{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Purpose of this notebook: to check whether the statistical analysis in the paper \"We look like our names\" holds.\n",
    "\n",
    "Link to paper: https://www.researchgate.net/profile/Jacob_Goldenberg/publication/314103043_We_Look_Like_Our_Names_The_Manifestation_of_Name_Stereotypes_in_Facial_Appearance/links/58b7d4d445851591c5d70ce3/We-Look-Like-Our-Names-The-Manifestation-of-Name-Stereotypes-in-Facial-Appearance.pdf\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class HypothesisTest(object):\n",
    "\n",
    "    def __init__(self, prob):\n",
    "        self.prob = prob\n",
    "        self.MakeModel()\n",
    "        #self.actual = self.TestStatistic(data)\n",
    "\n",
    "    def PValue(self, iters=1000):\n",
    "        self.test_stats = [self.TestStatistic(self.RunModel()) \n",
    "                           for _ in range(iters)]\n",
    "\n",
    "        count = sum(1 for x in self.test_stats if x >= self.actual)\n",
    "        return count / iters\n",
    "\n",
    "    def TestStatistic(self, data):\n",
    "        raise UnimplementedMethodException()\n",
    "\n",
    "    def MakeModel(self):\n",
    "        pass\n",
    "\n",
    "    def RunModel(self):\n",
    "        raise UnimplementedMethodException()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Study 1A "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class FaceNameTest1A(HypothesisTest):\n",
    "\n",
    "    def TestStatistic(self):\n",
    "        return test_stat\n",
    "\n",
    "    def RunModel(self):\n",
    "        n = 20\n",
    "        sample = [random.choice('TFFFF') for _ in range(20)]\n",
    "        counter = Counter(sample)\n",
    "        data = counter['T'], counter['F']\n",
    "        return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 18)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test1A = FaceNameTest1A(0.2)\n",
    "test1A.RunModel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Important data: \n",
    "\n",
    "- One hundred twenty-one Israeli students from alocal online panel (60 women, all native speakers, Mage = 27.77 years [SD  4.08]) participated in the study in return for the equivalent of US$2.30.\n",
    "- We presented 20 photos (10 female) one at a time on a computer screen. For each target, five suggested given names appeared below the headshot, including the true name of the depicted person and four filler names\n",
    "-  First, we created for each participant a proportion score that averaged his or her accurate choices and then computed the mean accuracy proportion for all participants."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's write a function for the outcome of an individual experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def one_person_experiment():\n",
    "    \"Returns proportion score.\"\n",
    "    sample = [random.choice('TFFFF') for _ in range(20)]\n",
    "    counter = Counter(sample)\n",
    "    trues = counter['T']\n",
    "    return trues / 20\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.35"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_person_experiment()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can define a group experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def group_experiment():\n",
    "    \"Returns mean proportion score.\"\n",
    "    samples = [one_person_experiment() for _ in range(121)]\n",
    "    return sum(samples) / len(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1975206611570246"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "group_experiment()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now do this 10000 times and plot a cumulative histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "outcomes = [group_experiment() for _ in range(10000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use('bmh')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x833e588>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Us0XEk8B/Be4DPgs8Akx1NBQg6Udo/FD/eqeznE72nJLOBe4CfjEivtGJbDPy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x83d1b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(outcomes, bins=50);\n",
    "plt.xlabel('mean proportion')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x9937cc0>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7yQg1PywvP0L1Ug480PywvPwI1SvU/LC8/AjVSznwQPPD8vIjVK9Q88Py8iNU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\n63UCf9mqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9937cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(outcomes, bins=50, range=(0.1, 0.3), cumulative=True, normed=True, label='sampled distribution\\nof test statistic');\n",
    "plt.xlabel('mean proportion')\n",
    "plt.vlines(0.28, 0, 1, label='measured')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Experiment 1B "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ruling out popularity. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def one_person_experiment():\n",
    "    \"Returns proportion score.\"\n",
    "    sample = [random.choice('TFFF') for _ in range(25)]\n",
    "    counter = Counter(sample)\n",
    "    trues = counter['T']\n",
    "    return trues / 25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.28"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_person_experiment()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def group_experiment():\n",
    "    \"Returns mean proportion score.\"\n",
    "    samples = [one_person_experiment() for _ in range(64)]\n",
    "    return sum(samples) / len(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25437499999999996"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "group_experiment()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "outcomes = [group_experiment() for _ in range(10000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x9508d68>"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x95ebc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(outcomes, bins=50, range=(0.1, 0.3), cumulative=True, normed=True, label='sampled distribution\\nof test statistic');\n",
    "plt.xlabel('mean proportion')\n",
    "plt.vlines(0.2991, 0, 1, label='measured')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}