IntroDS005.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Introduction to Data Science<br/>\n",
    "[Oregon Curriculum Network](http://www.4dsolutions.net/ocn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notebooks: \n",
    "[[1](IntroDS001.ipynb)]\n",
    "[[2](IntroDS002.ipynb)]\n",
    "[[3](IntroDS003.ipynb)]\n",
    "[[4](IntroDS004.ipynb)]\n",
    "[[5](IntroDS005.ipynb)]\n",
    "[[6](IntroDS006.ipynb)]\n",
    "[[Appendix](Appendix.ipynb)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# STATISTICAL TESTS\n",
    "\n",
    "The formal idea of a p-value is nuanced.  How rare would our sample be, if drawn at random from a population?  \n",
    "\n",
    "The null hypothesis, that chance explains the difference, is either: \n",
    "\n",
    "* correctly embraced\n",
    "* incorrently embraced (type 1 error, false positive)\n",
    "* correctly rejected, or \n",
    "* incorrectly rejected (type 2 error, false negative)\n",
    "\n",
    "One may accept that some alternative hypothesis is the case, based on a low enough probability that the null hypothesis explains the data.  \n",
    "\n",
    "If the probability or p-value remains higher than the threshold cut-off (the critical value), that doesn't mean the null hypothesis is therefore true, or that it's true with a certain probability.  \n",
    "\n",
    "All we know is there's insufficient evidence to dismiss it.\n",
    "\n",
    "Judging an hypothesis to be more or less probable, given the data, is more what a Bayesian line of thinking would head towards.  The Frequentist turns it around:  given the null hypothesis, how likely is this data?  If the value is low enough, the null hypothesis must be false.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.673658\n",
       "1    3.139568\n",
       "2    5.441804\n",
       "3    3.466903\n",
       "4    3.594128\n",
       "dtype: float64"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "import pandas as pd\n",
    "\n",
    "sample = pd.Series(stats.norm(loc=3.0, scale=1.4).rvs(100))\n",
    "sample.head()  # play with this, check tail?  Practice slicing?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Series([], dtype: float64)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample.iloc[155:160] # up to but no including"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    100.000000\n",
       "mean       3.028628\n",
       "std        1.298260\n",
       "min       -0.504926\n",
       "25%        2.318881\n",
       "50%        3.145365\n",
       "75%        3.831305\n",
       "max        6.357647\n",
       "dtype: float64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uzvxDwPOTfGDcSAurql3dn3uAW5mddl2pdgI753zy+yizvwhWBIt/8bzkxMC6L0uvB7ZX1XVj51lIkqkkJ3fLTwBeCDw4bqrDq6o3V9VTq2qa2b+//1hVvz1yrHklObH7op9uyuRFwIo9Sq2q/gv4VpKzuk0vAFbMwQmjnLm7mq3GS04kuRm4AFibZCfwlqq6ftxU89oAvAq4r5s3B7i6O+N7JVoH3Ngd8XUM8OGqWhWHSK4ipwK3zu4TsAb4YFV9ctxIC/p94KZuB/EbwKtHzvMTHs4pSY1xqkeSGmPxS1JjLH5JaozFL0mNsfglqTEWvyQ1xuKXpMZY/JLUmP8H30DbhUNeMQ8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "sample.plot(kind=\"hist\", bins=10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## T-Test\n",
    "\n",
    "The form of play here is to practice generating data samples, including some that shouldn't register as different, and seeing if they do.\n",
    "\n",
    "People who run the same T-Test over and over, until they get p < 0.05, may be falling into a pitfall, in not continuing those tests.  See what results you get here.\n",
    "\n",
    "Beyond the T-test: ANOVA, Tukey, with Chi-Squared in there somewhere.\n",
    "\n",
    "What we're looking for in all these cases is whether we really looking at a difference that makes a difference.  Are these two sets of data worth distinguishing?  What if we have more than two sets?\n",
    "\n",
    "ANOVO is good at detecting the presence of outliers, without saying who they are.  Tukey is good at comparing the sets pairwise and deciding which pairs might have an above threshold difference, meaning a low probability of differing by chance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import ttest_ind\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "before = np.random.normal(2.1, 0.9, 1000)\n",
    "after  = np.random.normal(2.1, 0.7, 1000)\n",
    "\n",
    "results = ttest_ind(before, after)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like try the same $\\mu$ for both, and just mess with the $\\sigma$, by making the curve sharper.  Try plotting both.\n",
    "\n",
    "Remember, a lot of these tests are pretty worthless if we can't assume a normal distrubution on the part of what our samples sample.  \n",
    "\n",
    "The height of the barley plant needs to taper off symmetrically on both sides of some mean, with no equally salient peak somewhere else."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-0.6419145524341681, pvalue=0.5210023022335031)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\tilde{\\chi}^2$ Test\n",
    "\n",
    "$$\n",
    "\\tilde{\\chi}^2=\\frac{1}{d}\\sum_{k=1}^{n} \\frac{(O_k - E_k)^2}{E_k}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VTcizojd+a0VxFQXZiQwbHOt0FL8z++J0IsKEFSV2Utb0zore+KV9NSfZUdVgJ2HPICkuipl5KbxaXG2Hb0yvrOiNX1pRXIUIXD9hqNNR/Nbcggwq60+xuey401GMn7OiN35HVVlRXMW03GSGhNAEI+fqi/lDiI4Is6tvTK+s6I3f2VndwL6aJrvaphcJMZFcOSaNV0uqcXfY4RtzZlb0xu+sKK4mIkyYM84O2/RmbkEGx062sm5/rdNRjB+zojd+5ZPDNpflpZAcF+V0HL935Zg04qLCWWFDIpizsKI3fmVzWT2V9afs2nkvxUSGc/XF6by2/bDNJ2vOyKuiF5HZIrJHREpF5IEeXv+2iOwUkRIReUtEhnd5zS0iWz0fy7tva0xXK4qriIoI4+qLhzgdJWDMLRjKiVPtvF9q88manvVa9CISDiwG5gD5wG0ikt9ttS1AoapOAJ4HHu3y2ilVnej5mOej3CYIuTuUlduquXJ0Ggk2VZ7XLhuVyqABkSy3oYvNGXizRz8VKFXV/araBiwF5nddQVXXqmqz5+k6IDQn9jQXZP3+WmoaW+1qm3MUFRHGtePTWbPzCKfabEpmczpvij4TKO/yvMKz7EzuAV7r8jxGRIpEZJ2ILOhpAxG517NOUU2Nvf0MVcuLq4iLCufKMWlORwk4cydk0NTmZu2eo05HMX7Im6LvabaHHi/aFZE7gELg510WD1PVQuDLwK9FZORpn0x1iaoWqmphamqqF5FMsGlzdfDa9sN8MX8IA6LCnY4TcKaNGExqQrQdvjE98qboK4CuU85nAaf9NInILOAHwDxVbf1kuapWef7dD7wDTLqAvCZIvV9aw4lT7XbY5jyFhwnXjR/K23uO0tjS7nQc42e8KfqNQJ6I5IpIFHAr8JmrZ0RkEvAEnSV/tMvyJBGJ9jxOAWYAO30V3gSP5VurGDQgkpl59o7ufM0tyKDN1cGanUecjmL8TK9Fr6ouYBGwGtgFLFPVHSLyiIh8chXNz4F44Llul1GOBYpEpBhYC/xUVa3ozWecanOzZucR5oxLJyrCbu04X5OHJZKZOMDmkzWnifBmJVVdBazqtuyhLo9nnWG7D4HxFxLQBL+3dx+lqc1tQxJfIBFhbkEGv39vP3VNbXZnsfmU7T4Zx60oriIlPpppIwY7HSXgzS0YiqtDeW27jWhp/pcVvXFUY0s7b+85yvUThhIe1tMFXuZc5A8dyIjUOBv7xnyGFb1x1Bs7jtDm6mBugY1U6QsiwryCDNYfqOPwiRan4xg/YUVvHLWipIrMxAFMHpbkdJSgMbcgA1VYuc0O35hOVvTGMXVNbby/9xhzCzIQscM2vjIyNZ6LMwba4RvzKSt645jXtlfj6lA7bNMH5hZksLW8nrLa5t5XNkHPit44ZvnWKkamxpE/dKDTUYLOJ5OqryixvXpjRW8ccvhECxsO1tlhmz6SlRTLlOFJdvjGAFb0xiGvllShit0k1YfmThjK7sONfHyk0ekoxmFW9MYRK4qrGJc5kBGp8U5HCVrXThhKmGB79caK3vS/Q7VNFFecsHlh+1haQgyXjhzMiuIqVHscWdyECCt60+8+2cO83g7b9Ll5BRkcrG1me2WD01GMg6zoTb9bUVxN4fAkMhMHOB0l6F1zcTqR4cLy4kqnoxgHWdGbfrXncCN7jjQyb6LtzfeHxNgoLs9L5dWSajo67PBNqLKiN/1qRXEVYQJzxtlNUv1l3sQMqk+0UHTouNNRjEOs6E2/UVWWF1cxY1QKqQnRTscJGbPGDiEmMsyuvglhXhW9iMwWkT0iUioiD/Tw+rdFZKeIlIjIWyIyvMtrd4nIXs/HXb4MbwJLccUJyuqabV7YfhYXHcFVY4ewals1LneH03GMA3otehEJBxYDc4B84DYRye+22hagUFUnAM8Dj3q2TQYeBqYBU4GHRcSGKQxRK4qriAoP45qL052OEnLmTsigtqmND/fVOh3FOMCbPfqpQKmq7lfVNmApML/rCqq6VlU/GT1pHZDleXwNsEZV61T1OLAGmO2b6CaQuDuUV0uq+PzoVAYNiHQ6Tsj5wuhUEqIj7PBNiPKm6DOB8i7PKzzLzuQe4LVz2VZE7hWRIhEpqqmp8SKSCTQbD9ZxpKHVDts4JCYynKsvTuf1HYdpdbmdjmP6mTdF39OIUz1epyUidwCFwM/PZVtVXaKqhapamJqa6kUkE2he2VrFgMhwZo1NczpKyJpbMJTGFhd/22M7U6HGm6KvALK7PM8CTnv/JyKzgB8A81S19Vy2NcGt1eVmZUkVs8elExsV4XSckDVjVArJcVEst8M3Icebot8I5IlIrohEAbcCy7uuICKTgCfoLPmjXV5aDVwtIkmek7BXe5aZELJ291EaWlwsmHS2I36mr0WGhzFnXDpv7jpCU6vL6TimH/Va9KrqAhbRWdC7gGWqukNEHhGReZ7Vfg7EA8+JyFYRWe7Ztg74MZ1/LDYCj3iWmRDy0pZKUhOimTFysNNRQt78iZm0tHewesdhp6OYfuTV+2hVXQWs6rbsoS6PZ51l2yeBJ883oAls9c1trN1dw52XDici3O7Pc1rh8CSykgbw0pZKFk7O6n0DExTsN8/0qZXbqmlzd3CDHbbxC2Fhwg2TMvmg9BhHGlqcjmP6iRW96VMvb6lkVFo8F2fYvLD+4oZJmXQovLLVRrQMFVb0ps+U1zWz8eBxbpiUafPC+pERqfFMzE7kxc1W9KHCit70mZe3dBbJfBuS2O8snJzJ7sON7KyyCUlCgRW96ROqyktbK5mam0xWUqzTcUw310/IICJMeGlLhdNRTD+wojd9YlvlCfbXNLHQTsL6peS4KK4Yk8bLW6tsRMsQYEVv+sRLWyqJCg9jznibYMRfLZyUSU1jKx/YiJZBz4re+JzL3cGK4iquGptmI1X6sSvHpjEwJoKXNtvhm2BnRW987p09NRw72WbXzvu56IhwrpuQweodNiRCsLOiNz733KZyUuI7jwEb//alyZmcanfz+nYbEiGYWdEbnzp2spW3dh3lhkmZRNqQB35vyvAkhiXH8vwmO3wTzOw30fjUy1sqcXUoNxVm976ycZyIcOOULD7aX0tZbXPvG5iAZEVvfEZVea6ogoLsRC4akuB0HOOlG6dkIdJ5yM0EJyt64zPbKk+w50gjNxfaqIiBJCNxAJfnpfL8pgrcHT1OHmcCnBW98ZnniiqIjgizeWED0C2XZFN9ooX39to0g8HIit74REu7m1e2VjJ7XDoDY+za+UBz1dg0kmIjWVZkh2+CkVdFLyKzRWSPiJSKyAM9vH65iGwWEZeI3NjtNbdn1qlPZ54yweeNnUdoaHFxs52EDUjREeHcMCmLNTuPUHuytfcNTEDptehFJBxYDMwB8oHbRCS/22plwFeAZ3v4FKdUdaLnY14Pr5sg8FxROZmJA7h0hE0XGKhuuSSbdrfy0hYbvjjYeLNHPxUoVdX9qtoGLAXmd11BVQ+qaglgoyOFoPK6Zt4vPcaXpmQRFmbjzgeq0ekJFGQnsqyoHFU7KRtMvCn6TKDrgbsKzzJvxYhIkYisE5EFPa0gIvd61imqqbGTQYFm6cYyhM49QhPYbinM5uMjJymuOOF0FOND3hR9T7to5/LnfpiqFgJfBn4tIiNP+2SqS1S1UFULU1NTz+FTG6e1uzv468YKrhyTRmbiAKfjmAt0fcFQYiLD+OvGMqejGB/ypugrgK67allAlbdfQFWrPP/uB94BJp1DPuPn1uw8wrGTrdw+bbjTUYwPDIyJZF5BBi9vqaKhpd3pOMZHvCn6jUCeiOSKSBRwK+DV1TMikiQi0Z7HKcAMYOf5hjX+55n1h8hMHMDlF9k7sWBxx/ThnGp385LNKRs0ei16VXUBi4DVwC5gmaruEJFHRGQegIhcIiIVwE3AEyKyw7P5WKBIRIqBtcBPVdWKPkgcONbEB6W13DY1m3A7CRs0JmQlUpA1iKfWHbKTskEiwpuVVHUVsKrbsoe6PN5I5yGd7tt9CIy/wIzGT/1lQxkRYWLXzgeh26cP53vPl7D+QB3T7ZLZgGd3xprz0tLu5rmicr6YP4S0gTFOxzE+NndCBoMGRPLUukNORzE+YEVvzsvr2w9zvLndTsIGqQFR4dw4JYvV2w9ztLHF6TjmAlnRm/Py1LpD5AyO5XMj7W19sLp92jBcHcpfN9j4N4HOit6cs+LyejYdOs7fXZpjd8IGsRGp8Vw2KoW/bCjD5bab3gOZFb05Z3/84ADx0RHcZOPOB707pg+n6kQLb+466nQUcwGs6M05OdrQwspt1dw4JYsEG4446M0a23nH85PvH3A6irkAVvTmnDy97hCuDuUrn8txOorpBxHhYdw9I4cNB+soqah3Oo45T1b0xmst7W6eWV/GVWPSyEmJczqO6Se3XJJNfHQEf7C9+oBlRW+8tqK4itqmNu6eket0FNOPEmIiubkwm5Ul1VSfOOV0HHMerOiNV1SVP35wkNFDEuySyhB094wcOlT5nw/tBqpAZEVvvPJBaS07qxu4e0YOInZJZajJTo7lmovTeXb9IZpaXU7HMefIit545fG/7SMtIZobJp/LnDMmmHxtZi4NLS5e2FzhdBRzjqzoTa9KKup5v/QY91yWS3REuNNxjEMmD0tiYnYiv3tvv91AFWCs6E2vHv/bPhJiIvjytGFORzEOEhHuv2IU5XWnWF7s9dxDxg9Y0ZuzOnCside2H+bO6cPtBinDVWPSGJOewGPv7KOjw8aqDxReFb2IzBaRPSJSKiIP9PD65SKyWURcInJjt9fuEpG9no+7fBXc9I8l7+4jMjzMLqk0AISFCf/whZGUHj3JGzsPOx3HeKnXoheRcGAxMAfIB24Tkfxuq5UBXwGe7bZtMvAwMA2YCjwsIkkXHtv0h8MnWnhhUyU3F2aRmhDtdBzjJ66fkEHO4FgWr91nM1AFCG/26KcCpaq6X1XbgKXA/K4rqOpBVS0Bup+huQZYo6p1qnocWAPM9kFu0w8ee6eUDlX+/vKRTkcxfiTcs1e/rfIE7+495nQc4wVvij4T6DogdYVnmTcuZFvjoKr6UyzdUM5NhVlkJ8c6Hcf4mRsmZTF0UAyL3y51OorxgjdF39PdMd6+X/NqWxG5V0SKRKSopqbGy09t+tJj75SiKPdfMcrpKMYPRUWEcd/nR7LhYB0flNpevb/zpugrgK6zP2cB3l5b5dW2qrpEVQtVtTA1NdXLT236SmX9Kf66sZybCrPJSrK9edOzW6dmkzEohkdX77Fj9X7Om6LfCOSJSK6IRAG3Asu9/PyrgatFJMlzEvZqzzLjx37reTtue/PmbKIjwvnWrDyKy+ttYhI/12vRq6oLWERnQe8ClqnqDhF5RETmAYjIJSJSAdwEPCEiOzzb1gE/pvOPxUbgEc8y46fKapt5rqicWy7JJjNxgNNxjJ/70uQsclPi+MUbe+y6ej8W4c1KqroKWNVt2UNdHm+k87BMT9s+CTx5ARlNP/r5G3uICBcWXZHndBQTACLCw/g/X7yIb/5lCytKqpg/0a618Ed2Z6z5VHF5PSuKq/j6zBGkD4pxOo4JENePH8qY9AR+teZj2m0MHL9kRW+AzvHm/2PVLgbHRfH3n7fr5o33wsKE780ezcHaZp5eZ+PV+yMregPAW7uOsv5AHf80K4/4aK+O6BnzqStGpzEzL4Vfv7mX+uY2p+OYbqzoDS53Bz99fTcjUuK4daqNUGnOnYjww+vyaWxp59dv7nU6junGit7w9LpDlB49yfdmjyEy3H4kzPkZnZ7AbVOH8ZTn58n4D/utDnE1ja38Ys3HzMxL4ZqLhzgdxwS4b3/xImIjw/nJyp1ORzFdWNGHuJ+9vpuWdjc/mnexzQVrLtjg+Gi+cdUo1u6pYc3OI07HMR5W9CFs06E6nt9UwT2XjWBkarzTcUyQuHtGLqOHJPDwK9ttInE/YUUfotrdHfzryzsYOiiGb1xpQx0Y34kMD+M/Fo6j6kQLv1rzsdNxDFb0IWvJu/vZWd3Aw3PzibPLKY2PTRmezO3ThvHkBwfYXnnC6Tghz4o+BJUebeS/3tzLtePTmT1uqNNxTJD63uwxJMdF8/2XtuG2cXAcZUUfYtwdylWoB5sAAA7fSURBVPeeLyE2Opx/mzfO6TgmiA0aEMmP5uVTUnGCJ97d53SckGZFH2L++MEBNpfV8/DcfJsH1vS568YP5brxQ/nVmo/ZWdXgdJyQZUUfQnYfbuDR1Xu4akwaC2yUQdMPRIR/XzCOxNgovr1sK60ut9ORQpIVfYhoaXfzzb9sYdCASB69cYJdM2/6TVJcFI9+aQK7DzfyyzfsKhwnWNGHiP9YtYuPj5zkFzcVMDjeDtmY/nXFmDS+PG0YT7y7n7V7bDaq/uZV0YvIbBHZIyKlIvJAD69Hi8hfPa+vF5Ecz/IcETklIls9H4/7Nr7xxuodh/nzR4f4+sxcLr/I5uQ1znjo+nzGpCfw7b9upar+lNNxQkqvRS8i4cBiYA6QD9wmIvndVrsHOK6qo4BfAT/r8to+VZ3o+bjPR7mNl0qPnuQ7y4qZkDWI714z2uk4JoTFRIbz2O2TaXN1sOjZzTZJST/yZo9+KlCqqvtVtQ1YCszvts584H88j58HrhI7COy4xpZ2/v6pIqIjwnj8jilER4Q7HcmEuBGp8fz0SxPYXFbPT1bucjpOyPCm6DOB8i7PKzzLelzHM5n4CWCw57VcEdkiIn8TkZk9fQERuVdEikSkqKam5py+AdOzjg7lu88Vc7C2mcW3TybDJvo2fmJuQQZfnZHLnz48yDPrbUaq/uBN0fe0Z979NrczrVMNDFPVScC3gWdFZOBpK6ouUdVCVS1MTbVjyL7w6Oo9rN5xhO9fO5bpIwb3voEx/egH143lC6NTeeiVHXxQeszpOEHPm6KvALK7PM8Cqs60johEAIOAOlVtVdVaAFXdBOwDLrrQ0Obs/vzRQR7/2z7umD6Mr87IcTqOMacJDxN+c9skRqbG8Q9Pb6L0aKPTkYKaN0W/EcgTkVwRiQJuBZZ3W2c5cJfn8Y3A26qqIpLqOZmLiIwA8oD9voluevLGjsP8aPkOZo0dwr/NG2fXyxu/lRATyR/uuoSoiHDu+P0GyuuanY4UtHotes8x90XAamAXsExVd4jIIyIyz7PaH4DBIlJK5yGaTy7BvBwoEZFiOk/S3qeqdb7+Jkyndz+uYdFftjA+K5Hf3DaJ8DAreePfspNjeeqeqTS3ubjzD+s52tjidKSgJKr+NapcYWGhFhUVOR0j4HxQeoyv/mkjI1LjefZr00iKi3I6kjFe21x2nDt+v55hybE887VpdlPfeRCRTapa2NNrdmdsEPiw9Bj3/M9GclPieMZK3gSgycOSWHJnIQeONXHLknUcabA9e1+yog9wr22r5it/3Miw5Fie/to0kq3kTYC6LC+F//nqVKrrT3HT4x/ZMXsfsqIPYE+tO8Q/PruZ8VmDWPb3l5Jib3dNgJs+YjBPf20a9c1t3Pj4hzY7lY9Y0Qcgl7uDn6zcyb++vJ0rR6fx9D3TSIy1PXkTHCYNS2LZfZcSERbGTY9/xOvbDzsdKeBZ0QeY401t3PXHDfzuvQP83aXDeeLOKQyIsqENTHAZkz6Ql++fwej0BO57ehP//dZem47wAljRB5BNh+q4/jfvs/HAcR69cQKPzB9HRLj9LzTBKTUhmqX3TmfBxAx+ueZj7npyAzWNrU7HCkjWEgGg3d3BL9/Yw02Pf0RYGCy771JuLszufUNjAlxMZDi/umUi/7lwPBsP1nHtf7/H2t02nv25sqL3c9sqTrDwsQ/577dLuWFSFqu+OZOJ2YlOxzKm34gIt00dxiuLZpAUG8ndf9rIPy3dQl1Tm9PRAkaE0wFMz06caucXb+zhqXWHSImP5rHbJ3Pt+KFOxzLGMWPSB7LiG5fx2Np9LF5bynt7j/Evs8fwpSlZdhd4L+zOWD/T0u7mmfVlPLa2lOPNbfzdpTl8++qLGBgT6XQ0Y/zG7sMNfP/FbWwuq2dMegI/vC6fy/JSnI7lqLPdGWtF7yda2t28tKWS37y1l6oTLcwYNZgH54xlXOYgp6MZ45dUlZXbqvnZ67sprzvF9BHJLLoijxmjBofkYH5W9H7s2MlWnl53iKfXHeLYyTYKshP53jWjmTEqtPdOjPFWq8vN0+vKWPLuPo40tFKQnchXZ+Qwe1x6SM2qZkXvZ1zuDt7be4wXNlfwxs4jtLk6uHJMGl+7LJdLR4bm3ogxF6rV5ebFzZU88bd9HKxtJjkuihunZHFzYTaj0uKdjtfnrOj9QJurg/UHanlr11FWbqumprGVxNhI5hdkcOelOSHxg2hMf+joUD7Yd4xn15fxxs4juDuUMekJXDd+KHPGD2VkalxQ7kxZ0TtAVSk9epINB+v4sLSWdz+uobHVRXREGJ+/KJWFk7O4ckwaURF2hasxfeVoQwsrt1WzsqSaokPHAchKGsDMvFQuz0th+ojBQTPaqxV9H1NVqk+0sKu6gZ1VDWyrPEHRoeOfXuc7ZGA0V4xOY9bYIcwYlWJDFhjjgOoTp3hz5xHe3XuMj/bVcrLVBUDO4FgmZicyMTuR8VmDGJWWwKABgXeV2wUXvYjMBv4LCAd+r6o/7fZ6NPBnYApQC9yiqgc9rz0I3AO4gW+q6uqzfS1/LXqXu4PapjYq609RVtvModpmDtU2caiumX01J6lvbv903dyUOKYMT2JqbjLTcpMZlhwblG8VjQlU7e4Oisvr2XCwjq1l9Wwpr//M8ApDBkaTl5bAqLR4spNjyUwc0PmRNICk2Ei//H0+W9H3esOUZ87XxcAX6ZwEfKOILFfVnV1Wuwc4rqqjRORW4GfALSKST+ccsxcDGcCbInKRqrov7Fs6Nx0dSpu7gzZ3B63tnf+2tLs52eKiscVFY0s7ja2dj096ntc1t1HT2EpNYyvHTrZS29RG97+JQwfFMHxwLHPGpZM/dCD5GQMZnT6Q+Gi7D80YfxYZHkZhTjKFOclA57vyqhMt7KpqYO/Rk+w92kjp0ZMsKyqnue2zdTUgMpyUhCiS46JJjo0kOS6awfFRJMVGMXBABPHREcRGRRAXHU5cVARx0Z2PY6MiiI4IIyo8jLB+vsHLm0aaCpSq6n4AEVkKzAe6Fv184Eeex88Dv5XOP3nzgaWq2goc8MwpOxX4yDfx/1ddUxu3PPERra4O2lydZd7m6qDV5abdfW6Hp2KjwkkcEEnqwBiykmKZNCyJ1IRoUhOiGTowhpyUWLKSYomJtEMwxgQDEfl0r31W/pBPl6sqx5vbqTx+isr6zo+q+lMcO9lKXVMbRxtb2X24kdqmNtpcHV5/vYgwISoijMjwMKI85R8VEca4zEH85rZJPv/+vCn6TKC8y/MKYNqZ1lFVl4icAAZ7lq/rtm1m9y8gIvcC9wIMGzbM2+yfERURxqi0eKIiwjr/akaEERUeTnTk//5HjO7yWnREOAkxnX99E2IiSYiJ+PS5jQhpjIHOPwDJcVEkx0UxPuvMNy+qKs1tbhpbXDS1uWhqddHU6u78t63zcXObi1ZXB+2endBP/m1z66fPs5MH9Mn34U3R9/Qeo/su8pnW8WZbVHUJsAQ6j9F7kek08dER/L87ppzPpsYYc0FExHOIxj8P23qz61oBdB0TNwuoOtM6IhIBDALqvNzWGGNMH/Km6DcCeSKSKyJRdJ5cXd5tneXAXZ7HNwJva+flPMuBW0UkWkRygTxgg2+iG2OM8Uav7zM8x9wXAavpvLzySVXdISKPAEWquhz4A/CU52RrHZ1/DPCst4zOE7cu4P7+vuLGGGNCnd0wZYwxQeBs19Hb5SXGGBPkrOiNMSbIWdEbY0yQs6I3xpgg53cnY0WkBjjUZVEKcMyhON6yjL5hGX3DMvpGoGUcrqqpPa3kd0XfnYgUnelMsr+wjL5hGX3DMvpGMGW0QzfGGBPkrOiNMSbIBULRL3E6gBcso29YRt+wjL4RNBn9/hi9McaYCxMIe/TGGGMugBW9McYEuYAqehH5roioiKQ4naU7EfmxiJSIyFYReUNEMpzO1J2I/FxEdntyviQiiU5n6k5EbhKRHSLSISJ+c2mbiMwWkT0iUioiDzidpyci8qSIHBWR7U5n6YmIZIvIWhHZ5fl//C2nM3UnIjEiskFEij0Z/83pTGciIuEiskVEXu1t3YApehHJpnOC8jKns5zBz1V1gqpOBF4FHnI6UA/WAONUdQLwMfCgw3l6sh1YCLzrdJBPiEg4sBiYA+QDt3kmvvc3fwJmOx3iLFzAd1R1LDAduN8P/zu2AleqagEwEZgtItMdznQm3wJ2ebNiwBQ98Cvge/QwFaE/UNWGLk/j8MOcqvqGqro8T9fROeOXX1HVXaq6x+kc3UwFSlV1v6q2AUvpnPjer6jqu3TOB+GXVLVaVTd7HjfSWVKnzSHtJO100vM00vPhd7/LIpIFXAf83pv1A6LoRWQeUKmqxU5nORsR+YmIlAO345979F19FXjN6RABIhMo7/K8x0nujfdEJAeYBKx3NsnpPIdEtgJHgTWq6ncZgV/TuePb4c3KfjOTrYi8CaT38NIPgO8DV/dvotOdLaOqvqKqPwB+ICIPAouAh/s1IL1n9KzzAzrfRj/Tn9k+4U1GP+PVJPfGOyISD7wA/FO3d8J+wTML3kTPOayXRGScqvrNeQ8RuR44qqqbROQL3mzjN0WvqrN6Wi4i44FcoFhEoPNww2YRmaqqh/sx4hkz9uBZYCUOFH1vGUXkLuB64Cp16CaKc/jv6C9sknsfEZFIOkv+GVV90ek8Z6Oq9SLyDp3nPfym6IEZwDwRuRaIAQaKyNOqeseZNvD7Qzequk1V01Q1R1Vz6Pylm9zfJd8bEcnr8nQesNupLGciIrOBfwHmqWqz03kCyEYgT0RyRSSKzjmRlzucKeBI557aH4BdqvpLp/P0RERSP7kaTUQGALPws99lVX1QVbM8fXgr8PbZSh4CoOgDyE9FZLuIlNB5mMnvLh0DfgskAGs8l4E+7nSg7kTkBhGpAC4FVorIaqczeU5gLwJW03kCcZmq7nA21elE5C/AR8BoEakQkXucztTNDOBO4ErPz99Wz16pPxkKrPX8Hm+k8xh9r5cv+jsbAsEYY4Kc7dEbY0yQs6I3xpggZ0VvjDFBzoreGGOCnBW9McYEOSt6Y4wJclb0xhgT5P4/y7gRNJ598BYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1000 equally spaced points between -4 and 4 inclusive\n",
    "domain = np.linspace(stats.norm.ppf(0.0001, 0, 1), stats.norm.ppf(0.9999, 0, 1), 1000)   \n",
    "y = stats.norm.pdf(domain, 0, 1) # from scipy.stats\n",
    "plt.plot(domain,y);              # total area under pdf == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "ax1 = plt.subplot('111')\n",
    "df = 20\n",
    "domain = np.linspace(stats.chi2.ppf(0.01, df), stats.chi2.ppf(0.99, df), 100) \n",
    "plt.title(f\"Chi2 df = {df}\")\n",
    "y = stats.chi2.pdf(domain, df) # from scipy.stats\n",
    "plt.plot(domain,y);            # total area under pdf == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "ax1 = plt.subplot('111')\n",
    "plt.title(\"${\\chi}^2$ CMF\")\n",
    "y = stats.chi2.cdf(domain, df) \n",
    "plt.plot(domain, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## F-Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statistics import variance\n",
    "import scipy\n",
    "\n",
    "sampleA = np.random.normal(1000, 100, 15)\n",
    "sampleB = np.random.normal(1000, 110, 20)\n",
    "\n",
    "F = variance(sampleA) / variance(sampleB)\n",
    "df1 = len(sampleA) - 1\n",
    "df2 = len(sampleB) - 1\n",
    "survival = scipy.stats.f.sf(F, df1, df2)\n",
    "pvalue   = scipy.stats.f.cdf(F, df1, df2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7775959531095484"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "survival"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.22240404689045118"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fail to reject the Null Hypothesis H0\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "if pvalue < alpha:\n",
    "    print(\"Reject the Null Hypothesis H0\")\n",
    "else:\n",
    "    print(\"Fail to reject the Null Hypothesis H0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=1.3335698683229018, pvalue=0.26369112973930436)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "\n",
    "sampleA = stats.norm(loc=3.0, scale=1.4).rvs(1000)\n",
    "sampleB = stats.norm(loc=3.0, scale=1.4).rvs(1000)\n",
    "sampleC = stats.norm(loc=3.1, scale=1.4).rvs(1000)\n",
    "\n",
    "stats.f_oneway(sampleA, sampleB, sampleC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/oOuu8IBd-yo\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1a23fcc150>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('oOuu8IBd-yo')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Example Online Tutorial](https://towardsdatascience.com/1-way-anova-from-scratch-dissecting-the-anova-table-with-a-worked-example-170f4f2e58ad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ANCOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ? stats.norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tukey"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For Further Reading\n",
    "\n",
    "Windish, Donna M, and Marie Diener-West. [“A clinician-educator's roadmap to choosing and interpreting statistical tests.”](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1924630/) Journal of general internal medicine vol. 21,6 (2006): 656-60. doi:10.1111/j.1525-1497.2006.00390.x"
   ]
  },
  {
   "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}