statistics|\n",
      "\n",
      "Let's calculate 95% the confidence interval of the sample mean of Klout Scores. For large samples we can solve the following inequality with an alpha level of $\\alpha=.05$.\n",
      "\n",
      "$$\\bar{x}-z_{\\alpha/2}\\cdot\\frac{\\sigma}{\\sqrt{n}}\\lt\\mu_{estimator}\\lt\\bar{x}+z_{\\alpha/2}\\cdot\\frac{\\sigma}{\\sqrt{n}}$$ "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# First we need our sample mean\n",
      "# This is called the point estimate\n",
      "klout_xbar = data.scores.mean()\n",
      "klout_xbar"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "37.71905483253817"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We also need the standard error of the sample\n",
      "# Since our sample size is large (> 30) we can use\n",
      "# the sample standard deviation as an approximation of sigma\n",
      "klout_s = data.scores.std()\n",
      "klout_s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "16.044314979048973"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The we need to find the z score to calculate the\n",
      "# lower and upper bound of our confidence interval\n",
      "# This is called the critical value\n",
      "critical_value = stats.norm.ppf(alpha / 2) * -1.\n",
      "critical_value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "1.959963984540054"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# An easier way to get the critical values calling scipy.stats\n",
      "# interval function. The alpha .95 being a littbe bit misleading since\n",
      "# it is not our alpha but our confidence coefficient\n",
      "zscore_interval = stats.norm.interval(alpha=confidence_coef)\n",
      "zscore_interval"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(-1.959963984540054, 1.959963984540054)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# We need the standard error to calculate the bounds\n",
      "klout_SE = klout_s / math.sqrt(n)\n",
      "klout_SE"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "0.49561054484656208"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the lower and upper bound Klout Score \n",
      "# for the confidence interval\n",
      "klout_CI_mean_lower = klout_xbar - critical_value * klout_SE\n",
      "klout_CI_mean_upper = klout_xbar + critical_value * klout_SE\n",
      "klout_CI_mean_lower, klout_CI_mean_upper"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(36.747676014280636, 38.690433650795704)"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## So what does it all mean?\n",
      "A confidence interval is a 'parameter catcher'. In this case we try to catch the real population mean from a sample by declaring a confidence interval. This mean we are 95% sure that the real population mean of Klout Scores lies somewhere fixed between 36.75 and 38.69.\n",
      "\n",
      "Klout.com states their mean score is 40, so we did not catch the true population mean parameter. Since our calculations seems to be correct, this could mean that:\n",
      "- Maybe our sample mean falls way below the population mean. Note we we're only 95% confident.\n",
      "- Maybe Klout's communication on the average score is simplified to an easy to remember value of 40."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The effect of sample size\n",
      "Sample size effects the bounds of the confidence interval. The smaller the sample, the less confident we are, so the wider the confidence interval. Let's try this with a random sample from the Klout Score data of $n=50$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's create a sample of 50 random Klout Scores\n",
      "n_50 = 50\n",
      "data_50 = data.ix[np.random.choice(data.index, n_50)]\n",
      "data_50.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "        scores\n",
        "210  32.895053\n",
        "781  16.037027\n",
        "301  59.956514\n",
        "478  56.466763\n",
        "142  58.382079"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot the sample and note a similar bimodal distribution shape\n",
      "p=sns.distplot(data_50.scores)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qGtk2EaNL/eYyT/RJJ0Xj/qEeHhrupTlYxiVL1xBUkEue2tNv/pDOzmWe6NNO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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x17a94cf8>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get the point estimate\n",
      "klout_50_xbar = data_50.scores.mean()\n",
      "klout_50_xbar"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "40.880360456600002"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get the sample standard deviation as an approximation of sigma\n",
      "klout_50_s = data_50.scores.std()\n",
      "klout_50_s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "15.539291223531244"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the standard error for this sample size\n",
      "klout_50_SE = klout_50_s / math.sqrt(n_50)\n",
      "klout_50_SE"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "2.197587639798309"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the lower and upper bound Klout Score \n",
      "# for the confidence interval of our sample of n=50\n",
      "klout_50_CI_mean_lower = klout_50_xbar - critical_value * klout_50_SE\n",
      "klout_50_CI_mean_upper = klout_50_xbar + critical_value * klout_50_SE\n",
      "klout_50_CI_mean_lower, klout_50_CI_mean_upper"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "(36.573167829724937, 45.187553083475066)"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "With this sample size, we are 95% sure that the population mean lies within the range of *klout_50_CI_mean_lower* to *klout_50_CI_mean_upper*. Although this confidence interval does catch the mean parameter, it has also a much wider range. "
     ]
    }
   ],
   "metadata": {}
  }
 ]
}