causality_analysis_simulated_data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "44.475\n",
      "1819.78\n"
     ]
    }
   ],
   "source": [
    "# get sample sizes\n",
    "\n",
    "print(0.075*593)\n",
    "print(0.01*181978)\n",
    "\n",
    "num_inf = 45\n",
    "num_norm = 1820"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.00000000e+00 -9.64661983e-01  3.34839342e-01]\n",
      " [ 1.50000000e-01 -1.64437138e+00  1.00268228e-01]\n",
      " [ 3.00000000e-01  1.86678775e+00  6.20882069e-02]\n",
      " [ 4.50000000e-01  8.59443801e-01  3.90206286e-01]\n",
      " [ 6.00000000e-01  1.71004441e+00  8.74241679e-02]\n",
      " [ 7.50000000e-01 -1.02102293e+00  3.07376138e-01]\n",
      " [ 9.00000000e-01  2.75911894e+00  5.85243028e-03]\n",
      " [ 1.05000000e+00  1.78725326e+00  7.40590824e-02]\n",
      " [ 1.20000000e+00  2.75961558e+00  5.84357872e-03]\n",
      " [ 1.35000000e+00  3.95537756e+00  7.92748506e-05]\n",
      " [ 1.50000000e+00  2.07093512e+00  3.85022785e-02]\n",
      " [ 1.65000000e+00  3.07806334e+00  2.11387691e-03]\n",
      " [ 1.80000000e+00  4.70753162e+00  2.69237232e-06]\n",
      " [ 1.95000000e+00  4.40464224e+00  1.11977197e-05]\n",
      " [ 2.10000000e+00  4.03400716e+00  5.70480778e-05]\n",
      " [ 2.25000000e+00  5.75245754e+00  1.02590756e-08]\n",
      " [ 2.40000000e+00  5.23280746e+00  1.85778416e-07]\n",
      " [ 2.55000000e+00  6.59217463e+00  5.62670629e-11]\n",
      " [ 2.70000000e+00  6.39168471e+00  2.06802125e-10]\n",
      " [ 2.85000000e+00  6.94797901e+00  5.10354451e-12]\n",
      " [ 3.00000000e+00  5.90524847e+00  4.17506408e-09]\n",
      " [ 3.15000000e+00  5.67526373e+00  1.60257244e-08]\n",
      " [ 3.30000000e+00  6.93460151e+00  5.59714918e-12]\n",
      " [ 3.45000000e+00  8.66083936e+00  9.96343974e-18]\n",
      " [ 3.60000000e+00  9.95070080e+00  9.15711774e-23]\n",
      " [ 3.75000000e+00  8.65195809e+00  1.07380130e-17]\n",
      " [ 3.90000000e+00  8.98852549e+00  5.99601140e-19]\n",
      " [ 4.05000000e+00  9.65929245e+00  1.42483735e-21]\n",
      " [ 4.20000000e+00  7.63168471e+00  3.67483372e-14]\n",
      " [ 4.35000000e+00  8.65768805e+00  1.02317469e-17]\n",
      " [ 4.50000000e+00  8.61770100e+00  1.43238503e-17]\n",
      " [ 4.65000000e+00  9.20002173e+00  9.30270294e-20]\n",
      " [ 4.80000000e+00  1.18324380e+01  3.37004909e-31]\n",
      " [ 4.95000000e+00  1.08367217e+01  1.40447967e-26]\n",
      " [ 5.10000000e+00  1.20634237e+01  2.55091130e-32]\n",
      " [ 5.25000000e+00  1.05217553e+01  3.43464934e-25]\n",
      " [ 5.40000000e+00  1.18312117e+01  3.41616295e-31]\n",
      " [ 5.55000000e+00  1.10860890e+01  1.05490799e-27]\n",
      " [ 5.70000000e+00  1.21052200e+01  1.59189074e-32]\n",
      " [ 5.85000000e+00  1.36095179e+01  2.77000476e-40]\n",
      " [ 6.00000000e+00  1.43339692e+01  2.77714832e-44]]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(422)\n",
    "\n",
    "# define variables\n",
    "norm_mu = 30\n",
    "inf_mu = 30\n",
    "sigma = 3\n",
    "increment = norm_mu*.005\n",
    "iter = 40\n",
    "\n",
    "results = np.empty((iter + 1, 3))\n",
    "\n",
    "# simulate data and perform t-tests\n",
    "for i in range(iter + 1):\n",
    "    inf = np.random.normal(inf_mu, sigma, num_inf)\n",
    "    norm = np.random.normal(norm_mu, sigma, num_norm)\n",
    "    t = stats.ttest_ind(inf, norm)\n",
    "    results[i] = [inf_mu-norm_mu, t[0], t[1]]\n",
    "    inf_mu += increment\n",
    "                  \n",
    "print(results)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n = 300\n",
    "\n",
    "# plot results\n",
    "plt.scatter(results[:,0]/norm_mu, -np.log(results[:,2]))\n",
    "plt.xlabel(\"Percent BMI Difference\")\n",
    "plt.ylabel(\"-log(p-value)\")\n",
    "# p = 0.05\n",
    "plt.hlines(-np.log(0.05), xmin = 0, xmax = (inf_mu-norm_mu)/norm_mu)\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.00000000e+00 -1.92691800e-03  4.94360596e-01]\n",
      " [ 1.50000000e-01  3.06568775e-01  4.79277280e-01]\n",
      " [ 3.00000000e-01  6.69151702e-01  4.46107110e-01]\n",
      " [ 4.50000000e-01  1.00923710e+00  3.67390470e-01]\n",
      " [ 6.00000000e-01  1.33780259e+00  2.85498171e-01]\n",
      " [ 7.50000000e-01  1.70127986e+00  2.08706225e-01]\n",
      " [ 9.00000000e-01  1.91871081e+00  1.61406419e-01]\n",
      " [ 1.05000000e+00  2.31361765e+00  9.13480027e-02]\n",
      " [ 1.20000000e+00  2.74886928e+00  4.94256071e-02]\n",
      " [ 1.35000000e+00  2.99553218e+00  3.54551568e-02]\n",
      " [ 1.50000000e+00  3.28122507e+00  2.14124108e-02]\n",
      " [ 1.65000000e+00  3.63876156e+00  9.98338466e-03]\n",
      " [ 1.80000000e+00  3.97871147e+00  4.61459640e-03]\n",
      " [ 1.95000000e+00  4.26783350e+00  3.20109774e-03]\n",
      " [ 2.10000000e+00  4.66322712e+00  8.37959366e-04]\n",
      " [ 2.25000000e+00  5.00983249e+00  3.39963924e-04]\n",
      " [ 2.40000000e+00  5.35533974e+00  2.04044001e-04]\n",
      " [ 2.55000000e+00  5.65662772e+00  6.00056885e-05]\n",
      " [ 2.70000000e+00  5.94932225e+00  2.43885792e-05]\n",
      " [ 2.85000000e+00  6.24602143e+00  6.35239771e-06]\n",
      " [ 3.00000000e+00  6.62673355e+00  1.13766503e-06]\n",
      " [ 3.15000000e+00  6.92611437e+00  7.91797624e-07]\n",
      " [ 3.30000000e+00  7.31040434e+00  9.18020257e-08]\n",
      " [ 3.45000000e+00  7.58369009e+00  6.80373174e-08]\n",
      " [ 3.60000000e+00  7.91089141e+00  6.83017915e-09]\n",
      " [ 3.75000000e+00  8.29235976e+00  3.79271472e-10]\n",
      " [ 3.90000000e+00  8.57201504e+00  8.58085472e-09]\n",
      " [ 4.05000000e+00  8.92291140e+00  2.75091496e-11]\n",
      " [ 4.20000000e+00  9.25074512e+00  3.91882252e-13]\n",
      " [ 4.35000000e+00  9.61532526e+00  3.36549180e-13]\n",
      " [ 4.50000000e+00  9.95838178e+00  1.10829165e-13]\n",
      " [ 4.65000000e+00  1.03080758e+01  4.07162329e-17]\n",
      " [ 4.80000000e+00  1.05761143e+01  8.62325333e-16]\n",
      " [ 4.95000000e+00  1.09526468e+01  4.70874796e-18]\n",
      " [ 5.10000000e+00  1.12975762e+01  2.71732484e-18]\n",
      " [ 5.25000000e+00  1.16025349e+01  1.45830804e-18]\n",
      " [ 5.40000000e+00  1.19466084e+01  1.56472573e-20]\n",
      " [ 5.55000000e+00  1.22494499e+01  2.48963747e-21]\n",
      " [ 5.70000000e+00  1.25685586e+01  1.60729433e-23]\n",
      " [ 5.85000000e+00  1.29429110e+01  2.91610500e-25]\n",
      " [ 6.00000000e+00  1.32761776e+01  5.33291453e-26]]\n"
     ]
    }
   ],
   "source": [
    "## AVERAGES ##\n",
    "\n",
    "np.random.seed(422)\n",
    "\n",
    "# define variables\n",
    "norm_mu = 30\n",
    "inf_mu = 30\n",
    "sigma = 3\n",
    "increment = norm_mu*.005\n",
    "iter = 40\n",
    "\n",
    "results_avg = np.empty((iter + 1, 3))\n",
    "\n",
    "# simulate data and perform t-tests\n",
    "for i in range(iter + 1):\n",
    "    t = np.empty((1000, 2))\n",
    "    # average for each new value of inf_mu\n",
    "    for j in range(1000):\n",
    "        inf = np.random.normal(inf_mu, sigma, num_inf)\n",
    "        norm = np.random.normal(norm_mu, sigma, num_norm)\n",
    "        t[j] = stats.ttest_ind(inf, norm)\n",
    "    t_0 = np.average(t[:,0])\n",
    "    t_1 = np.average(t[:,1])\n",
    "    results_avg[i] = [inf_mu-norm_mu, t_0, t_1]\n",
    "    inf_mu += increment\n",
    "                  \n",
    "print(results_avg)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": [
    "## AVERAGES ##\n",
    "\n",
    "# plot results\n",
    "plt.scatter(results_avg[:,0]/norm_mu, -np.log(results_avg[:,2]))\n",
    "plt.xlabel(\"Percent BMI Increase\")\n",
    "plt.ylabel(\"-log(p-value)\")\n",
    "# p = 0.05\n",
    "plt.hlines(-np.log(0.05), xmin = 0, xmax = (inf_mu-norm_mu)/norm_mu, label='p<0.05')\n",
    "# p = 0.05 / 300 (Bonferroni - subset)\n",
    "plt.hlines(-np.log(0.05/300), xmin = 0, xmax = (inf_mu-norm_mu)/norm_mu, color = \"RED\", label = \"Bonferroni (subset of phenotypes)\")\n",
    "# p = 0.05 / 17,000 (Bonferroni - all)\n",
    "plt.hlines(-np.log(0.05/17000), xmin = 0, xmax = (inf_mu-norm_mu)/norm_mu, color = \"ORANGE\", label = \"Bonferroni (all UKBB phenotypes)\")\n",
    "\n",
    "plt.legend()\n",
    "plt.savefig(\"Scatterplot1.png\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.04  0.045 0.05  0.055 0.06  0.065 0.07  0.075 0.08  0.085 0.09  0.095\n",
      " 0.1   0.105 0.11  0.115 0.12  0.125 0.13  0.135 0.14  0.145 0.15  0.155\n",
      " 0.16  0.165 0.17  0.175 0.18  0.185 0.19  0.195 0.2  ]\n",
      "[0.085 0.09  0.095 0.1   0.105 0.11  0.115 0.12  0.125 0.13  0.135 0.14\n",
      " 0.145 0.15  0.155 0.16  0.165 0.17  0.175 0.18  0.185 0.19  0.195 0.2  ]\n",
      "[0.1   0.105 0.11  0.115 0.12  0.125 0.13  0.135 0.14  0.145 0.15  0.155\n",
      " 0.16  0.165 0.17  0.175 0.18  0.185 0.19  0.195 0.2  ]\n"
     ]
    }
   ],
   "source": [
    "# find passing mean difference vals\n",
    "\n",
    "pass_vec = []\n",
    "for i in range(iter + 1): \n",
    "    if results_avg[i,2] <= 0.05:\n",
    "        pass_vec.append([results_avg[i,0]/norm_mu,results_avg[i,2]])\n",
    "\n",
    "b_pass_vec = []\n",
    "for i in range(iter + 1): \n",
    "    if results_avg[i,2] <= (0.05/300):\n",
    "        b_pass_vec.append([results_avg[i,0]/norm_mu,results_avg[i,2]])\n",
    "        \n",
    "b_pass_vec_2 = []\n",
    "for i in range(iter + 1): \n",
    "    if results_avg[i,2] <= (0.05/17000):\n",
    "        b_pass_vec_2.append([results_avg[i,0]/norm_mu,results_avg[i,2]])\n",
    "      \n",
    "pass_vec = np.array(pass_vec)\n",
    "b_pass_vec = np.array(b_pass_vec)\n",
    "b_pass_vec_2 = np.array(b_pass_vec_2)\n",
    "\n",
    "print(pass_vec[:,0])\n",
    "print(b_pass_vec[:,0])\n",
    "print(b_pass_vec_2[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lNr3pm623tLRws3UgYblP2WB7raTPS3p/RDy11HvBRsQeSXuk2pW7+VWYhpk3W+/p6VGlUuFm60Cicj3it92qWujfFhFfyJp/aLsje79D0o/yrAE1xWJRpVJp1q0XS6WSisVio0sDUGd5juqxpJKkakTcOOOtL0m6Jnt+jaQv5lUDfqJaraqnp2dWW09Pj6rVaoMqAtAoeR7xXyHp7ZL6bB/KHq+T9JeSXmP7QUmvyV4jZ4VCQZVKZVZbpVJhPn4gQbn18UdERdJ8Hfq/mdd2Mbfp+fhP7eOnqwdID/PxJ4L5+AFMYz5+AGhSzMcPAJBE8ANAcgh+AEgMwQ8AiSH4ASAxK2JUj+0JST9odB1N5GJJP250EcAc2DfPrZ+NiPZTG1dE8OPcsj061xAvoNHYN+uDrh4ASAzBDwCJIfjTtKfRBQDzYN+sA/r4ASAxHPEDQGIIfgBIDMG/QtmemnGDm0PZDe2Xuu562++d8Xqj7Tuz51favuvcV4xmZvvIEpb5DdsPZPvrBcv47I+c8vrfs5+dtseWXy0I/pXr2YjYOuPx8FJWst0iab2kk8EfEeMR8aac6gSmvVXSp7L99dnFFnbNKkmzgj8ifj2vAlNB8DcR2y22P2n7P23fb/tdWfuVtkds75X0HdVud/ni7Mjrk/MdOdleY3s4+7z7bL+hzl8JK0y2r+23faft79m+LQvwd0r6XUkftX1btuyuGfvq9Vlbp+2q7b+VdK9q9+2+INtXp9c77b+L+fZ9zI07cK1cF9g+lD1/KCLeKGlA0v9GxCtsny/pm7a/li1zmaSuiHgo6xbqioitUu2XbZ5tDEnaFxHvsL1e0j22/y0i/i+fr4QmsU3SL0sal/RNSVdExC22eyTdFRF32t4u6VLV9ktL+pLtV0p6RNIvSPqDiHivJNl+8/S+uoA59/2IeCiXb7jCEfwr17Nz/DJsl/RS29PdNj+t2i/Xc5LuOYNfgu2SXm/7Q9nrNkmXSKqeYc1Iwz0RcViSsoOTTkmVU5bZnj3uy16vVW1ffUTSDyLiW8vc5nz7PsE/B4K/uVjSYER8dVajfaWkMzlKt6TfiYj/Oge1IR3HZjyf0tw5Y0kfj4h/mNVY++/zTPfV0/Z9zI0+/ubyVUnvsd0qSbZ/3vaaOZZ7WtK6JX7eoG1nn7ftnFWK1H1V0jtsr5Uk25tsv2CeZSen9+lFPm8p+z7EEX+zuUW1f6vvzcJ6QtKOUxeKiMdsfzM7ofsVSZ+Z5/P+TNKnJd2ffd7Dkq7OoW4kJiK+Zrsg6T+y44ojkt6m2n8Ip9qj2j54b0S8dZ6PXNK+jxqmbACAxNDVAwCJIfgBIDEEPwAkhuAHgMQQ/ACQGIIfABJD8ANAYv4fxR+uEf5MvaEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot null hypothesis box plots (no diff from normal pop)\n",
    "\n",
    "norm_mu = 30\n",
    "inf_mu = 30\n",
    "sigma = 3\n",
    "inf_null = np.random.normal(inf_mu, sigma, num_inf)\n",
    "norm_null = np.random.normal(norm_mu, sigma, num_norm)\n",
    "t_null = stats.ttest_ind(inf, norm)\n",
    "\n",
    "data = [norm_null, inf_null]\n",
    "\n",
    "plt.boxplot(data)\n",
    "plt.hlines(30, xmin = 0.5, xmax = 2.5)\n",
    "plt.xticks([1, 2], ['Fertile', 'Infertile'])\n",
    "plt.ylabel(\"BMI\")\n",
    "plt.savefig(\"Boxplot1.png\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot null hypothesis box plots (both diff from normal pop)\n",
    "\n",
    "norm_mu = 30\n",
    "inf_mu = 30\n",
    "sigma = 3\n",
    "inf_null = np.random.normal(inf_mu, sigma, num_inf)\n",
    "norm_null = np.random.normal(norm_mu, sigma, num_norm)\n",
    "t_null = stats.ttest_ind(inf, norm)\n",
    "\n",
    "data = [norm_null, inf_null]\n",
    "data = np.array(data)+5\n",
    "\n",
    "plt.boxplot(data)\n",
    "plt.hlines(30, xmin = 0.5, xmax = 2.5)\n",
    "plt.xticks([1, 2], ['Fertile', 'Infertile'])\n",
    "plt.ylabel(\"BMI\")\n",
    "plt.savefig(\"Boxplot2.png\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "# plot 20% increase box plots (one diff from normal)\n",
    "\n",
    "data = [norm, inf]\n",
    "plt.boxplot(data)\n",
    "plt.hlines(30, xmin = 0.5, xmax = 2.5)\n",
    "plt.xticks([1, 2], ['Fertile', 'Infertile'])\n",
    "plt.ylabel(\"BMI\")\n",
    "plt.savefig(\"Boxplot3.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": [
    "# plot 20% increase box plots (one diff from normal)\n",
    "\n",
    "data = [norm, inf]\n",
    "data = np.array(data)+5\n",
    "plt.boxplot(data)\n",
    "plt.hlines(30, xmin = 0.5, xmax = 2.5)\n",
    "plt.xticks([1, 2], ['Fertile', 'Infertile'])\n",
    "plt.ylabel(\"BMI\")\n",
    "plt.savefig(\"Boxplot4.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": [
    "# plot 4% increase box plots (more borderline)\n",
    "\n",
    "norm_mu = 30\n",
    "inf_mu = 30 + 8*(norm_mu*.005)\n",
    "sigma = 3\n",
    "inf_null = np.random.normal(inf_mu, sigma, num_inf)\n",
    "norm_null = np.random.normal(norm_mu, sigma, num_norm)\n",
    "t_null = stats.ttest_ind(inf_null, norm_null)\n",
    "\n",
    "data = [norm_null, inf_null]\n",
    "\n",
    "plt.boxplot(data)\n",
    "plt.hlines(30, xmin = 0.5, xmax = 2.5)\n",
    "plt.xticks([1, 2], ['Fertile', 'Infertile'])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1.25\n",
      "1.5\n",
      "1.75\n",
      "2.0\n",
      "2.25\n",
      "2.5\n",
      "2.75\n",
      "3.0\n",
      "3.25\n",
      "3.5\n",
      "3.75\n",
      "4.0\n",
      "4.25\n",
      "4.5\n",
      "4.75\n",
      "5.0\n",
      "[[1.    0.015 0.03  0.03 ]\n",
      " [1.25  0.02  0.035 0.035]\n",
      " [1.5   0.025 0.04  0.04 ]\n",
      " [1.75  0.03  0.05  0.05 ]\n",
      " [2.    0.03  0.055 0.055]\n",
      " [2.25  0.03  0.06  0.06 ]\n",
      " [2.5   0.035 0.065 0.065]\n",
      " [2.75  0.04  0.07  0.07 ]\n",
      " [3.    0.045 0.08  0.08 ]\n",
      " [3.25  0.045 0.095 0.095]\n",
      " [3.5   0.05  0.1   0.1  ]\n",
      " [3.75  0.055 0.105 0.105]\n",
      " [4.    0.055 0.105 0.105]\n",
      " [4.25  0.06  0.105 0.105]\n",
      " [4.5   0.065 0.115 0.115]\n",
      " [4.75  0.07  0.125 0.125]\n",
      " [5.    0.07  0.13  0.13 ]]\n"
     ]
    }
   ],
   "source": [
    "## STANDARD DEVIATION vs. LOWEST EXPECTED REJECTED PERCENT INCREASE ##\n",
    "\n",
    "# define variables\n",
    "norm_mu = 30\n",
    "inf_mu = 30\n",
    "sigma = 1\n",
    "increment = .25\n",
    "increment2 = norm_mu*.005\n",
    "iter = 16\n",
    "iter2 = 160\n",
    "\n",
    "results_sd = np.empty((iter + 1, 4))\n",
    "\n",
    "# simulate data and perform t-tests\n",
    "\n",
    "for s in range(iter + 1):\n",
    "    results_temp = np.empty((iter2 + 1, 3))\n",
    "    norm_mu = 30\n",
    "    inf_mu = 30\n",
    "    # repeat previous process for each value of sigma\n",
    "    for i in range(iter2 + 1):\n",
    "        t = np.empty((100, 2))\n",
    "        # average for each new value of inf_mu\n",
    "        for j in range(100):\n",
    "            inf = np.random.normal(inf_mu, sigma, num_inf)\n",
    "            norm = np.random.normal(norm_mu, sigma, num_norm)\n",
    "            t[j] = stats.ttest_ind(inf, norm)\n",
    "        t_0 = np.average(t[:,0])\n",
    "        t_1 = np.average(t[:,1])\n",
    "        results_temp[i] = [inf_mu-norm_mu, t_0, t_1]\n",
    "        inf_mu += increment2\n",
    "    # find smallest significant value (normal)\n",
    "    v = []\n",
    "    for i in range(iter2 + 1): \n",
    "        if results_temp[i,2] <= 0.05:\n",
    "            v.append([results_temp[i,0]/norm_mu,results_temp[i,2]])\n",
    "    v = np.array(v)\n",
    "    # find smallest significant value (Bonferroni)\n",
    "    b = []\n",
    "    for i in range(iter2 + 1): \n",
    "        if results_temp[i,2] <= (0.05/300):\n",
    "            b.append([results_temp[i,0]/norm_mu,results_temp[i,2]])\n",
    "    b = np.array(b)\n",
    "    b2 = []\n",
    "    for i in range(iter2 + 1): \n",
    "        if results_temp[i,2] <= (0.05/300):\n",
    "            b2.append([results_temp[i,0]/norm_mu,results_temp[i,2]])\n",
    "    b2 = np.array(b2)\n",
    "    print(sigma)\n",
    "    results_sd[s] = [sigma, v[0,0], b[0,0], b2[0,0]]\n",
    "    sigma += increment\n",
    "    \n",
    "print(results_sd)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "# plot sd vs. smallest rejected p-value\n",
    "\n",
    "# plot results (normal)\n",
    "plt.scatter(results_sd[:,0], results_sd[:,1])\n",
    "plt.xlabel(\"BMI Standard Deviation\")\n",
    "plt.ylabel(\"Smallest Percent Increase with Rejected P-Value (Normal)\")\n",
    "plt.ylim([0, 0.15])\n",
    "plt.savefig(\"Scatterplot2.png\")\n",
    "plt.show()\n",
    "\n",
    "# plot results (Bonferroni - subset)\n",
    "plt.scatter(results_sd[:,0], results_sd[:,2], color = \"RED\")\n",
    "plt.xlabel(\"BMI Standard Deviation\")\n",
    "plt.ylabel(\"Smallest Percent Increase with Rejected P-Value (Bonf. subset)\")\n",
    "plt.ylim([0, 0.15])\n",
    "plt.savefig(\"Scatterplot3.png\")\n",
    "plt.show()\n",
    "\n",
    "# plot results (Bonferroni - all)\n",
    "plt.scatter(results_sd[:,0], results_sd[:,3], color = \"ORANGE\")\n",
    "plt.xlabel(\"BMI Standard Deviation\")\n",
    "plt.ylabel(\"Smallest Percent Increase with Rejected P-Value (Bonf. all)\")\n",
    "plt.ylim([0, 0.15])\n",
    "plt.savefig(\"Scatterplot4.png\")\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "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
}