Categorical comparison vs. Correlation

Categorical Comparison vs. Correlation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# T-test works well for comparing categories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "cats = np.random.normal(3,2,100)\n",
    "dogs = np.random.normal(3.5,2,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot([cats, dogs]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-2.7559348517984787, pvalue=0.006398917300031993)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import ttest_ind\n",
    "ttest_ind(cats,dogs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comapring Continuous Numeric Values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "height = np.random.normal(66,6,100)\n",
    "weight = (30+2*np.sqrt(height)) + np.random.normal(0,2,size=(100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Suppose we have the height and weight of various people. There is a slight trend, but also a lot of noise.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'weight')"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8Cnwh+5tbgetHeG4JpGiATK13OEqvepLpodTez7Yqx076Xa3FPN4Ug0JVPWa2wsw+nNXzY2Yvy3r0Pbn7Nndf4+7rgEuBve7+blrr/bSvFP458J2RWy+l23L+BqaWLztm26TSDiGrbkZZaCvEoGuslUWjqrIiqd/VWszjTTEoWtVzPTAPvD77+VFak7m+NMJrbgduNLOrgaeBK0d4DgmkX9oh5CX9JHqOw/aqyx50jbmyaFRVViRtOX/DcTl+gOXLLOrxphgUDfxnuvsl2T14cfdFs2yN2QLc/Q7gjuz7Q7QqfSRSeQEydNCKseqm7EHXGPdxXFVWJLXfM1X1DK9o4P+JmU3RGtDFzM5kwMQtqZfQQSuGWvZuZQ+6xriP46q6IinVsZGqFQ38HwG+ApxhZjfSGri9IlSjJD6hg1YMtex5ygwsse7jOFKvSGqqooH/V4E9wM3A94Gr3P0HwVpVgiYvIhZC6KBVdc9xEuq6j+p1p2eYwd1/SmtRtpfSWr7hL9z994K1bAx1HETLU8bJbZz7x5YZtIr2HFM+oat3LLEotDontBZbA14FnAu8F1h0940B2/acYVfnnN2+N7d3WqclZstY0XHY56g66MawiqVISnqtzln0Rixfo7Ui553AN4BXxbzGTh0H0bqVMdgay/1ji6pjVYxIFYqmer4FvBL4x7TuvHXIzO509ygjaR0H0bqVcXJL7QQ5bnurvmIRiUWhmbvufrW7vwF4O/BDWjn/QyEbNo4qZ59OShnrp6e2Bvs47W2niRYOLeIcHfdJfeasyCiKLtnwPjPbBewHNtFaWO3NIRs2jlGm56emjJNbaifIcdobw81ORGJRNNUzBfwOMN++/WLsqs5HdwqRYiijQiS1KpNx2puX+oPq01pNSD81YR9TU7iqp0op33NXlShHVRUAdu9b4Opd+3PvKVtlpVdqVVWj0P9/tca9566MSCmGlipz7Dtuv7/njcSrTGsN87+R6hiF/v/jpMAfWGqVM6FUGQB6vddOtRP6hvnfSDWA6v8/TkVz/DKiJpSWFlFlAOh1DFaPsbxyO+UyvWI57vDU4tLQ6Zdh/jdSDaD6/4+TevyBpVY5E0qVpaNlHoPulMuTzyxxaHFppPTLMO1KrfS2Tf//cVLgD6wJpaVFVBkAyjwGeSmXTsOkX4ZpV6oBtHsfp6eW8/zlJ3D1rv21uANZqlTVIxOTYlVKt/Vb9+QOFHcy4IHt5d9rKPX3TxU+kzfWWj0iZYhpbsWoeuWsu/8mhNTfvxBrLaV+MqyKUj0iQ8hLuXRKIf1SlbIHqFMtcY2BAn8kdu9bYHb7XtZv3aPcZ8S6c9anrljO9NTyRo/fFFX2AHWqJa4xUKqnBONebjblxjF1kXrKpSpl38wn1RLXGKjHP6YyLjfVc5EmKLvCLdUS1xioxz+mMgas1HORlA1zxVvm1VJd72E8CQr8YyojaMc2u1GVEqNp4vtWZZoytdVlY6LAP6YygnZMPReNN4ymqe9b1bfD1HjLaJTjH1MZMypjmt2r8YbRNPV9U5oyTerxj6msy81Yei76II+mqe9bbGlKKUaBvwSxBO1BiuSg9UEeTVPft5jSlFKcUj0NUbTsNNXFwKrW1PctpjSlFKcef0MUHYRTpcRomvy+pXLFK0cp8DfEMDlofZBHo/dNUhE81WNmy8xsn5l9qWv7H5jZ06FfX1o0y1FE2iaR478KuLdzg5nNANMTeG3JNDUHLSLHC5rqMbM1wAXAx4Brsm3LgB3Au4C3h3x9OarJOegqNHEWr6QjdI7/E8AHgZM7tr0PuM3dHzezng80s83AZoC1a9eGbGPtdQeh373kbAWhgJo6i1fSESzVY2YXAgfcfb5j2yrgncAfDHq8u+909xl3n1m5cmWoZtZeXW9WEfP9C5o6i1fSETLHPwtcZGYPAjcB5wH3AD8HfC/bvsLMvhewDY1XxyAU+8msqbN4JR3BAr+7b3P3Ne6+DrgU2Ovup7r7i9x9Xbb9GXf/uVBtqFIsPdI6BqHYT2aqoJLYaeZuADH1SOsYhGI/mamCSmI3kcDv7ne4+4U52396Eq8/aTH1SKsMQqGuemI/mWkZA4mdZu4GEFOPtKoyzjIqW3qVRKawMJhm8UrMFPgDiG2lxiqC0Lg36Chy4lCdvMhoFPgDSKFHGtq4Vz2DThzqUYuMToO7ASjHO34ePqZ0mUjdqMcfSNN7pONe9cSWLhOpE/X4JYhxr3rO3biS7gU9mpYuEwlFPX4JZtSrnt37FvjC/ALesc2Ad7yy2VdRImVR4JeBJr3SZN7ArgNfv+9gsNcUaRIFfumripUmNbA7mJZ9lnEoxy99VTELOfaZuVWLaUkQSZN6/PKcvF5kFb3vfhVB6umOPzlORIFfgN4pnekVy3nymaXj/j5k77vXzFxANzhBqTAZnwJ/BEL0Yod9zl69yOedeAJTy5dNfBZyXkXQ7Pa96umiOQ4yPuX4KxYiXzvKc/bqLT61uBTNLGT1dFs0x0HGpR5/xULka0d5zn69yFhmIaunqzkOUg71+CsWohc7ynOmcPOQFNoYmuY4SBkU+CsWonRxlOdMYWG5FNoYmtJdUgaleioWYgnnUZ8zlpROPym0MSSlu6QM6vFXLEQvVj3j+lK6S8pg7j74ryo2MzPjc3NzVTdDJAqaxCZFmdm8u890b1eqRyQxTU93yfiU6hERaRgFfhGRhlHgFxFpGAV+EZGGUeAXEWkYBX4RkYZR4BcRaRgFfhGRhlHgFxFpGAV+EZGGCb5kg5ktA+aABXe/0MxuBGaAJeB/Ab/u7sff1DVRWkdFRGI3iR7/VcC9HT/fCGwEzgKmgCsn0IaJCHEbRRGRsgUN/Ga2BrgAuK69zd2/7BlaPf41IdswSf1ueShShd37Fpjdvpf1W/cwu32vOiEChO/xfwL4IHCk+xdmthz4V8BX8h5oZpvNbM7M5g4eTOO2cro7ksREV6DSS7DAb2YXAgfcfb7Hn/wR8Bfu/o28X7r7TnefcfeZlStXhmpmqULcRlFkVLoClV5C9vhngYvM7EHgJuA8M/s0gJl9BFgJXBPw9SdOd0eSmOgKVHoJFvjdfZu7r3H3dcClwF53f7eZXQmcD1zm7selgFKmWx5KTHQFKr1UcQeuTwEPAXeaGcAt7v6fKmhHELo7koyrrJLgLedvYNstdx+T7tEVqMCEAr+73wHckX2v2z2K9NAekG0H6/aALDB08G//veaVSDcFYZGI9BuQHSVg6wpU8mjJBpGIaEBWJkGBXyQiGpCVSVDgF4mISoJlEpTjF4mIBmRlEhT4RSKjAVkJTakeEZGGUY+/IXSfABFpU+BvgDInBYlI+pTqaQCt0iginRT4G0CTgkSkkwJ/A2hSkIh0UuBvAE0KEpFOGtxtAE0KEpFOCvwNoUlBItKmVI+ISMMo8IuINIwCv4hIwyjwi4g0jAK/iEjDmLtX3YaBzOwg8NAQDzkN+EGg5kxaXfalLvsB9dmXuuwHaF96eYm7r+zemETgH5aZzbn7TNXtKENd9qUu+wH12Ze67AdoX4alVI+ISMMo8IuINExdA//OqhtQorrsS132A+qzL3XZD9C+DKWWOX4REemtrj1+ERHpQYFfRKRhkg/8Zvagmd1tZvvNbC7b9gIz+3Mz+2729dSq21lEj335qJktZNv2m9lbqm5nEWY2bWY3m9l9Znavmb0uxePSYz+SOyZmtqGjvfvN7Edm9v7Ujkmf/UjumACY2dVmdo+ZfdvMPmtmzzez9WZ2V3ZMdpnZT5X+uqnn+M3sQWDG3X/Qse23gL939+1mthU41d3/Q1VtLKrHvnwUeNrdf7uqdo3CzG4AvuHu12X/uCuAD5HYcemxH+8nwWPSZmbLgAXgNcBvkNgxaevaj18jsWNiZquB/wn8vLsvmtnngC8DbwFucfebzOxTwDfd/ZNlvnbyPf4e3gbckH1/A7CpwrY0jpmdArwB+BMAd/+Jux8isePSZz9S90bg/7j7QyR2TLp07keqTgSmzOxEWp2Kx4HzgJuz3wc5JnUI/A581czmzWxztu2F7v44QPb19MpaN5y8fQF4n5l9y8z+NPZL8cxLgYPA9Wa2z8yuM7OTSO+49NoPSO+YdLoU+Gz2fWrHpFPnfkBix8TdF4DfBh6mFfCfAuaBQ+7+bPZnjwKl30GpDoF/1t1fAbwZ+A0ze0PVDRpD3r58EjgTOJvWP8fHK2xfUScCrwA+6e7nAP8X2Fptk0bSaz9SPCYAZOmqi4DPV92WceTsR3LHJDs5vQ1YD6wCTqL12e9Wej4++cDv7o9lXw8AtwKvBp4wsxcDZF8PVNfC4vL2xd2fcPfD7n4E+GNa+xe7R4FH3f2u7OebaQXQ1I5L7n4kekza3gz8jbs/kf2c2jFpO2Y/Ej0m/wJ4wN0PuvsScAvwemA6S/0ArAEeK/uFkw78ZnaSmZ3c/h54E/Bt4Dbg8uzPLge+WE0Li+u1L+0PZebttPYvau7+d8AjZrYh2/RG4G9J7Lj02o8Uj0mHyzg2PZLUMelwzH4kekweBl5rZivMzDj6Ofk68MvZ3wQ5JklX9ZjZS2n1jKF1Wf4Zd/+Ymf0s8DlgLa03953u/vcVNbOQPvvy32ldvjrwIPDr7ZxszMzsbOA64KeA79OqujiB9I5L3n78PmkekxXAI8BL3f2pbFuKn5W8/Uj1c/IfgUuAZ4F9wJW0cvo3AS/Itr3b3f+h1NdNOfCLiMjwkk71iIjI8BT4RUQaRoFfRKRhFPhFRBpGgV9EpGEU+KXxzGydmRWu+zaz95rZrw74myvM7L/1+N2Hhm2jSJkU+EWG5O6fcvc/G+MpFPilUgr8Ii3LzOyPs7XRv2pmU2Z2ppl9JVs07xtmthGeu0fCB7LvX5UtDHanme3ounJYlT3+u9lS4ZjZdlqrMe43sxsnv5siCvwibS8D/tDdfwE4BLyD1k2v/727vxL4APBHOY+7Hnivu78OONz1u7Npzco8C7jEzM5w963Aoruf7e6/EmhfRPo6cfCfiDTCA+6+P/t+HlhHa8Gsz7eWUQHgeZ0PMLNp4GR3/6ts02eACzv+5GsdSwr8LfASWksNiFRKgV+kpXMtlMPAC2mti352n8dYn9/lPac+bxIFpXpE8v0IeMDM3glgLS/v/AN3fxL4sZm9Ntt0acHnXjKz5eU1VWQ4Cvwivf0K8B4z+yZwD62bZnR7D7DTzO6kdQXwVIHn3Ql8S4O7UhWtzikyBjP7aXd/Ovt+K/Bid7+q4maJ9KWco8h4LjCzbbQ+Sw8BV1TbHJHB1OMXEWkY5fhFRBpGgV9EpGEU+EVEGkaBX0SkYRT4RUQa5v8D2KIOPDg4hIQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(height,weight);\n",
    "plt.xlabel('height')\n",
    "plt.ylabel('weight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question: Do taller people weigh more than shorter people?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### We could just split this into two groups, choosing the mean value as a threshold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample1 = weight[height<height.mean()]\n",
    "sample2 = weight[height>=height.mean()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## By doing this, we can perform a two-sample t-test, as if it were categorical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/land/anaconda3/lib/python3.7/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1,2)\n",
    "\n",
    "axs[0].scatter(height[height<height.mean()], weight[height<height.mean()])\n",
    "axs[0].scatter(height[height>height.mean()], weight[height>height.mean()])\n",
    "axs[1].boxplot([weight[height<height.mean()],weight[height>height.mean()]]);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-3.7868129617579447, pvalue=0.00026318530898211554)"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import ttest_ind\n",
    "ttest_ind(sample1, sample2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The t-test shows us there is a signficant difference between the two groups, which is a valid conclusion. But in dividing the two groups, we have lost information. We no longer know how far to the left or right, inside the group each data point is."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### By using the pearson correlation test, we test not just the difference due to two groups, but the difference due to values across a whole range of data. Often, we'll see greater signficance in correlation tests (if a correlation truly exists)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.4501710655403607, 2.611235184744756e-06)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "from scipy.stats import pearsonr\n",
    "pearsonr(height, weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}