CUPED p-hacking.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-15T15:40:48.706011Z",
     "start_time": "2021-08-15T15:40:48.065707Z"
    }
   },
   "outputs": [],
   "source": [
    "import scipy\n",
    "from math import sqrt\n",
    "from scipy import stats\n",
    "from numpy import cov, linspace\n",
    "from statistics import mean\n",
    "from numpy.random import normal\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-15T15:40:48.716973Z",
     "start_time": "2021-08-15T15:40:48.707909Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_AB_samples(before_mean, before_sigma, eps_sigma, treatment_lift, N):\n",
    "    A_before = list(normal(loc=before_mean, scale=before_sigma, size=N))\n",
    "    B_before = list(normal(loc=before_mean, scale=before_sigma, size=N))\n",
    "    A_after  = [x + normal(loc=0, scale=eps_sigma) for x in A_before]\n",
    "    B_after  = [x + normal(loc=0, scale=eps_sigma) + treatment_lift for x in B_before]\n",
    "    return A_before, B_before, A_after, B_after\n",
    "\n",
    "def get_cuped_adjusted(A_before, B_before, A_after, B_after):\n",
    "    cv = cov([A_after + B_after, A_before + B_before])\n",
    "    theta = cv[0, 1] / cv[1, 1]\n",
    "    mean_before = mean(A_before + B_before)\n",
    "    A_after_adjusted = [after - (before - mean_before) * theta for after, before in zip(A_after, A_before)]\n",
    "    B_after_adjusted = [after - (before - mean_before) * theta for after, before in zip(B_after, B_before)]\n",
    "    return A_after_adjusted, B_after_adjusted\n",
    "\n",
    "def get_cuped_adjusted_lr(A_before, B_before, A_after, B_after):\n",
    "    lr = stats.linregress(A_before + B_before, A_after + B_after)\n",
    "    mean_after = mean(A_after + B_after)\n",
    "    A_after_adjusted = [mean_after + after - (lr.intercept + before * lr.slope) for after, before in zip(A_after, A_before)]\n",
    "    B_after_adjusted = [mean_after + after - (lr.intercept + before * lr.slope) for after, before in zip(B_after, B_before)]\n",
    "    return A_after_adjusted, B_after_adjusted\n",
    "\n",
    "def lift(A, B):\n",
    "    return mean(B) - mean(A)\n",
    "\n",
    "def expected_lift_ratio(A_before, B_before, A_after, B_after):\n",
    "    cv = cov([A_after + B_after, A_before + B_before])\n",
    "    corr = cv[0, 1] / (sqrt(cv[0, 0]) * sqrt(cv[1, 1]))\n",
    "    return 1 - corr**2\n",
    "\n",
    "def p_value(A, B):\n",
    "    return stats.ttest_ind(A, B, alternative='greater')[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-15T15:44:08.114451Z",
     "start_time": "2021-08-15T15:40:48.719441Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulating 10000 A/B tests, true treatment lift is 0...\n",
      "Traditional    A/B testing, mean lift = -0.01, variance of lift = 5.81\n",
      "CUPED adjusted A/B testing, mean lift = -0.01, variance of lift = 0.79\n",
      "Hacked A/B testing, mean lift = 0.88, variance of lift = 2.53\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "before_mean = 100 \n",
    "before_sigma = 50\n",
    "eps_sigma = 20\n",
    "treatment_lift = 0\n",
    "num_simulations = 10*1000\n",
    "\n",
    "print('Simulating %s A/B tests, true treatment lift is %d...' % (num_simulations, treatment_lift))\n",
    "\n",
    "traditional_lifts, adjusted_lifts, hacked_lifts = [], [], []\n",
    "for i in range(num_simulations):\n",
    "    print('%d/%d' % (i, num_simulations), end='\\r')\n",
    "    A_before, B_before, A_after, B_after = get_AB_samples(before_mean, before_sigma, eps_sigma, treatment_lift, N)\n",
    "    A_after_adjusted, B_after_adjusted = get_cuped_adjusted(A_before, B_before, A_after, B_after)\n",
    "    traditional_lifts.append(lift(A_after, B_after))\n",
    "    adjusted_lifts.append(lift(A_after_adjusted, B_after_adjusted))\n",
    "    hacked_lifts.append(max(\n",
    "        lift(A_after, B_after),\n",
    "        lift(A_after_adjusted, B_after_adjusted)\n",
    "    ))\n",
    "    \n",
    "print('Traditional    A/B testing, mean lift = %.2f, variance of lift = %.2f' % (mean(traditional_lifts), cov(traditional_lifts)))\n",
    "print('CUPED adjusted A/B testing, mean lift = %.2f, variance of lift = %.2f' % (mean(adjusted_lifts), cov(adjusted_lifts)))\n",
    "print('Hacked A/B testing, mean lift = %.2f, variance of lift = %.2f' % (mean(hacked_lifts), cov(hacked_lifts)))\n",
    "\n",
    "bins = linspace(-5, 5, 100)\n",
    "plt.figure(figsize=(14, 7))\n",
    "plt.hist(traditional_lifts, bins, alpha=0.5, label='traditional')\n",
    "plt.hist(adjusted_lifts,    bins, alpha=0.5, label='adjusted')\n",
    "plt.hist(hacked_lifts,      bins, alpha=0.5, label='hacked', color='red')\n",
    "plt.xlabel('lift')\n",
    "plt.ylabel('count')\n",
    "plt.legend(loc='upper right')\n",
    "plt.title('lift histogram')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-15T15:44:08.371115Z",
     "start_time": "2021-08-15T15:44:08.116787Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = linspace(-5, 5, 100)\n",
    "plt.figure(figsize=(14, 7))\n",
    "# plt.hist(traditional_lifts, bins, alpha=0.5, label='traditional')\n",
    "# plt.hist(adjusted_lifts,    bins, alpha=0.5, label='adjusted')\n",
    "plt.hist(hacked_lifts,      bins, alpha=0.5, label='hacked', color='red')\n",
    "plt.xlabel('lift')\n",
    "plt.ylabel('count')\n",
    "plt.legend(loc='upper right')\n",
    "plt.title('lift histogram')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-15T15:46:53.578979Z",
     "start_time": "2021-08-15T15:44:08.373697Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulating 10000 A/B tests, true treatment lift is 0...\n",
      "False positive rate (expected: 0.050):\n",
      "Traditional: 0.051\n",
      "CUPED:       0.051\n",
      "p-hacked:    0.075\n"
     ]
    }
   ],
   "source": [
    "N = 1000\n",
    "before_mean = 100 \n",
    "before_sigma = 50\n",
    "eps_sigma = 20\n",
    "treatment_lift = 0\n",
    "num_simulations = 10*1000\n",
    "p_crit = 0.05\n",
    "traditional_fps, cuped_fps, phack_fps = 0, 0, 0\n",
    "\n",
    "print('Simulating %s A/B tests, true treatment lift is %d...' % (num_simulations, treatment_lift))\n",
    "\n",
    "traditional_lifts, adjusted_lifts = [], []\n",
    "traditional_pvalues, adjusted_pvalues = [], []\n",
    "for i in range(num_simulations):\n",
    "    print('%d/%d' % (i, num_simulations), end='\\r')\n",
    "    A_before, B_before, A_after, B_after = get_AB_samples(before_mean, before_sigma, eps_sigma, treatment_lift, N)\n",
    "    A_after_adjusted, B_after_adjusted = get_cuped_adjusted(A_before, B_before, A_after, B_after)\n",
    "    adjusted_pvalue = p_value(A_after_adjusted, B_after_adjusted)\n",
    "    if p_value(A_after, B_after) < p_crit:\n",
    "        traditional_fps += 1\n",
    "    if p_value(A_after_adjusted, B_after_adjusted) < p_crit:\n",
    "        cuped_fps += 1\n",
    "    if lift(A_after, B_after) < lift(A_after_adjusted, B_after_adjusted):\n",
    "        if p_value(A_after, B_after) < p_crit:\n",
    "            phack_fps += 1\n",
    "    else:\n",
    "        if p_value(A_after_adjusted, B_after_adjusted) < p_crit:\n",
    "            phack_fps += 1\n",
    "\n",
    "print('False positive rate (expected: %.3f):' % p_crit)\n",
    "print('Traditional: %.3f' % (traditional_fps/num_simulations))\n",
    "print('CUPED:       %.3f' % (cuped_fps/num_simulations))\n",
    "print('p-hacked:    %.3f' % (phack_fps/num_simulations))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-15T15:46:53.584907Z",
     "start_time": "2021-08-15T15:46:53.581035Z"
    }
   },
   "outputs": [],
   "source": [
    "### no correlation\n",
    "\n",
    "def get_AB_samples_nocorr(mu, sigma, treatment_lift, N):\n",
    "    A_before = list(normal(loc=mu, scale=sigma, size=N))\n",
    "    B_before = list(normal(loc=mu, scale=sigma, size=N))\n",
    "    A_after  = list(normal(loc=mu, scale=sigma, size=N))\n",
    "    B_after  = list(treatment_lift + normal(loc=mu, scale=sigma, size=N))\n",
    "    return A_before, B_before, A_after, B_after"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-15T15:47:05.131248Z",
     "start_time": "2021-08-15T15:46:53.587445Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulating 1000 A/B tests, true treatment lift is 2...\n",
      "Traditional    A/B testing, mean lift = 2.00, variance of lift = 5.75\n",
      "CUPED adjusted A/B testing, mean lift = 1.99, variance of lift = 5.74\n",
      "CUPED lift variance / tradititional lift variance = 1.00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000\n",
    "mu = 100 \n",
    "sigma = 50\n",
    "treatment_lift = 2\n",
    "num_simulations = 1000\n",
    "\n",
    "print('Simulating %s A/B tests, true treatment lift is %d...' % (num_simulations, treatment_lift))\n",
    "\n",
    "traditional_lifts, adjusted_lifts = [], []\n",
    "traditional_pvalues, adjusted_pvalues = [], []\n",
    "for i in range(num_simulations):\n",
    "    print('%d/%d' % (i, num_simulations), end='\\r')\n",
    "    A_before, B_before, A_after, B_after = get_AB_samples_nocorr(mu, sigma, treatment_lift, N)\n",
    "    A_after_adjusted, B_after_adjusted = get_cuped_adjusted(A_before, B_before, A_after, B_after)\n",
    "    traditional_lifts.append(lift(A_after, B_after))\n",
    "    adjusted_lifts.append(lift(A_after_adjusted, B_after_adjusted))\n",
    "    traditional_pvalues.append(p_value(A_after, B_after))\n",
    "    adjusted_pvalues.append(p_value(A_after_adjusted, B_after_adjusted))\n",
    "    \n",
    "print('Traditional    A/B testing, mean lift = %.2f, variance of lift = %.2f' % (mean(traditional_lifts), cov(traditional_lifts)))\n",
    "print('CUPED adjusted A/B testing, mean lift = %.2f, variance of lift = %.2f' % (mean(adjusted_lifts), cov(adjusted_lifts)))\n",
    "print('CUPED lift variance / tradititional lift variance = %.2f' % (cov(adjusted_lifts)/cov(traditional_lifts)))\n",
    "\n",
    "# large_N = 1000*1000\n",
    "# A_before, B_before, A_after, B_after = get_AB_samples(before_mean, before_sigma, eps_sigma, treatment_lift, large_N)\n",
    "# elr = expected_lift_ratio(A_before, B_before, A_after, B_after)\n",
    "# print('CUPED lift variance / tradititional lift variance = %.2f (expected = %.2f)' % (cov(adjusted_lifts)/cov(traditional_lifts), elr))\n",
    "\n",
    "bins = linspace(-6, 10, 50)\n",
    "plt.figure(figsize=(14, 7))\n",
    "plt.hist(traditional_lifts, bins, alpha=0.5, label='traditional')\n",
    "plt.hist(adjusted_lifts,    bins, alpha=0.5, label='adjusted')\n",
    "plt.xlabel('lift')\n",
    "plt.ylabel('count')\n",
    "plt.legend(loc='upper right')\n",
    "plt.title('lift histogram')\n",
    "plt.show()\n",
    "\n",
    "bins = linspace(0, 1, 20)\n",
    "plt.figure(figsize=(14, 7))\n",
    "plt.hist(traditional_pvalues, bins, alpha=0.5, label='traditional')\n",
    "plt.hist(adjusted_pvalues,    bins, alpha=0.5, label='adjusted')\n",
    "plt.legend(loc='upper right')\n",
    "plt.title('p-values')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(14, 7))\n",
    "plt.scatter(traditional_lifts, adjusted_lifts, marker='.')\n",
    "plt.xlabel('traditional lift')\n",
    "plt.ylabel('adjusted list')\n",
    "plt.axvline(x=treatment_lift)\n",
    "plt.axhline(y=treatment_lift)\n",
    "plt.title('traditional lift vs CUPED adjusted lift')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(10, 10))\n",
    "plt.plot([0,1],[0,1])\n",
    "plt.scatter(traditional_pvalues, adjusted_pvalues, marker='.')\n",
    "plt.xlabel('traditional p-values')\n",
    "plt.ylabel('adjusted p-values')\n",
    "plt.title('traditional p-value vs CUPED adjusted p-value')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-15T15:48:05.970766Z",
     "start_time": "2021-08-15T15:47:05.134698Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulating 10000 A/B tests, true treatment lift is 0...\n",
      "False positive rate (expected: 0.050):\n",
      "Traditional: 0.052\n",
      "CUPED:       0.052\n",
      "p-hacked:    0.053\n"
     ]
    }
   ],
   "source": [
    "N = 1000\n",
    "mu = 100 \n",
    "sigma = 50\n",
    "treatment_lift = 0\n",
    "num_simulations = 10000\n",
    "p_crit = 0.05\n",
    "traditional_fps, cuped_fps, phack_fps = 0, 0, 0\n",
    "\n",
    "print('Simulating %s A/B tests, true treatment lift is %d...' % (num_simulations, treatment_lift))\n",
    "\n",
    "traditional_lifts, adjusted_lifts = [], []\n",
    "traditional_pvalues, adjusted_pvalues = [], []\n",
    "for i in range(num_simulations):\n",
    "    print('%d/%d' % (i, num_simulations), end='\\r')\n",
    "    A_before, B_before, A_after, B_after = get_AB_samples_nocorr(mu, sigma, treatment_lift, N)\n",
    "    A_after_adjusted, B_after_adjusted = get_cuped_adjusted(A_before, B_before, A_after, B_after)\n",
    "    adjusted_pvalue = p_value(A_after_adjusted, B_after_adjusted)\n",
    "    if p_value(A_after, B_after) < p_crit:\n",
    "        traditional_fps += 1\n",
    "    if p_value(A_after_adjusted, B_after_adjusted) < p_crit:\n",
    "        cuped_fps += 1\n",
    "    if p_value(A_after, B_after) < p_crit or p_value(A_after_adjusted, B_after_adjusted) < p_crit:\n",
    "        phack_fps += 1\n",
    "\n",
    "print('False positive rate (expected: %.3f):' % p_crit)\n",
    "print('Traditional: %.3f' % (traditional_fps/num_simulations))\n",
    "print('CUPED:       %.3f' % (cuped_fps/num_simulations))\n",
    "print('p-hacked:    %.3f' % (phack_fps/num_simulations))"
   ]
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