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@canyon289
Created February 20, 2021 00:35
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Seeing if I can explain AB Testing
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{
"cells": [
{
"cell_type": "markdown",
"id": "substantial-bacteria",
"metadata": {},
"source": [
"# A/B tests from scratch"
]
},
{
"cell_type": "markdown",
"id": "minimal-orange",
"metadata": {},
"source": [
"## What's the point\n",
"We want to know if one thing is better than the other thing but we want to use principled math to do it. Here's the basic version of how its done"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "secure-anxiety",
"metadata": {},
"outputs": [],
"source": [
"from scipy import stats\n",
"import matplotlib.pyplot as plt\n",
"import arviz as az\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"id": "unavailable-catering",
"metadata": {},
"source": [
"## Step 1: Find two data generating distributions\n",
"It doesn't matter what they are, they just gotta generate data. We'll see why in a second"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "virgin-confusion",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.7248617951383403"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.seed(0)\n",
"def dist_1():\n",
" \"\"\"Bimodel mixture model\"\"\"\n",
" first_dist = stats.bernoulli(p=.7).rvs()\n",
" \n",
" if first_dist:\n",
" return stats.norm(loc=5, scale=1).rvs()\n",
" else:\n",
" return stats.norm(loc=0, scale=1).rvs()\n",
"\n",
"sample_size_1 = 100\n",
"samples_1 = np.array([dist_1() for _ in range(sample_size_1)])\n",
"np.mean(samples_1)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "civil-tutorial",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.35"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Double check against expected mean\n",
"0*.3 + .7*.5"
]
},
{
"cell_type": "markdown",
"id": "greek-plant",
"metadata": {},
"source": [
"### Here's the distribution\n",
"It's bimodal and that might seem scary because people like models that can follow parameters but like we said above no one cares"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "nuclear-mainland",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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lVpfT6jQMlHJzySfPkZ5foqeInHBzYgwA7yd53tGBhoFSbm5VSjoBvl5cNdBzZyh1VkynQMbHd+H9pNNU2j1r8joNA6XcmK3CzqffZTJ1QFfa+/tYXY5LuCUxhvT8ErYcybW6lFalYaCUG9v4fQ75xeV6iqgBrhoYQWigr8ddSHY6DERkvogcF5FSEUkWkQmXaNtNRP4pIgdFpFJE3qylzVwRMbU8Ahr5XpRSNaxKTadjoC8T+4RZXYrL8PfxZmZCNOv3Z3G2yGZ1Oa3GqTAQkdnAIuAZIAHYCqwVkdg6XuIP5ALPAjsu0XUx0K36wxhT6lzpSqlLuVBazhf7s5k+JBJfnaG0QWaPjKG80vDht6etLqXVOPsd8jjwpjHmFWPMAWPMAiATeLC2xsaYE8aYR4wxbwJnL9GvMcZkVX80qHqlVJ3W7cumrMLOjAQ9RdRQfbsGMywmlBW7TnnMKmj1hoGI+AEjgPU1Nq0HxjVx/+1EJE1ETovIJyKS0MT+lFIOq1PTienUjuGxHa0uxSXNGRnD4TOFpJzKt7qUVuHMkUEXwBuoeY92NtCUsWqHgJ8ANwC3AqXAFhHpXVtjEblPRJJEJCknJ6cJu1XK/Z25UMqWI7ncMFRnKG2s6UMjCfTzZsVOz7iQbNmJRGPMNmPMW8aYVGPMJmA2cBRYUEf7JcaYRGNMYliYXgxT6lLW7M7EbtBTRE3Q3t+H6UO6sWZPBoUesAqaM2GQC1QCETWejwCa7Ry/MaYSSAJqPTJQSjlvdWo6AyNDiA8PtroUlzZ7ZCzFtko+3ZNhdSktrt4wMMbYgGRgao1NU6kaVdQspOpYdghVF6aVUo10LKeQPacLmDFM1y1oquGxofQOb8+7HnDPgbOniV4A5orIPSLSX0QWAZHAYgARWSoiS6u/QESGicgwIATo5Ph6QLXtvxaRq0Wkp6Pda1SFweImvyulPNiq1AxE4LqheoqoqUSE2SNjSDmZz/fZ7r0KmlNhYIxZATwKPAmkAuOBa40xaY4msY5HdSmOxwTgOsd/f1ZteyiwBDhA1cikKGCiMWZnw9+GUgrAGMOqlHTG9epM1w56/2ZzuDEhCl9v918FzekLyMaYl4wxccYYf2PMCGPMxmrbJhljJtVoL7U84qptf8wY093RX7gx5mpjzLbmeFNKeaqUU/mcPFvMDXqKqNl0bu/PVQO68uG3pymrqLS6nBajtyUq5UZWp6Tj7+PFNYN0htLmNHtkDOeKq+7odlcaBkq5ifJKO2v2ZDKlfwQhAb5Wl+NWxsd3ISq0He+68T0HGgZKuYnNh3M5W2RjRoKeImpuXl7CnJExbD6Sy/HcIqvLaREaBkq5iY9S0gkN9OVynaG0RcweFYOPl/DO9rT6G7sgDQOl3EBhWQXr92cxbXA3/Hz0x7olhAcHcM2grryffJoSm/tdSNbvGqXcwPp9WZSW2/UUUQu7Y0x3CkrKWeOGdyRrGCjlBlalZhAV2o4ROkNpixrVoxN9ItrzthueKtIwUMrF5VwoY/PhHGYkROLlpTOUtiQR4fYx3dlzuoDdbja1tYaBUi5uze6MqhlK9UazVnFjQhSBft4s3eZeRwcaBkq5uIszlPaO0BlKW0NwgC+zhkezZncGORfKrC6n2WgYKOXCjuUUsltnKG11d18WR7ndzjI3unagYaCUC9MZSq3RM6w9V/YL553taZSWu8cwUw0DpVyUMYbVqTpDqVXmje9JXpGNVSnpVpfSLDQMlHJRKafyScvTGUqtMqZnJwZGhvDa5uMYY6wup8k0DJRyUTpDqbVEhHnje3D4TCEbD+daXU6TaRgo5YLKK+18ojOUWm76kEjCg/15ddMxq0tpMg0DpVzQN4dyyNMZSi3n5+PFXePi2HQ4l4NZ560up0k0DJRyQR+mnKZzkB+T+uoMpVb78ehYAv28WbzhqNWlNImGgVIuJr/Yxpf7z3D9sEh8vfVH2GqhgX7cPqY7H+/OIC3Pddc60O8kpVzMJ3sysVXamTU82upSlMM943vg4+3F4m9c9+hAw0ApF/PBt6fpGxHMwMgQq0tRDuEhAcwZGcPK5NNk5JdYXU6jaBgo5UKO5hSScjKfWSOiENEZStuS+y/vhTGwZKNrjizSMFDKhXz0bTpeojOUtkVRoe24MSGKd3eddMkJ7DQMlHIRdrvho5R0JvQOIzxEp59oi+ZPjsdWYXfJawcaBkq5iO3H8kjPL2HWCL1w3Fb16BLErOHRLNueRmaBa1070DBQykV88G06wf4+XDUgwupS1CU8cmVvjDG8+NURq0tpEA0DpVxAUVkFa/dmMm1INwJ8va0uR11CTKdAbh0Vy3u7TrnUfQcaBkq5gM++y6TYVqmniFzEw5Pj8fEWXvjie6tLcZqGgVIuYMWuU/QMCyKxe0erS1FOCA8JYN74HqxOzSDl5Dmry3GKhoFSbdyRM4UkpZ1jdmKM3lvgQh6cFE9YsD+//WS/S6x3oGGgVBv3ftIpfLyEmTr9hEtp7+/DL67uS8rJfD7enWF1OfVyOgxEZL6IHBeRUhFJFpEJl2jbTUT+KSIHRaRSRN6so90sEdkvImWOf29sxHtQym2VV9r54NvTXNEvnLBgf6vLUQ100/BoBkaG8OzagxSVVVhdziU5FQYiMhtYBDwDJABbgbUiElvHS/yBXOBZYEcdfY4FVgDvAMMc/74vIqMbUL9Sbu1fB86QW2hjzqgYq0tRjeDlJfz2hoFknS/lT58ftLqcS3L2yOBx4E1jzCvGmAPGmAVAJvBgbY2NMSeMMY8YY94EztbR56PA18aYPzj6/AOwwfG8UgpYseskESH+TOyt6xa4qhHdOzF3XBxLt6Wx/Vie1eXUqd4wEBE/YASwvsam9cC4Jux7bC19rqurTxG5T0SSRCQpJyenCbtVyjVkFZTyzfc53DQiGh9dt8Cl/eLqvnTvHMgvV+6h2NY2Txc58x3WBfAGsms8nw00ZSXurg3p0xizxBiTaIxJDAvTv5KU+1uZfAq7gVsS9RSRqwv08+HPs4Zw8mwxz607ZHU5tdI/N5Rqg+x2w4qkU4zt2ZnunYOsLkc1g9E9OzN3XBxvbDnBN9+3vbMbzoRBLlAJ1JwQJQLIasK+s1qgT6XcwsbDOZw6W8Jto+sao6Fc0a9+1I9+XYN5bEVqm5vIrt4wMMbYgGRgao1NU6kaVdRY21qgT6Xcwjs7TtI5yI+rBzblTKxqawJ8vfn7j4dTVl7JI8tTqKi0W13SD5w9TfQCMFdE7hGR/iKyCIgEFgOIyFIRWVr9BSIyTESGASFAJ8fXA6o1WQRcISK/EpF+IvIEMBlY2LS3pJRryywo4V8HsrllZAx+Pnom1930CmvPMzMHs+vEOf77o71t5u5kH2caGWNWiEhn4EmgG7AXuNYYk+ZoUtuxbEqNr68D0oA4R59bRWQO8Hvgt8BRYLYxptb7EpTyFO/uPIUBbh2pp4jc1Q3DojhyppAXvzpCoL83/zN9gOVTjTgVBgDGmJeAl+rYNqmW5+p9Z8aYlcBKZ2tQyt1VVNpZsesUE3uHEds50OpyVAt6fGofisoqeX3LcYL8fPj51X0trcfpMFBKtbwvD2STdb6Up28YaHUpqoWJCE9N70+xrYK/fX2Edn7ePDQ53rJ6NAyUakPe3HqCqNB2XNkv3OpSVCsQEf5w42BKyit5bt0hvL2E+yf2tOSUkYaBUm3EoawLbD92lv+6pp/ecexBvL2E528eSoXd8Ozagxw5U8jT1w8kyL91fz1rGKj/UFZRyd70ApJOnCP1VD6nzhWTVVDK+dIK7HaDCHQO8ic8xJ/4sPYMie5AYlwnBkaGWH4RzJW9te0E/j5ezBmpdxx7Gl9vL16ck0CvsPa8+NVhkk6c5U+zhjC6Z+dWq0HDQAFwOPsCH+/OYOvRPL47XYDNMf65e+dAenQJYnBUBzq088PbCyrtkFdYRtb5UjYdyeXDlHQAokLb8aNBXZkzKpb48PZWvh2XU1BczkffpnPDsEg6BvlZXY6ygJeX8PjUPozr1Zmfvbeb2Uu2M6V/OL+8ph99IoJbfP/SVsa4NkRiYqJJSkqyugyXV1RWwYcp6fxzx0kOZJ7HS2BYTCiJcZ0Y0b0jw2M71juHvjGGzIJSNh/J5fO9WWw+nIut0s6kvmHMnxTPqB6dWunduLZXNx3j958e4JMF4xkU1cHqcpTFSmxVo4wWbzjKhbIKLovvzOS+4Yzt1Zn+XUPw8mrcEbiIJBtjEmvdpmHgeTILSnhl43HeTz7FhdIKBkWFcNPwaKYNiWzyAiq5hWW8s/0ky7ankVtYxlUDInji2v706KLz69Sl0m6Y/PwGwoP9WflgUyYCVu7mbJGNd7an8WFKOsdziwCYOy6O31zfuNFmGgYKqAqBlzcc5d2dp7Abw7WDu3HXuDiGx4Y2+7n+Elslr20+xssbjmKrtPPolD7cP7GnXhitxRf7s7l3aRIv3prAdUMjrS5HtVGZBSVsO5pHjy5BJMR2bFQfGgYeLr/YxsIvD/PPHSexG8PNiTHMn9SLmE4tf1PTmQul/ObjfXz2XRZDY0L535uHEB/e8uc/Xckti7eRnl/CN7+YpGGpWtSlwkAvILux8ko772xP4y9fHuZCaTm3JMbw0OT4VgmBi8KDA3jpxyNYszuDp1bvZdpfN/PHmYN1cXeHlJPn2HniLE9NH6BBoCylYeCmNh3O4ek1+zlyppDL4jvz1PQB9OsaYlk91w2NZHTPTjyyPIXH39vN7lP5PDl9AL4e/gvw1U3HCQ7wYbYOJ1UW0zBwM2eLbPzuk/18lJJO986BLLljBFMHRLSJ8f/hwQG8PW80z649yKubj3Mir5jFt4+gnZ+31aVZ4mReMWv3ZnLfxF60b+UbjJSqSb8D3YQxhjV7Mnn6430UlJTzyJW9eWhyL/x92tYvWh9vL56cPoD48PY88dF33Pn6Dl6bO5KQAF+rS2t1r285jreXMHdcnNWlKKVh4A6yCkp5ctV3fHngDEOjO/DOvaMtPSXkjDmjYgkO8OXRFSncumQ7b/1kFF3aN21YqyvJL7axYtcprh8aRdcOAVaXo5SGgatbszuD//7oO2yVdp6c1p+7L+uBdyNvSGlt04Z0I8jfmwfeTuaWf2zj7XmjiQxtZ3VZreKdHScpKa/k3ok9rC5FKcD5lc5UG3O+tJzHVqSyYHkKvcLb8/lPJ3LPhJ4uEwQXTeobzrJ5o8k5X8bNi7dxLKfQ6pJaXFFZBa9tPs7lfcLa/BGc8hwaBi5ox7E8frRwEx/vzuCxKX14//6xxLnwHb4j4zqx/L4xlJZXcss/tnEo64LVJbWopdvSOFtk46dTeltdilI/0DBwIRWVdp5fd4g5r2zH11tY+cBYfjqlt1uMTx8U1YH3HhiLt5dwx2s7OJlXbHVJLeJCaTn/2HiUyX3DGN7Iu0iVagmu/1vEQ2Tkl3DrK9v529dHuHlENJ8+MqHRt6S3Vb3C2vP2vNHYKu3c8foOzlwotbqkZvfW1hPkF5fz6JQ+Vpei1L/RMHAB/zqQzbV/3cT+jPMsnD2MP980tNUXvmgtvSOCeWPuSHIulHHnazspKCm3uqRmc760nCUbjzGlfzhDY0KtLkepf6Nh0IZV2g3PrzvEvLeSiOzQjjULxjMjIcrqslpcQmxH/nHHCI7mFDLvzV2U2CqtLqlZvL75OOdLK/SoQLVJGgZtVEFxOfPe2vXDaaEP54+jZ5jnLBgzoXcYi+YkkHzyHA++k4ytwm51SU1ytsjGq5uOc/XACF2vQLVJGgZt0KGsC1z/981sOZLL72YM4s83DSHAt23dSdwarh3cjWduHMyGQzn8cuVu7HbXm2H3ope+PkKxrYKfX9XX6lKUqpV7nnh2YZ/uyeQXK3cT5O/D8nvHkBjn2SuF3ToqlrNFNp5bd4hOQf48Nb1/m5hnqSHS80tYuj2NWcOj6d0Kyxcq1RgaBm1Epd3w/PpDvLzhKMNjQ3n59hFEhOg0BQDzJ/Uit7CM17ccp0uwH/MnxVtdUoP8+fODADw6Va8VqLZLw6ANyC+2sWB5CpsO53Lb6Fh+fd2ANjfBnJVEhKemDeBskY0/f36IzkF+zB4Za3VZTtl6NJfVqRk8cmVvojxkqg3lmjQMLHYg8zz3LUsiu6CMP84czK2jXOOXXGvz8hKeu2ko54rLeeLD7wgN9OPqgV2tLuuSbBV2/mf1PmI6tWP+pF5Wl6PUJekFZAt9sieDmS9tpazczrv3j9EgqIefjxcv/3g4g6NDWbA8hR3H8qwu6ZJe33KcI2cK+c11Az1yAIByLRoGFrDbDf+7/hAP/zOFAZEhfLJgvE5N4KQgfx/emDuSmI7tuGdpEvszzltdUq1O5Bax8MvvmdI/giv7R1hdjlL10jBoZUVlFTz4TjIvfnWE2YkxLL93DOF6obhBOgX5sXTeaNr7+3DXGzvb3DxGlXbDz9/fjZ+3F7+fMcjqcpRyitNhICLzReS4iJSKSLKITKin/eWOdqUickxEHqix/TciYmo8shr7RlxBen4JNy3exhf7s3lq+gCenTUYPx/N48aICm3H0p+MwlZRNY9RzoUyq0v6wRtbjpOUdo7fXD9QF65RLsOp30QiMhtYBDwDJABbgbUiUutJbhHpAXzmaJcA/BF4UURm1Wh6COhW7TG4Ee/BJew4lsf1L27m9NliXp87knnje7jcePm2pndEMK/PHUn2+VLmvrGTC6XWz2N05Ewhz607xJT+EdzoAVOHKPfh7J+ljwNvGmNeMcYcMMYsADKBB+to/wCQYYxZ4Gj/CvAW8PMa7SqMMVnVHjmNehdtmDGGt7ae4Mev7qBDO18+eugyJvUNt7ostzGie0devn0Eh7IucN/SZErLrZvHqKyikp+9l0o7P2+emTlIw165lHrDQET8gBHA+hqb1gPj6njZ2FrarwMSRaT6yuc9RSTDcfrpXRHpeYk67hORJBFJyslxjcwoLa/kvz7Yw68/3sflfcJY9fBlxId7zvxCrWVy33Ceu3kI247l8diKVCotmrbi6TX72X26gGdnDiY8WE8PKdfizJFBF8AbyK7xfDZQ10DvrnW093H0B7ADmAtcA9zreM1WEelcW4fGmCXGmERjTGJYWJgTZVsrs6CE2Uu2817SaR65Ip5X7kwkJMC3/heqRrkxIZonp/Vn7d4sfv7+bioqW3diu6XbTvDPHSd54PJeXDOoW6vuW6nmYNlNZ8aYtdW/FpHtwDHgLuAFS4pqJhsOneHx93ZTVl7J4ttHcM2gtn1zlLu4Z0JPSssreX799xSWVfDirQmtMr5/4/c5PL1mP1f2C+cXV+tEdMo1OXNkkAtUAjUHS0cAdY3+yaqjfYWjv/9gjCkE9gEuuzBseaWdZ9ceZO4buwgP9ufjBeM1CFrZw1f05unrB/LF/mzufmMXBcUte1H5UNYFHvrnt/QOb8+iWxPw9tLrBMo11RsGxhgbkAxMrbFpKlWjhWqzrY72ScaYWn86RSQA6EfVhWmXcyK3iJte3srib45y66gYVj10Gb08aP2BtuSucXEsnD2MpLSz3PjSFk7kFrXIfpLTznHLP7bRztebV+9KpL2brj6nPIOzo4leAOaKyD0i0l9EFgGRwGIAEVkqIkurtV8MRInIQkf7e6i6PvD8xQYi8rzjXoQeIjIaWAkEUTXqyGUYY1iZfJppf93EibxiXv7xcP440zPXH2hLZiRE8c49YzhXbGPGS1vYcOhMs/a/4dAZbn91Bx0DffngwXFEdwxs1v6Vam1OhYExZgXwKPAkkAqMB641xqQ5msQ6HhfbHweuBSY62v838Igx5oNq3UYDy6m61+BDoAwYU63PNi/7fCn3L0vm5+/vZlBUB9b+dAI/GqwXD9uKUT06seqhy+gaEsDcN3bxp88PNnno6cWhwve8lUTPsCDef2AcMZ00CJTrE2Ncb/WoxMREk5SUZNn+7XbD8l0nefazg9gq7Tw2tQ/3Tuip54vbqNLySp5es4/lO08R2ymQp6YPYEr/8AbfB3DqbDG//ngfXx08w+S+Yfz11gSCdYSYciEikmyMSax1m4ZBw+xNL+DpNfvYdeIcY3t25o8zBxPXJciSWlTDbD2Sy68/3sfhM4VM6N2FeeN7MLF3GF71hHhBSTmLvznKa5uP4yXwq2v6cde4OL2pTLkcDYNmkJFfwvPrDvFhSjodA3351Y/6cUtijP5CcDHllXbe2nqCxd8cJbfQRmynQKYP6cYV/cLp0SWIAF9vvL2ErIJSdp/O5+uDZ/h8Xxal5XZmJkTxi2v60q2DLlKjXJOGQRMUllWweMNRXtl0DGPg7vFxPDQ5Xm8gc3G2Cjvr9mXx7q6TbD92ts67ljsG+nLNoK7cMSaOAZEhrVylUs3rUmGgY+HqcOZ8KW9vT2Pp9jTyi8u5bmgkv7y6r14sdBN+Pl5cNzSS64ZGkl9sY+fxs6Tnl2CrsFNhN3QK8mNwVAf6dQ3Gx1tnllXuT8OgmvOl5Xy+N4vVqelsO5qHAab0j+ChyfEMiwm1ujzVQkID/biqjS+hqVRL8+gwyCssY8/pAlJP5bP7dD5bj+Zhq7DTvXMgD0+O58bh0fTQi8NKKQ/gUWGw/VgeL351mLxCG3lFth8WRBGB3uHtuW1ULDcMi2RYTKheGFZKeRSPCgNjoLTcTnTHQIZEd6BXWHuGxoQyKKqDTiWglPJoHvUbcGyvznzwYF1LMCillOfSYRJKKaU0DJRSSmkYKKWUQsNAKaUUGgZKKaXQMFBKKYWGgVJKKTQMlFJKoWGglFIKDQOllFJoGCillELDQCmlFBoGSiml0DBQSimFhoFSSik0DJRSSqFhoJRSCg0DpZRSaBgopZRCw0AppRQaBkoppWhAGIjIfBE5LiKlIpIsIhPqaX+5o12piBwTkQea2qdSSqmW4VQYiMhsYBHwDJAAbAXWikhsHe17AJ852iUAfwReFJFZje1TKaVUyxFjTP2NRHYAe4wx91Z77jCw0hjzRC3t/wTMNMb0rvbcq8BAY8zYxvRZXWJioklKSqq3bqWUUv9HRJKNMYm1bav3yEBE/IARwPoam9YD4+p42dha2q8DEkXEt5F9KqWUaiHOnCbqAngD2TWezwa61vGarnW093H01+A+ReQ+EUkSkaScnBwnylZKKeUslxlNZIxZYoxJNMYkhoWFWV2OUkq5FR8n2uQClUBEjecjgKw6XpNVR/sKR3/SiD6VUkq1kHqPDIwxNiAZmFpj01SqRgDVZlsd7ZOMMeWN7FMppVQLcebIAOAFYJmI7AS2AA8AkcBiABFZCmCMudPRfjHwsIgsBP4BXAbMBW51tk+llFKtx6kwMMasEJHOwJNAN2AvcK0xJs3RJLZG++Mici3wF+BBIAN4xBjzQQP6VEop1Uqcus+grdH7DJRSquGadJ+BUkop96dhoJRSSsNAKaWUi14zEJEcoLEXmrtQda+Dp9PPQT+Di/RzqOIJn0N3Y0ytd+26ZBg0hYgk1XUBxZPo56CfwUX6OVTx9M9BTxMppZTSMFBKKeWZYbDE6gLaCP0c9DO4SD+HKh79OXjcNQOllFL/yROPDJRSStWgYaCUUkrDQCmllIeGgYh0EpEXReSgiJSIyCkRedkxi6pbE5H5InJcREpFJFlEJlhdU2sSkSdEZJeInBeRHBFZIyKDrK7LSo7PxIjI36yupbWJSDcRecvxvVAqIvtF5HKr67KCR4YBVesmRAG/BAYDtwMTgeVWFtXSRGQ2sAh4BkigaiGhtSISe8kXupdJwEvAOOAKqlbf+1JEOllZlFVEZAxwH7DH6lpam4iEUrWWigDTgP7AAuCMhWVZRkcTOTjWX/gECDXGnLe6npYgIjuAPcaYe6s9dxhYaYx5wrrKrCMi7YECYIYxZo3V9bQmEekAfAvcA/wa2GuMedjaqlqPiDwDXG6MuczqWtoCTz0yqE0IUAYUW11ISxARP2AEsL7GpvVU/ZXsqYKp+jk4Z3UhFlhC1R8CX1tdiEVmADtEZIWInBGRVBF5WETE6sKsoGHAD4eLvwNeMcZUWFxOS+kCeAPZNZ7PBrq2fjltxiIglap1uz2GiNwLxFO10qCn6gnMB44BV1P1vfAs8JCVRVnFrcJARH7vuBB2qcekGq9pD6wB0qm6hqA8hIi8AIwHZhljKq2up7WISF+qrhvdZowpt7oeC3kB3xpjnjDGpBhj3gD+ioeGgVNrILuQhcDb9bQ5efE/HEHwmePL6caY0haqqy3IBSqBiBrPRwBZrV+OtUTkL8AcYLIx5pjV9bSysVQdKe6rdkbEG5goIg8AQcaYMquKa0WZwP4azx0AfmpBLZZzqzAwxuTi5HzkIhIMrKVqJME1xpjClqzNasYYm4gkA1OB96ttmgp8YE1V1hCRRcBsqoLgoNX1WGAVUHMR8TeAw1QdMdhauyCLbAH61niuD41fK8WluVUYOMsRBOupumg8AwgSkSDH5rPGGHf9YXgBWCYiO6n6QXiAqmG2iy2tqhWJyN+BO6j6/35ORC5eLyl09z8ILjLG5AP51Z8TkSKqvvf3WlGTRf4CbBWR/wZWUDXc+hHg/1lalUU8cmip47pBXSMoJhtjNrRaMa1MROZTdW2kG7AXeMwYs9HaqlqPiNT1Df+0MeY3rVlLWyIiG/CwoaUAIjKNqqOhvlSdQv4b8KLxwF+MHhkGSiml/p1bjSZSSinVOBoGSimlNAyUUkppGCillELDQCmlFBoGSiml0DBQSimFhoFSSing/wP7dmatfdP0bQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax= plt.subplots()\n",
"az.plot_dist(samples_1);"
]
},
{
"cell_type": "markdown",
"id": "marked-branch",
"metadata": {},
"source": [
"### Second Distribution\n",
"For this one I'll be lazy and use a Poisson distribution. Again in this nominal case no one cares what the distribution of data generating processes are"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "creative-rescue",
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(0)\n",
"sample_size_2 = 100\n",
"samples_2 = stats.poisson(4).rvs(100)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "forward-practitioner",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD4CAYAAADlwTGnAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAAAWuklEQVR4nO3df5Af9X3f8efLEsLYjvmls4dIwicPqhMFd4Q5BG1qtQWDRXAkphW2GAIiQ6xkHHWSMkkjNw20ijMDaad0PENdFAuMbX5GDsNNEJFJwWmnLUQHyAhBFB9CRifjcOanG2KwzKt/fD9Kv3w56fak269An9djZud2P/vZfe+OdN/X7e53d2WbiIioz7sO9wZERMThkQCIiKhUAiAiolIJgIiISiUAIiIqNfNwb8BUzJ4924ODg4d7MyIi3lEefvjhH9ge6G1/RwXA4OAgIyMjh3szIiLeUSR9d6L2nAKKiKhUAiAiolIJgIiISiUAIiIqlQCIiKhUAiAiolIJgIiISiUAIiIqlQCIiKjUO+pO4KjX4Np7Wq+x65oLWq8R8XaSI4CIiEolACIiKpUAiIioVAIgIqJSCYCIiEo1CgBJSyXtkDQqae0E86+U9ISkxyT9d0kf6pq3StJ3yrCqq/10SdvKOr8oSdOzSxER0cSkASBpBnA9cD6wELhY0sKebo8CQ7b/IbAR+MOy7AnA1cCZwGLgaknHl2W+BHwWWFCGpYe8NxER0ViTI4DFwKjtnbZfB24Hlnd3sP2A7VfL5IPA3DL+SeA+2y/YfhG4D1gq6STg/bYftG3gq8CFh747ERHRVJMAmAPs7poeK237cwVw7yTLzinjTdcZERHTbFrvBJb0S8AQ8E+ncZ2rgdUAJ5988nStNg5R7syNeOdrcgSwB5jXNT23tL2JpE8Avwsss/3aJMvu4f+fJtrvOgFsr7c9ZHtoYOAtL7WPiIiD1CQAtgALJM2XNAtYCQx3d5B0GnADnQ//57pmbQbOk3R8ufh7HrDZ9rPAK5LOKt/+uQy4exr2JyIiGpr0FJDtvZLW0PkwnwHcaHu7pHXAiO1h4D8C7wP+uHyb8xnby2y/IOn36YQIwDrbL5TxzwFfAY6hc83gXiIiom8aXQOwvQnY1NN2Vdf4Jw6w7I3AjRO0jwCnNt7SiIiYVrkTOCKiUgmAiIhKJQAiIiqVAIiIqFQCICKiUgmAiIhKJQAiIiqVAIiIqFQCICKiUgmAiIhKJQAiIiqVAIiIqFQCICKiUgmAiIhKJQAiIiqVAIiIqFSjAJC0VNIOSaOS1k4wf4mkRyTtlbSiq/2fS9raNfxI0oVl3lckPd01b9F07VRERExu0jeCSZoBXA+cC4wBWyQN236iq9szwOXAb3Uva/sBYFFZzwnAKPDNri6/bXvjIWx/REQcpCavhFwMjNreCSDpdmA58PcBYHtXmffGAdazArjX9qsHvbURETFtmpwCmgPs7poeK21TtRK4raftDyQ9Juk6SUdPtJCk1ZJGJI2Mj48fRNmIiJhIXy4CSzoJ+Ciwuav588DPAGcAJwC/M9GyttfbHrI9NDAw0Pq2RkTUokkA7AHmdU3PLW1T8WngLts/3tdg+1l3vAbcROdUU0RE9EmTANgCLJA0X9IsOqdyhqdY52J6Tv+UowIkCbgQeHyK64yIiEMwaQDY3gusoXP65kngTtvbJa2TtAxA0hmSxoCLgBskbd+3vKRBOkcQf9Gz6lskbQO2AbOBL0zD/kRERENNvgWE7U3App62q7rGt9A5NTTRsruY4KKx7bOnsqERETG9cidwRESlEgAREZVKAEREVCoBEBFRqQRARESlEgAREZVKAEREVCoBEBFRqQRARESlGt0JHG9/g2vvab3GrmsuaL1GRPRPjgAiIiqVAIiIqFQCICKiUgmAiIhKJQAiIiqVAIiIqFSjAJC0VNIOSaOS1k4wf4mkRyTtlbSiZ95PJG0tw3BX+3xJD5V13lFeNxkREX0yaQBImgFcD5wPLAQulrSwp9szwOXArROs4u9sLyrDsq72a4HrbJ8CvAhccRDbHxERB6nJEcBiYNT2TtuvA7cDy7s72N5l+zHgjSZFy4vgzwY2lqab6bwYPiIi+qRJAMwBdndNjzHBO34P4N2SRiQ9KOnC0nYi8FJ54fwB1ylpdVl+ZHx8fAplIyLiQPrxKIgP2d4j6cPA/ZK2AS83Xdj2emA9wNDQkFvaxoiI6jQ5AtgDzOuanlvaGrG9p/zcCXwLOA14HjhO0r4AmtI6IyLi0DUJgC3AgvKtnVnASmB4kmUAkHS8pKPL+Gzg54EnbBt4ANj3jaFVwN1T3fiIiDh4kwZAOU+/BtgMPAncaXu7pHWSlgFIOkPSGHARcIOk7WXxnwVGJH2bzgf+NbafKPN+B7hS0iidawIbpnPHIiLiwBpdA7C9CdjU03ZV1/gWOqdxepf738BH97POnXS+YRQREYdB7gSOiKhUAiAiolIJgIiISiUAIiIqlQCIiKhUAiAiolIJgIiISiUAIiIqlQCIiKhUAiAiolIJgIiISiUAIiIqlQCIiKhUAiAiolIJgIiISjUKAElLJe2QNCpp7QTzl0h6RNJeSSu62hdJ+j+Stkt6TNJnuuZ9RdLTkraWYdG07FFERDQy6QthJM0ArgfOBcaALZKGu97sBfAMcDnwWz2LvwpcZvs7kn4aeFjSZtsvlfm/bXvjIe5DREQchCZvBFsMjJY3eCHpdmA58PcBYHtXmfdG94K2/7pr/HuSngMGgJcOdcMjIuLQNDkFNAfY3TU9VtqmRNJiYBbwVFfzH5RTQ9fte3l8RET0R18uAks6Cfga8Mu29x0lfB74GeAM4AQ6L4mfaNnVkkYkjYyPj/djcyMiqtAkAPYA87qm55a2RiS9H7gH+F3bD+5rt/2sO14DbmI/L4i3vd72kO2hgYGBpmUjImISTQJgC7BA0nxJs4CVwHCTlZf+dwFf7b3YW44KkCTgQuDxKWx3REQcokkDwPZeYA2wGXgSuNP2dknrJC0DkHSGpDHgIuAGSdvL4p8GlgCXT/B1z1skbQO2AbOBL0znjkVExIE1+RYQtjcBm3raruoa30Ln1FDvcl8Hvr6fdZ49pS2NOIINrr2n9Rq7rrmg9RrxzpI7gSMiKpUAiIioVAIgIqJSCYCIiEolACIiKpUAiIioVAIgIqJSCYCIiEolACIiKtXoTuCI2uTO3KhBjgAiIiqVAIiIqFQCICKiUgmAiIhKJQAiIiqVAIiIqFSjAJC0VNIOSaOS1k4wf4mkRyTtlbSiZ94qSd8pw6qu9tMlbSvr/GJ5NWRERPTJpAEgaQZwPXA+sBC4WNLCnm7PAJcDt/YsewJwNXAmnZe+Xy3p+DL7S8BngQVlWHrQexEREVPW5AhgMTBqe6ft14HbgeXdHWzvsv0Y8EbPsp8E7rP9gu0XgfuApeWF8O+3/aBtA1+l82L4iIjokyYBMAfY3TU9Vtqa2N+yc8r4pOuUtFrSiKSR8fHxhmUjImIyb/uLwLbX2x6yPTQwMHC4Nyci4ojRJAD2APO6pueWtib2t+yeMn4w64yIiGnQJAC2AAskzZc0C1gJDDdc/2bgPEnHl4u/5wGbbT8LvCLprPLtn8uAuw9i+yMi4iBNGgC29wJr6HyYPwncaXu7pHWSlgFIOkPSGHARcIOk7WXZF4DfpxMiW4B1pQ3gc8CXgVHgKeDead2ziIg4oEaPg7a9CdjU03ZV1/gW3nxKp7vfjcCNE7SPAKdOZWMjImL6vO0vAkdERDsSABERlUoARERUKgEQEVGpBEBERKUSABERlUoARERUKgEQEVGpBEBERKUSABERlUoARERUKgEQEVGpBEBERKUSABERlWr0OOiYusG197ReY9c1F7ReIyKOXDkCiIioVKMAkLRU0g5Jo5LWTjD/aEl3lPkPSRos7ZdI2to1vCFpUZn3rbLOffM+MJ07FhERBzZpAEiaAVwPnA8sBC6WtLCn2xXAi7ZPAa4DrgWwfYvtRbYXAZcCT9ve2rXcJfvm237ukPcmIiIaa3IEsBgYtb3T9uvA7cDynj7LgZvL+EbgnPKy924Xl2UjIuJtoEkAzAF2d02PlbYJ+5SXyL8MnNjT5zPAbT1tN5XTP783QWAAIGm1pBFJI+Pj4w02NyIimujLRWBJZwKv2n68q/kS2x8FPl6GSyda1vZ620O2hwYGBvqwtRERdWgSAHuAeV3Tc0vbhH0kzQSOBZ7vmr+Snr/+be8pP38I3ErnVFNERPRJkwDYAiyQNF/SLDof5sM9fYaBVWV8BXC/bQNIehfwabrO/0uaKWl2GT8K+BTwOBER0TeT3ghme6+kNcBmYAZwo+3tktYBI7aHgQ3A1ySNAi/QCYl9lgC7be/sajsa2Fw+/GcAfw780bTsUURENNLoTmDbm4BNPW1XdY3/CLhoP8t+Czirp+1vgdOnuK0RETGNcidwRESlEgAREZVKAEREVCoBEBFRqQRARESlEgAREZVKAEREVCoBEBFRqQRARESlEgAREZVKAEREVCoBEBFRqQRARESlEgAREZVKAEREVKpRAEhaKmmHpFFJayeYf7SkO8r8hyQNlvZBSX9XXvy+VdJ/61rmdEnbyjJf3N9L4SMioh2TBoCkGcD1wPnAQuBiSQt7ul0BvGj7FOA64NqueU/ZXlSGX+tq/xLwWWBBGZYe/G5ERMRUNTkCWAyM2t5p+3U67/Zd3tNnOXBzGd8InHOgv+glnQS83/aD5d3BXwUunOrGR0TEwWvySsg5wO6u6THgzP31Ke8Qfhk4scybL+lR4BXg39n+n6X/WM8650xUXNJqYDXAySef3GBzI2Iyg2vvab3GrmsuaL1GHJq2LwI/C5xs+zTgSuBWSe+fygpsr7c9ZHtoYGCglY2MiKhRkwDYA8zrmp5b2ibsI2kmcCzwvO3XbD8PYPth4CngH5T+cydZZ0REtKhJAGwBFkiaL2kWsBIY7ukzDKwq4yuA+21b0kC5iIykD9O52LvT9rPAK5LOKtcKLgPunob9iYiIhia9BlDO6a8BNgMzgBttb5e0DhixPQxsAL4maRR4gU5IACwB1kn6MfAG8Gu2XyjzPgd8BTgGuLcMERHRJ00uAmN7E7Cpp+2qrvEfARdNsNw3gG/sZ50jwKlT2diIiJg+uRM4IqJSCYCIiEolACIiKpUAiIioVAIgIqJSCYCIiEolACIiKpUAiIioVAIgIqJSCYCIiEolACIiKpUAiIioVAIgIqJSCYCIiEolACIiKpUAiIioVKMAkLRU0g5Jo5LWTjD/aEl3lPkPSRos7edKeljStvLz7K5lvlXWubUMH5i2vYqIiElN+kaw8k7f64FzgTFgi6Rh2090dbsCeNH2KZJWAtcCnwF+APyi7e9JOpXOayXndC13SXkzWERE9FmTI4DFwKjtnbZfB24Hlvf0WQ7cXMY3AudIku1HbX+vtG8HjpF09HRseEREHJomATAH2N01Pcab/4p/Ux/be4GXgRN7+vxL4BHbr3W13VRO//yeJE1UXNJqSSOSRsbHxxtsbkRENNGXi8CSfo7OaaFf7Wq+xPZHgY+X4dKJlrW93vaQ7aGBgYH2NzYiohJNAmAPMK9rem5pm7CPpJnAscDzZXoucBdwme2n9i1ge0/5+UPgVjqnmiIiok+aBMAWYIGk+ZJmASuB4Z4+w8CqMr4CuN+2JR0H3AOstf2/9nWWNFPS7DJ+FPAp4PFD2pOIiJiSSQOgnNNfQ+cbPE8Cd9reLmmdpGWl2wbgREmjwJXAvq+KrgFOAa7q+brn0cBmSY8BW+kcQfzRNO5XRERMYtKvgQLY3gRs6mm7qmv8R8BFEyz3BeAL+1nt6c0389ANrr2n9Rq7rrmg9RoRcWD9/l1/J3+25E7giIhKJQAiIiqVAIiIqFQCICKiUgmAiIhKJQAiIiqVAIiIqFQCICKiUgmAiIhKNboTOCLiYPXjTlnInfgHI0cAERGVSgBERFQqARARUakEQEREpRIAERGVSgBERFSqUQBIWipph6RRSWsnmH+0pDvK/IckDXbN+3xp3yHpk03XGRER7Zo0ACTNAK4HzgcWAhdLWtjT7QrgRdunANcB15ZlF9J5h/DPAUuB/yppRsN1RkREi5ocASwGRm3vtP06cDuwvKfPcuDmMr4ROEeSSvvttl+z/TQwWtbXZJ0REdEi2T5wB2kFsNT2r5TpS4Ezba/p6vN46TNWpp8CzgT+PfCg7a+X9g3AvWWxA66za92rgdVl8iPAjoPb1YMyG/jBEVrvSN631Eu91HuzD9ke6G182z8KwvZ6YP3hqC1pxPbQkVjvSN631Eu91GumySmgPcC8rum5pW3CPpJmAscCzx9g2SbrjIiIFjUJgC3AAknzJc2ic1F3uKfPMLCqjK8A7nfn3NIwsLJ8S2g+sAD4y4brjIiIFk16Csj2XklrgM3ADOBG29slrQNGbA8DG4CvSRoFXqDzgU7pdyfwBLAX+HXbPwGYaJ3Tv3uHrN+nnvpZ70jet9RLvdRrYNKLwBERcWTKncAREZVKAEREVCoBMIF+PqZC0o2Sniv3UrRO0jxJD0h6QtJ2Sb/Rcr13S/pLSd8u9f5Dm/W66s6Q9KikP+1DrV2StknaKmmkD/WOk7RR0l9JelLSP2qx1kfKfu0bXpH0my3W+9fl/8njkm6T9O62apV6v1FqbW9rvyb6HZd0gqT7JH2n/Dy+jdqTsp2ha6BzUfop4MPALODbwMIW6y0BPgY83qf9Own4WBn/KeCvW94/Ae8r40cBDwFn9WE/rwRuBf60D7V2AbP78e9X6t0M/EoZnwUc16e6M4Dv07mpqI31zwGeBo4p03cCl7e4P6cCjwPvofOFmD8HTmmhzlt+x4E/BNaW8bXAtf36/9M95Ajgrfr6mArb/4PON6f6wvazth8p4z8EnqTzi9dWPdv+v2XyqDK0+s0DSXOBC4Avt1nncJB0LJ0PlA0Atl+3/VKfyp8DPGX7uy3WmAkcU+4neg/wvRZr/SzwkO1Xbe8F/gL4F9NdZD+/492Pz7kZuHC66zaRAHirOcDurukxWvyAPJzKU1tPo/NXeZt1ZkjaCjwH3Ge71XrAfwH+DfBGy3X2MfBNSQ+XR5e0aT4wDtxUTnF9WdJ7W665z0rgtrZWbnsP8J+AZ4BngZdtf7OtenT++v+4pBMlvQf4Bd58g2qbPmj72TL+feCDfar7JgmASkl6H/AN4Ddtv9JmLds/sb2Izh3fiyWd2lYtSZ8CnrP9cFs1JvBPbH+MztNtf13SkhZrzaRzOuFLtk8D/pbOKYRWlRs2lwF/3GKN4+n8ZTwf+GngvZJ+qa16tp+k8+TibwJ/BmwFftJWvQNsh2n5qHh/EgBvdcQ/pkLSUXQ+/G+x/Sf9qltOVTxA59Hgbfl5YJmkXXRO350t6est1tv3lyu2nwPuonMasS1jwFjXUdRGOoHQtvOBR2z/TYs1PgE8bXvc9o+BPwH+cYv1sL3B9um2lwAv0rkm1g9/I+kkgPLzuT7VfZMEwFsd0Y+pKI/p3gA8afs/96HegKTjyvgxwLnAX7VVz/bnbc+1PUjn3+5+2639FSnpvZJ+at84cB6dUwutsP19YLekj5Smc+jcad+2i2nx9E/xDHCWpPeU/6fn0LlG1RpJHyg/T6Zz/v/WNut16X58zirg7j7VfZO3/dNA+837efRFW/Uk3Qb8M2C2pDHgatsb2qpH5y/kS4Ft5bw8wL+1vamleicBN6vzEqB3AXfabv2rmX30QeCuzucVM4Fbbf9ZyzX/FXBL+QNlJ/DLbRYrwXYu8Ktt1rH9kKSNwCN0Hh3zKO0/MuEbkk4EfkznUTUvTXeBiX7HgWuAOyVdAXwX+PR01220beVrSBERUZmcAoqIqFQCICKiUgmAiIhKJQAiIiqVAIiIqFQCICKiUgmAiIhK/T/NlQQtHQv4wgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"az.plot_dist(samples_2);"
]
},
{
"cell_type": "markdown",
"id": "revised-procurement",
"metadata": {},
"source": [
"## Step 2: Characterize the mean\n",
"So in A/B testing all anyone really cares about the cares about is the mean."
]
},
{
"cell_type": "markdown",
"id": "fuzzy-thompson",
"metadata": {},
"source": [
"### Simulation example: Show distribution of sample means forms a gaussian"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "handled-anime",
"metadata": {},
"outputs": [],
"source": [
"# Number of times we're going to take a bunch of samples\n",
"num_independent_sampling_rounds = 1000\n",
"\n",
"# Number of samples we take each time\n",
"num_samples_each_time = 100\n",
"\n",
"samples = np.empty((num_independent_sampling_rounds, num_samples_each_time))\n",
"\n",
"for i in range(num_independent_sampling_rounds):\n",
" current_samples = [dist_1() for _ in range(num_samples_each_time)]\n",
" samples[i] = current_samples"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "speaking-tomorrow",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1000, 100)"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"samples.shape"
]
},
{
"cell_type": "markdown",
"id": "falling-computer",
"metadata": {},
"source": [
"And now we can plot the distribution of sample means. Crazy how this works huh"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "brown-bearing",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<AxesSubplot:>"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"means = samples.mean(axis=1)\n",
"az.plot_dist(means)"
]
},
{
"cell_type": "markdown",
"id": "tutorial-bottom",
"metadata": {},
"source": [
"### But in real life no one does this. The distribution of the mean is estimated from one sample\n",
"Sampling 1000 times with 100 random examples is expensive and people usually don't care about spending money on statistics. So we just one run trial use tha single trial to estimate the mean and dispersion of the mean\n",
"\n",
"We'll use our original samples from above"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "scenic-andrew",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3.7248617951383403, 2.3073402163632952)"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_dist_1 = samples_1.mean()\n",
"\n",
"# We'll do the bias correction for standard deviation\n",
"standard_error_of_mean_dist_1 = samples_1.std(ddof=1)\n",
"mean_dist_1, standard_error_of_mean_dist_1"
]
},
{
"cell_type": "markdown",
"id": "pharmaceutical-fifteen",
"metadata": {},
"source": [
"### We need to do the same thing for dist 2"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "direct-illustration",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(3.92, 2.0825392426001716)"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_dist_2 = samples_2.mean()\n",
"standard_error_of_mean_dist_2 = samples_2.std(ddof=1) \n",
"mean_dist_2, standard_error_of_mean_dist_2"
]
},
{
"cell_type": "markdown",
"id": "dimensional-beverage",
"metadata": {},
"source": [
"### Write these down as our best guesses"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "modular-cache",
"metadata": {},
"outputs": [],
"source": [
"dist_of_mean_1 = stats.norm(loc=mean_dist_1, scale=standard_error_of_mean_dist_1)\n",
"dist_of_mean_2 = stats.norm(loc=mean_dist_2, scale=standard_error_of_mean_dist_2)"
]
},
{
"cell_type": "markdown",
"id": "guided-latitude",
"metadata": {},
"source": [
"## Step 3: Figure out which population distribution we think is better by using the estimated distribution of means and a hypothesis testing framework\n",
"All the business people want to know which population has a better mean"
]
},
{
"cell_type": "markdown",
"id": "quick-catholic",
"metadata": {},
"source": [
"### Lets first plot things because plots are nice"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "remarkable-danish",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcaf4877280>"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"# Generate a grid of possible means\n",
"x = np.linspace(-10, 10, 100)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, dist_of_mean_1.pdf(x), label='Dist 1')\n",
"ax.plot(x, dist_of_mean_2.pdf(x), label='Dist 2');\n",
"ax.legend()"
]
},
{
"cell_type": "markdown",
"id": "colored-experience",
"metadata": {},
"source": [
"### Hypothesis testing rundown\n",
"Need to pick null hypothesis, which in our case is *Dist 1 is the best*, because in this A/B test framework of comparison of means we can reject or fail to reject a null hypothesis. We'll also set a \"confidence level\" in our case 95%, one tail, because that's the arbitrary choice people tend to make"
]
},
{
"cell_type": "code",
"execution_count": 57,
"id": "explicit-garden",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"7.520098718634501"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Use PPF to find place where 95% of distribution density 1 is covered\n",
"sig_threshold = dist_of_mean_1.ppf(.95)\n",
"sig_threshold"
]
},
{
"cell_type": "markdown",
"id": "governing-titanium",
"metadata": {},
"source": [
"#### The test: Is this 95% CDF value greater than the value of the mean of dist 2\n",
"In this case no, 3.92 is less than 7.52 so we fail to reject null hypothesis "
]
},
{
"cell_type": "markdown",
"id": "computational-experience",
"metadata": {},
"source": [
"### But let's run another one \n",
"Asssume we have another dist 2 with a mean of 8. Now we can reject the null hypothesis."
]
},
{
"cell_type": "code",
"execution_count": 46,
"id": "mineral-garlic",
"metadata": {},
"outputs": [],
"source": [
"dist_of_mean_2 = stats.norm(loc=8, scale=2)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "broadband-matter",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcaf49720d0>"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
},
{
"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": [
"# Generate a grid of possible means\n",
"x = np.linspace(-5, 15, 100)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, dist_of_mean_1.pdf(x), label='Dist 1')\n",
"ax.plot(x, dist_of_mean_2.pdf(x), label='Dist 2');\n",
"ax.legend();"
]
},
{
"cell_type": "markdown",
"id": "selected-wilson",
"metadata": {},
"source": [
"#### But there's another problem\n",
"Dist 2 has a lot of overlap with Dist 1. What we can do is calculate this thing called power which is the green area shown below."
]
},
{
"cell_type": "code",
"execution_count": 58,
"id": "previous-spray",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fcaf4c64670>"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Kg10+0fvnJCKUJE8jr62Kjs768ctrPkMnAM2v2e2Kh9/YR1xECI/eMG9SjhETHsLDq2az91g7b+6Z6CgoHlTyIVgiIO8i42IYw9HkaYQoO40HdG8gf6ITgObX1u+vZ29NBz9ePYfEqMkbj+amJRkszornlx8cpqt/aPwNJkPpJsi7EEIijDn+aVTHZdBnDmHokG8MC6G5RycAzW8NWG3858bDzEmL5aYlZzJCuftMJuHRG+bR1DXAHzaXTuqxRtVSBq3lMP0K7x/bDTaTmZKEHDLq9zNkHTA6HM1NOgFofuvFbdUca+3j4dWzMXmg1894FmXFc+uyTJ75ooKK5p5JP95JhhtYfTQBAJQmTyfO2k9dyfjz22q+QScAzS919g/x+80lnD89iYtmJHvtuD9cNQuLycTvPy7x2jEBR///hDxDxv53V1liDgBdB982NhDNbToBaH7pyU/LaOsd4uFVc7w6/ntqTDh3n5vD20W1VHrrKmCoHyo+8+mzf3BMFVkTlURk1VdGh6K5SScAze+09QzyzOeVXL8onQWZcV4//rcuzCfEbOKJT7zUFlD9JVj7YMaV3jneWahIzCO7s57W9mqjQ9HcoBOA5nee/6qKviEbD1063ZDjp8SEcdc52by5p9Y7E8iUfgzmUMi9YPKPdZbKEnOxoGguftPoUDQ36ASg+ZXeQSvPfVnB5bNTmTU1xrA4Hrx4GmaT8N9bvHAVULIJcs6H0KjJP9ZZOhaXTr/JwqAeHtovuJUARGSViBwRkVIReXiU9ReJyG4RsYrILSPW2USkyPlY57I8T0S2O/f5qnO6SU07rdd2HqOtd4hvX2JsY+iU2HDuWJ7F2l011Lb3Td6B2quh+YjP1/8Ps5nMVMZnktqwH5vdZnQ42jjGTQAiYgaeAFYDc4E7RWTuiGLVwH3AS6Psok8ptdj5uMFl+S+B3yilpgNtwP1nEL8WRIZsdv68tYKCnAQKchONDocHL56GUvD01orJO8hw908/qP8fVp6YR+pAN/XHdGOwr3PnCmAFUKqUKldKDQKvAGtcCyilKpVS+wC3BgR3TgR/GbDWueivOCaG17Qxvbevntr2Ph48w3H+PS09PoJrF6bxeuExugesk3OQ8k8gNgOSjZ/8xV2lzu6gHQfeMDgSbTzuJIAM4JjLzzWMMsfvaYSLSKGIbBORG53LkoB2pdTwp2bMfYrIA87tC4N5sudgp5TiT5+WMXNKNJf50ITt3zw/j64BK2/sqvH8zu02R/fP/EvAi11dz1ZrRDwtYdFYKj4zOhRtHN5oBM5RShUAdwG/FZEJnb4ppZ5SShUopQpSUlImJ0LN522vaOVwQxf/eEG+V+76ddfirHiWZMfz3JeVnh8ptGEf9LVB/qWe3e9kE6EsMY/s1kp6+zuMjkY7DXcSQC2Q5fJzpnOZW5RStc7ncmALsARoAeJFZHim7gntUws+L3xVRVxECNcvSjc6lFPcd14uFc09fHrUw1eoZZ84nvMv9ux+vaA8MZcIu5Xjh9cbHYp2Gu4kgJ3ADGevnVDgDmDdONsAICIJIhLmfJ0MnA8cVEop4BNguMfQvcA7Ew1eCw7HO/vZWNzAbQWZRIT6zkQow65ZkMaU2DCe+cLDjcHlWyB1HkT7TpWXuyrjM7EDvUffNzoU7TTGTQDOevqHgI3AIeA1pVSxiDwmIjcAiMhyEakBbgWeFJFi5+ZzgEIR2YvjC/8XSqmDznU/Ar4vIqU42gSe9uQb0wLHyzuqsdoVXz8nx+hQRhViNnH3yhy2ljRT2tjlmZ0O9UH1Nkf9vx/qDwmnJjqFyJqdOM73NF9kGb8IKKU2ABtGLHvE5fVOHNU4I7f7Elgwxj7LcfQw0rQxDdnsvLyjmotnppCb7Ls3Qt25IpvHN5fywldVPLpm/tnvsHob2Ab8NgEAVCXkcO6xXbR11pAYlzX+BprX6TuBNZ+26eBxjncOcPdK3zz7H5YUHcbq+VN5a08t/UMeuAGqfAuYQiDnvLPfl0EqErIdw0Ic1LW7vkonAM2nvfBVFRnxEVzqQ10/x3L78iw6+61s2O+BeXHLt0DWCgiLPvt9GaQ6LoMhMTFQ8qHRoWhj0AlA81nlTd18Vd7CXedkY/ahrp9jOTc/idykSF7ZeWz8wqfT2wr1e/26+gfAarZQFZtGQsM+7Mqte0Q1L9MJQPNZa3fVYDYJty47pXnJJ4kIty/PZkdFK2VN3We+o4rPAOX3CQCgKjGXzN42GhsPjl9Y8zqdADSfZLXZeWN3DRfPTCE1NtzocNx287IMLCbh1bO5CijfAqExkL7UY3EZpTzB0fjbptsBfJJOAJpP2lrSzPHOAW4r8I+z/2GpMeFcPieVN3bVMGg9w2qPyq2Qez6Y3eqk59Pqo6fQZw7BVr7Z6FC0UegEoPmk1wqPkRgVymWzpxgdyoTdsTyblp5BPjp0fOIbd9RCSynkXeT5wAxgN5moiM9kSuNhPTy0D9IJQPM5Ld0DfHToODctySDU4n//ohfNTCEtLpzXCs+gGqhyq+M5QBIAQGVCDikD3TTUbDc6FG0E//t0aQHv7aI6hmyK2wr88+Yhs0m4aUkGW0uaaezqn9jGFZ9BRKJjCIgAUeFsB+jU4wL5HJ0ANJ+ilOL1wmMszIwzdMrHs/W1pRnY7Ip1RXXub6SUIwHkXQimwPloNkUm0WkJR+nhoX1O4PyXaQGhuK6Tww1dftP1cyzTU2NYlBnHm7snMMhtWwV0HIPcCycvMCOIUJWQRVpzKUPWQaOj0VzoBKD5lLf21BJiFq5b6HvDPk/U15ZmcrC+k0P1ne5tMHyGnOd/wz+PpzIhm4ShPuqrthodiuZCJwDNZ1htdtbtreOSWakkRIUaHc5Zu35ROhaT8NYeN68CKrZC9FRInjG5gRmgIt7RDtB1eMM4JTVv0glA8xlflrXQ1DXA15ZMZMZR35UYFcqls1N5a08tVts49wScqP+/yK+mf3RXa0Q8baGRmKo+NzoUzYVOAJrPeHtPLTHhFr8Y+M1dNy/NoKlrgC/KWk5fsOkI9DQGVPfPk4hQlZBNRmsFA0MT7BmlTRqdADSf0Dto5YPiBq5dkEZ4iO/N+nWmLp2dSlxECG/uHmfS+BP1/wGaAIDK+GxirQM0VHxidCiak1sJQERWicgRESkVkYdHWX+RiOwWEauI3OKyfLGIfCUixSKyT0Rud1n3nIhUiEiR87HYI+9I80ubDh6nd9DGjQFS/TMszGLmmgVpzvdnHbtgxacQnw0Jvj3vwdkYvh+g68h7BkeiDRs3AYiIGXgCWA3MBe4UkbkjilUD9wEvjVjeC9yjlJoHrAJ+KyLxLut/qJRa7HwUndE70ALCm7trSY8LZ0VuotGheNyaxen0Dtr46FDj6AXsdqj6AnID9+wfoCM8lpawaCxVXxkdiubkzhXACqBUKVWulBoEXgHWuBZQSlUqpfYB9hHLjyqlSpyv64BGIMUjkWsBo6lrgM9Lm1mzJAOTH4z7P1ErchOZGhvOuqIxegMdPwB9bY4bwAJcZUIOWW1V9A2cxXDZmse4kwAyANdBTWqcyyZERFYAoUCZy+L/cFYN/UZEwsbY7gERKRSRwqampokeVvMDG/bXY7MrblwcWNU/w0wm4fpFaWw50kRbzyg3Qg2P/xNoN4CNojIhiyjbEA1lHxkdioaXGoFFJA14AfimUiemBvoxMBtYDiQCPxptW6XUU0qpAqVUQUqKvngIROv21jFrSoxfD/0wnjWLM7DaFe8faDh1ZcVWSMyHuMBMgK4qnfcD9Bz9wOBINHAvAdQCrqNyZTqXuUVEYoH3gH9VSm0bXq6UqlcOA8CzOKqatCBT09bLrqo2bljs/3f+ns689FjyU6J4Z2Q1kN0GVV8Gxdk/QFdYNI3hcYRWbxu/sDbp3EkAO4EZIpInIqHAHcA6d3buLP8W8LxSau2IdWnOZwFuBA5MIG4tQKzf55hA/bqFaQZHMrlEhDWLMthR2Up9R9/fV9TvhYGOgO7+OVJVQjZZ7cfo6e8wOpSgN24CUEpZgYeAjcAh4DWlVLGIPCYiNwCIyHIRqQFuBZ4UkWLn5rcBFwH3jdLd80UR2Q/sB5KBf/fkG9P8w7qiOhZlxZOTFGV0KJPuhsXpKAXr99b/feGJ+v8LjAnKAJUJWUTYrTSWfGh0KEHPrTnnlFIbgA0jlj3i8nonjqqhkdv9DfjbGPu8bEKRagGntLGbg/Wd/OS6kb2KA1NechQLM+N4Z28t37oo37GwYiskz4SYqcYG50Un2gFKPoAFtxocTXDTdwJrhnl3bx0igV/94+r6hekcqO2ksrkHbENQ/VXQ1P8P6wmNpD4igbBjO4wOJejpBKAZQinFu/vqOCcvkSmx4UaH4zXXOpPd+n11UFcEg91BVf8/rDohm+yOWrr7Wo0OJajpBKAZoriuk/KmHm5YFPhdH12lx0dQkJPAu3vrodI5/k+QXQGAox0gzG6jUXcHNZROAJoh1u+rx2ISVs8PnrrvYdctTOPI8S56jmxxzP0blWR0SF5XGZ+JHX0/gNF0AtC8TinF+n11nD89OSAmfpmoaxakESZDhNZtD4rhH0bTFxJBfWQiETWFRocS1HQC0Lxub00HNW19QdX46yo1Npy70psIsQ+ggrD6Z1h1Qg7ZnfV09ughXoyiE4Dmdev31hFqNnHVvOCr/hl2U0IZNiUcDl9odCiGqUzIIlTZaTyip4k0ik4AmlfZ7Yr39tdz0cxk4iJCjA7HMHP6iziocll3pNfoUAxTFZeBHaGvRLcDGEUnAM2rdle3Ud/Rz3ULA3vsn9Ma7CWkrpDquOWs31eHUsroiAzRHxJOTXQyUTW7g/Z3YDSdADSvWr+vnjCLiSvmTjE6FOMc2w72IWLmXMqx1j721QTvmDhVCTlkdx2nvbPO6FCCkk4AmtfYnNU/l85KJTrMrVFIAlPFZ2CysOjcVYSYxXFTWJCqTMjGgqL5yLtGhxKUdALQvGZnZStNXQMn7oYNWpVbIX0pcQmJXDgjhff21QdtFUh1XDpWMdGvB4YzhE4Amtes31dHRIiZy+ekGh2Kcfo7oXb3ieEfrl2QRl1HP7ur242NyyBD5hCqY6YQV7c3aJOgkXQC0LzCarPzwYEGLpuTSmRoEFf/VH8FynYiAVw5bwqhZhPv7asfZ8PAVZWQTWZPM61t5UaHEnR0AtC8YntFK83dg1wf7NU/FZ+BORSyHBPgxYaHcNHMFDbsr8duD84z4MqEbExAyyHdDuBtOgFoXrF+Xx1RoWYumRXE1T8AFZ9C5goIiTix6PpFaTR09rOrus3AwIxTEzuVQZOZwdJNRocSdNxKACKySkSOiEipiDw8yvqLRGS3iFhF5JYR6+4VkRLn416X5ctEZL9zn487p4bUAtCQs/rnirlTCA8xGx2OcXpaoGE/5F9y0uLL50whzGJi/d7g7A1kM1moik0jseEAdmU3OpygMm4CEBEz8ASwGpgL3CkiI6dwqgbuA14asW0i8FPgHByTvv9URBKcq/8IfAuY4XysOuN3ofm0L8taaOsd4toFQV79Mzz8c/7FJy2ODrNw6axU3tvfgC1Iq4GqEnJI72un8bieGtyb3LkCWAGUKqXKlVKDwCvAGtcCSqlKpdQ+YGT6vhrYpJRqVUq1AZuAVc4J4WOVUtuUo+n/eRwTw2sB6L19dcSEWbhoZorRoRirfAuExkD60lNWXbcojebuAbZXtHg/Lh9QkZANQPuhdQZHElzcSQAZwDGXn2ucy9wx1rYZztfj7lNEHhCRQhEpbGrSowb6m0Gro/rnymCv/gEo/9Qx+bv51F5Ql81OJSLEzPog7Q1UH51KrzkEW9lmo0MJKj7fCKyUekopVaCUKkhJCfIzSD/0eWkTnf1WrlsU5NU/bVXQVnFK9c+wyFALl89J5YMDDVhtwVcPbjeZqIzPYkrjIWw2q9HhBA13EkAtkOXyc6ZzmTvG2rbW+fpM9qn5kfV764kNt3DB9CBP3hWfOp5HNAC7um5hOq09g3xZFqTVQIk5JA/20nBsm9GhBA13EsBOYIaI5IlIKHAH4G5F3UbgKhFJcDb+XgVsVErVA50istLZ++ce4J0ziF/zYf1DNj48eJzV89MItfj8xebkKv8UoqdAyuwxi1wyK4XoMEvQjg1U7mwH6Dys2wG8ZdxPpVLKCjyE48v8EPCaUqpYRB4TkRsARGS5iNQAtwJPikixc9tW4N9wJJGdwGPOZQDfAf4ClAJlwPsefWea4bYcaaJ7QFf/oJTjCiDvYjhNb+fwEDNXzp3CBwcaGLQGXzVQS0QCraFRSPmnRocSNNy6J18ptQHYMGLZIy6vd3JylY5ruWeAZ0ZZXgjMn0iwmn95d18dSVGhnJsffJOen6TxIPQ0jVn/7+r6RWm8taeWz0ubuGx2kA2ZLUJFQg6zm0sYGOwlLDTS6IgCXpBfl2uTpXfQyuZDjaxeMBWLOcj/zYbPaPPGTwAXTE8hLiKE9XuDszdQZWIOUbYh6ks2Gh1KUAjyT6Y2WT461EjfkI3rg3nmr2HlWyBxGsRnjVs01GLi6nlT+PDgcfqHbJMfm48pT3D8jnqOrDc4kuCgE4A2KdbvrWNKbBjLcxONDsVY1kGo+sKt6p9h1y9Kp3vAypYjjZMYmG/qCY2iLjKRsGrdE8gbdALQPK6zf4gtR5q4dkE6JlOQD/F0bDsMdsO0y93e5Nz8JJKjQ1kXpGMDVSbmktNRR0fXcaNDCXg6AWge92HxcQZtdt37B6BsM5gsJ8b/d4fFbOLaBWl8fKiRrv6hSQzON5UnZBOi7DTp7qCTTicAzePW7a0jMyGCJVnxRodivLKPHcM/h8dOaLPrF6UzYLXz0aHgOwuuis90TBN5RPcMn2w6AWge1dQ1wBelzaxZnE7Qj/Dd3QT1e2HaZRPedGl2AhnxEawrCr5qoCFzCJWxaSTU7dbTRE4ynQA0j9qwvx6bXXHDInfHCwxg5Vscz9MnngBMJuG6RWlsLWmmrWfQs3H5gYqkPDJ622hs2Gt0KAFNJwDNo94pqmX21BhmTY0xOhTjlX0MEQmQtviMNr9hUTpWu2LDgeC7J6A0MReAtgNrjQ0kwOkEoHnMsdZedle3c8Ni3fcfpRwNwPmXgunMhsGemxZLfkpUUFYDHY9KpiMkAin92OhQAppOAJrHDHdb1Dd/AceLofs4THe/++dIIsINi9LZUdlKfUefB4PzAyKUJuaR6RwWQpscOgFoHrOuqI6CnASyEvUYLpQ5z1zzLz2r3dy4OAOlCMqrgPKkXMewEEffMzqUgKUTgOYRhxs6OXK8izW6+sehbDOkzIG4s2sMz02OYkl2PG/tCb7pMsoTsrEDvQf1/QCTRScAzSPe3lOH2SRcE+wTvwMMdEPVl2fU/XM0Ny7O4HBDF4fqOz2yP3/RFxLBsehUoqq36e6gk0QnAO2s2e2Kd4pquWhGMknRYUaHY7yKT8E2CDOv8sjurluYhtkkvF0UhFcBSflkdTfS1lpmdCgBya0EICKrROSIiJSKyMOjrA8TkVed67eLSK5z+ddFpMjlYReRxc51W5z7HF6X6sk3pnnPtvIW6jv6uWnpqFNCBJ+jGyE0BrLP88jukqLDuHhmCu/sqcNuD64z4bLEXExAs+4OOinGTQAiYgaeAFYDc4E7RWTuiGL3A21KqenAb4BfAiilXlRKLVZKLQbuBiqUUkUu2319eL1SKviGPgwQb+6pJTrMwlVzg2wCk9EoBSWbYNolYAn12G5vXJJBQ2c/2yqCa77g2tgpdJtDsephISaFO1cAK4BSpVS5UmoQeAVYM6LMGuCvztdrgcvl1HEA7nRuqwWQvkEb7++v55oFUwkPObP+7gGlYT901cGMqz262yvnTCEq1MzbQdYYrMREaVIeWY2HGBwKsq6wXuBOAsgAjrn8XONcNmoZ5xzCHcDIeQBvB14esexZZ/XPT0ZJGJof+PBgAz2DNm5aoqt/ABieyWqGZ+r/h0WEmlk1P4339zcE3UQxpUnTiLEOUH/4XaNDCTheaQQWkXOAXqXUAZfFX1dKLQAudD7uHmPbB0SkUEQKm5qavBCtNhFv7q4lIz6Cc/KCfOKXYUc/dAz9EOP56rCvLc2ga8DKhweDa4TQ0sQcbAg9xW8aHUrAcScB1AKuc9llOpeNWkZELEAc4FpZeQcjzv6VUrXO5y7gJRxVTadQSj2llCpQShWkpKS4Ea7mLY2d/WwtaeLGJXriFwB6WqBmJ8z0bPXPsHPzk0iPC2ftrppJ2b+v6g8Jd4wOWqW7g3qaOwlgJzBDRPJEJBTHl/nIOzPWAfc6X98CbFbOv5SImIDbcKn/FxGLiCQ7X4cA1wEH0PzKur112BW6+mdY6UeA8nj9/zCTSbh5WSaflzTR0NE/KcfwVaUp00nra6OpttDoUALKuAnAWaf/ELAROAS8ppQqFpHHROQGZ7GngSQRKQW+D7h2Fb0IOKaUKndZFgZsFJF9QBGOK4g/n+2b0bxHKcXaXTUsyoxjemq00eH4hpKNEJUC6Usm7RA3L83EruDNPcF1FXAkKR+Atn2vGhxJYLG4U0gptQHYMGLZIy6v+4Fbx9h2C7ByxLIeYNkEY9V8yP7aDg43dPHvN843OhTfYBuC0o9h1jVgmrymtdzkKJbnJrB2Vw3fvnha0Ey60xqZwPHwWCylm4wOJaDoO4G1M/Ja4THCLCauX6TH/gEcQz/0t8Os1ZN+qFuWZVLe1MOeY+2TfixfUpo8ney2ajo7g29gvMmiE4A2Yf1DNt4pqmP1/KnERYQYHY5vOLweLOFnNfyzu65ZkEZ4iCnoGoNLkvIJUXaO7x3Zm1w7UzoBaBO2sbiBrn4rtxVkjV84GCgFh9+DaZdDaNSkHy4mPIRr5qfx7t66oLonoDounV5zKFZ9P4DH6ASgTdhrhcfISoxgZf7Ie/2CVN1u6KyFOdd57ZC3LMukq9/K+0E0XaTdZOZoUh5ZDcX0D3QZHU5A0AlAm5Bjrb18UdrCrcuydN//YYfWg5hh5iqvHXJlfhK5SZG8vP3Y+IUDyOGUmUTbBqk/8LrRoQQEnQC0CVm7qwYRuHmZ7vt/wuH1kHs+RHrvbmiTSbhjRTY7KlspbQyes+HSxFz6TRYG9+sE4Ak6AWhus9rsvFZ4jAumJ5MRH2F0OL6h6Sg0H4XZ13v90LcsyyTELLyyI3iuAqxmCyWJOaTV7MZqHTA6HL+nE4Dmts2HG6nv6OcbK3OMDsV3HF7veJ59rdcPnRwdxlVzp/LG7pqgagw+nDqLWGs/9QffMjoUv6cTgOa2F7dXMzU2nMtn67l7Tji8HtKXnvXcv2fqzhXZtPUOsbG4wZDjG6EkMY8hMdG7V48uf7Z0AtDcUt3Sy2clTdyxIguLWf/bANB+DGp3ebX3z0jnTUsiKzGCl3dUGxaDtw1aQilJyCa1ejs225DR4fg1/UnW3PLSjmpMItyxPNvoUHzH8PDE824yLASTyfE32VbeSllTt2FxeNuR1FkkDPVSO1wFp50RnQC0cQ1YbbxWeIzLZ6cyNS7c6HB8x4E3IGMZJOYbGsZtBVmEmIUXvqoyNA5vOpKUj1WEnr0vGR2KX9MJQBvXBwcaaO0Z1I2/rppLoX4vzL/F6EhIiQnj2gVprN1VQ/eA1ehwvKI/JJzS+CxSK7/Q1UBnQScAbVx/21ZFdmIkF0xPNjoU33FgLSCGVv+4uve8XLoHrLwRROMDHZwyl6TBHuoOvm10KH5LJwDttPbVtLOzso17zs3Rd/4OUwr2r4XcCyA2zehoAFiSncCirHj++lUldntwzJp1OHkaAyYzfbufMzoUv6UTgHZaz35RSVSomduW64HfTmjYDy0lMP9moyM5yX3n5VDe1MPnpc1Gh+IVg5ZQDiXlk1G9g8HB4GkA9yS3EoCIrBKRIyJSKiIPj7I+TEReda7fLiK5zuW5ItInIkXOx59ctlkmIvud2zwuwTKzhR853tnP+n113FqQRWy4Hvb5hANrwWSBuWuMjuQk1yxIIzk6lL9+WWl0KF5zYOo8omyD1O1+3uhQ/NK4CUBEzMATwGpgLnCniMwdUex+oE0pNR34DfBLl3VlSqnFzseDLsv/CHwLmOF8eG8kLc0tL3xVhdWu+Ob5uUaH4jvsdjjwJky7zKtj/7gjzGLmrhXZbD7SSFVLj9HheEV5Qg6dljCsujfQGXHnCmAFUKqUKldKDeKY3H3kqc8a4K/O12uBy093Ri8iaUCsUmqbc/L454EbJxq8Nnn6h2y8uL2KK+ZMISdp8se49xvVX0HHMZ/o/TOar6/MwWISnv68wuhQvMJuMlGcOpvshmJ6OoNnaGxPcScBZACuo03VOJeNWsY5iXwHMDxYfJ6I7BGRT0XkQpfyrt0VRtsnACLygIgUikhhU1OTG+FqnvD2nlraeoe4/4I8o0PxLXtegLBYmOP9wd/cMSU2nJuWZPBa4TFauoNjsLQDU+cQquw0FP7Z6FD8zmQ3AtcD2UqpJcD3gZdEJHYiO1BKPaWUKlBKFaSkpExKkNrJ7HbF059XMDctlnPyfKuaw1D9HVD8tqPxNzTS6GjG9MBF+fQP2Xk+SG4Mq42ZSlNYDOb9a40Oxe+4kwBqAdcuIJnOZaOWERELEAe0KKUGlFItAEqpXUAZMNNZ3nVA+dH2qRlk06HjlDR288BF+ei2eRcH3gRrHyy52+hITmt6agxXzJnC819V0j8UBF1CRdiXNp/ctipaanYaHY1fcScB7ARmiEieiIQCdwDrRpRZB9zrfH0LsFkppUQkxdmIjIjk42jsLVdK1QOdIrLS2VZwD/COB96PdpaUUjzxSSnZiZFct9A3+rj7jD0vQOpcyFhqdCTj+vYl+bT1DvHJwX6jQ/GKorT52BBav/it0aH4lXETgLNO/yFgI3AIeE0pVSwij4nIDc5iTwNJIlKKo6pnuKvoRcA+ESnC0Tj8oFKq1bnuO8BfgFIcVwbve+YtaWfj89Jm9tV08O1LpulRP10dP+gY+XPJN8AProqW5SRSkJPA+j292JXvx3u2usKiOZyYw5SSj7AO9Rodjt+wuFNIKbUB2DBi2SMur/uBW0fZ7g3gjTH2WQjMn0iw2uR74pNSpsSG8bWlxoxv77P2/A1MIbDwdqMjcduDF0/jH58vpLE5k9x4o6OZfEUZi5nX+jbVhc+Qfe5DRofjF/QpnnbCrqpWtpW38q0L8wmzmI0Ox3dYB2HfKzBrNUT5z3hIl81OJSfJTGXNHOx2o6OZfKWJObSGRqJ2PWt0KH5DJwDthD9sLiUhMoS7ztFj/p/k0DrobYGl9xgdyYSYTMKt50TR2x9DRX3S+Bv4OSUm9qQtIKe5lPb6vUaH4xd0AtAA2F3dxidHmrj/gjwiQ92qGQwe2/4IidNg2uVGRzJhy/NDiY5sp6gsPSiuAvamLcAONH3+a6ND8Qs6AWgA/GrjEZKiQvnm+frGr5PUFEJtIZzzP8Dkfx8XESEv6yBdveGU1QX+VUBneAyHE3KYcnQjQwN6gLjx+N9/tOZxn5c082VZC/906XSiwvTZ/0m2/dFx5+/iu4yO5IwlJ9STFNvD3rJ07PbA7xFUmLWM2KF+anSX0HHpBBDklFL858bDpMeF8/WVuu7/JJ11cPBtR9fPsBijozljIrB4ei3dfeGU1PpPI/aZKk/IpiYygahdz6CCod7rLOgEEOQ2Fh9nb00H37tipu75M9LOp8FugxUPGB3JWctM6SA1voui0nSGrAH+sRdhe/YKUntaaNz3stHR+LQA/0/QTsdqs/PrD4+QnxKl+/2PNNQPu56FWddAov+3i4hAwexj9A2Esr8i8O/wPpg6i7aQCIY+/y+jQ/FpOgEEsZd3VFPS2M2/XD1L3/U7UtGLjq6fKx8cv6yfSI3vIW9qC8UVU+jpD+wJfmwmMzszl5LZXEpL+SdGh+Oz9Kc+SLX1DPKrD49y3rQkrp431ehwfIt1ED7/DWSugNwLxy/vR5bOrEEh7D6aOX5hP7c7fSH9JgsdW35udCg+SyeAIPVfm47SPWDlp9fP0yN+jrT3JcekL5f8yC/G/ZmImMhB5uYcp6wumeYO3x3S2hP6Q8LZlTaf7OqddOobw0alE0AQOlTfyYvbq7h7ZQ6zpvpv75ZJYRuCrb+GjGV+eeOXOxbm1xMeOsS2gzmoAB8t+qvs5djERPvGHxsdik/SCSDIKKV49N1i4iJC+OcrZhodju/Z+zK0V8PFDwfc2f+w0BAby2cdo7kjmiPHAnuSpe6waLZnLCSz8ku6agqNDsfn6AQQZNbuqmFbeSs/uHoWcZGB3RA4YbYh+OxXkL4EZlxpdDSTKj+9hbSkDnYdzaQ3wBuEt2Wfw6DJTPsHPzI6FJ+jE0AQOd7Zz7+tP8iKvETuXK5v+jrFnr9Be1VAn/0PE4Fz51Zhs5vYcTiw/xd6QyP4MmMJWTWFdFR+bnQ4PkUngCChlOJf3zrAgNXOL29eiMkU2F9wE9bfAZv/HbLPhZlXGx2NV8RGDbBoWh2VDYkca4wzOpxJtSO7gB5zCF36KuAkbiUAEVklIkdEpFREHh5lfZiIvOpcv11Ecp3LrxSRXSKy3/l8mcs2W5z7LHI+Uj32rrRTvLuvno8OHecHV80iLznK6HB8z2e/cvT7X/V/A/7s39X8vAbio3v5sjiX/sHAHQeqPyScL7IKyGw4QMuBN40Ox2eMmwCcc/o+AawG5gJ3isjcEcXuB9qUUtOB3wC/dC5vBq5XSi3AMWfwCyO2+7pSarHz0XgW70M7jcaufn62rphFWfH8wwX+f1erx7WUOQZ9W/x1R/1/EDGbFBcuLGdg0MKXxbkB3StoR1YBjWHR8P4PUdYBo8PxCe5cAawASpVS5UqpQeAVYM2IMmuAvzpfrwUuFxFRSu1RStU5lxcDESIS5onANffY7Ip/frWI3kErv7plIWZd9XOqTY+AJQwu/4nRkRgiKbaPpTNrqT6eENCDxVnNFj6ccTlJPc00fPQzo8PxCe4kgAzgmMvPNc5lo5ZxTiLfAYwcfPxmYLdSyjX1Puus/vmJjHE3kog8ICKFIlLY1NTkRriaqz9uKeWL0hYevWEeM6boPv+nKPsEDq+HC78PMcF7R/S83AamJnay41A2nT2Be45WmpzP/oQsEnc8xWBbpdHhGM4rjcAiMg9HtdD/cFn8dWfV0IXOx92jbauUekopVaCUKkhJCew+y562o6KV/9p0lDWL07mtIMvocHzPQDe8+11IzIeV/2R0NIYSgQsXVGASxad7p2G1Be6V4sczr0SUnea3/H+U17PlTgKoBVy/PTKdy0YtIyIWIA5ocf6cCbwF3KOUKhveQClV63zuAl7CUdWkeUhz9wDffXkP2YmR/MdNC/RwD6PZ9Ai0H4Mb/wgh4UZHY7ioiEEuXFhOS2dkQLcHtEfE8Wl2AenV22nZ/bzR4RjKnQSwE5ghInkiEgrcAawbUWYdjkZegFuAzUopJSLxwHvAw0qpL4YLi4hFRJKdr0OA64ADZ/VOtBP6h2w88Hwhbb2D/OGupUTrWb5OVfYJFD4N5/4TZK80OhqfkZXawZIZtZTXJXOwcorR4UyabTkrqY5MIPz9f8HWWTf+BgFq3ATgrNN/CNgIHAJeU0oVi8hjInKDs9jTQJKIlALfB4a7ij4ETAceGdHdMwzYKCL7gCIcVxB/9uD7ClpKKf5l7T52V7fzm9sXMz8jsPt3n5H+Tlj3PyFpBlz2f4yOxucszK8nZ0orhUeyqGuONTqcSWEzmXln7vWEWAdofeVOAvZyZxxunRoqpTYAG0Yse8TldT9w6yjb/Tvw72Psdpn7YWru+t3HJazbW8cPr57FNQsCf+KPCVMK1v8zdNbCP3wIIRFGR+RzROCCBRW81xPOJ0XTWLXiCEmxvUaH5XEt0Um8n38Ba8o+o+XTX5B0SfANGKfvBA4gr+6s5rcflXDz0ky+c8k0o8PxTdv+Gw6shUv/N2QtNzoanxVisXPlshJCLTY2Fc4M2J5BezKXUhyfQexn/0lf9Tajw/E6nQACxNpdNTz85n4unpnCz782Xzf6jqb8U/jwJzDnerjwB0ZH4/OiIga5quAoSsHGnbMCcxYxETbMvZZOcyi2l27F3jmyf0tg0wkgALxTVMsP1+7l/GnJPHn3Mj25+2jaj8Hab0LSdEevH50g3RIX3c9VBUcZHLI4kkBfqNEheVxPaBSvLLwJy2APnc9dC4OBV901Fp0A/Nzrhcf451eLWJmXxJ/vKSA8RH/5n6KnGf52s2O45ztegjB9Q9xEJMX1ckXBUfoGQtiwfTYd3YHXZbYpZgqvz15FbGsFrS/fDna70SF5hU4AfkopxW8/OsoP1+7jvGnJPH1fARGh+sv/FH1t8PyNjkle7nwZkqcbHZFfmpLQzaoVR7DZTby/YzYtATidZFnqTDbkriSx4jPa37g/KJKATgB+aMhm51/W7jvR4PvMfcuJDNV9/U8x0AV/uwWaj8Adf4PcC4yOyK8lxfay+pxDmE123t8xm8qGBKND8rjCnJV8lLGI+OI36Vj7zYBPAjoB+Jna9j5uf/IrXt9Vw/eumMGvbl1IqEX/GU/R3eQ486/bA7c+B9OvMDqigBAXNcC1Kw+REN3HlqLpFB7JxB5IXehF+Hz6pXyYsYi4g2/TtfY+sNuMjmrS6G8OP7Lp4HGu+d1Wjh7v5vd3LuF7V8zUvX1G03QE/nIZHC+G256H2dcaHVFAiQwfYtU5h5mZ1ciBijQ2Fc4MrB5CInw5/VI+yFhMzMF36Pzr9Y4JgwKQTgB+oKNviP/91n6+9XwhWYkRrP+fF3D9onSjw/JNZZ/A01fCUD988z2Yc53REQUks0lx3rwqzptfQVN7NG9/Pp+SmuTAuaFWhG0zLuXNvPOJrPqS3j+eh2o6anRUHqcrjn2YUor1++p59N2DtPYM8I8X5PHDVbN0N8/RWAdg87/Bl3+AlFlw12uQkGN0VAFvZmYzUxO7+GJ/Hl8cyKOyIYFz5lQTGxUYE67sy1lBU3Qydx58n6EnL0Su/x0hC28PmG7E+grAR+2ubuOuP2/nf768h7S4cNY9dAH/57q5+st/NA0H4M+XwZe/h2X3wbc26y9/L4qNHGDVisOsmF3F8bYY3vp8PtsPZTEwGBj/q/VJ+Ty17C6OhUYQ8tb/oO/Fm6GrweiwPEJfAfiYA7Ud/PajEj46dJzk6FAevWEeXz8nG4tZ5+pTdDfBlp/DrucgMgnufBVmrTI6qqAkAnNzG8lNa6WoJIPDVVMoq01mdnYjc3KOExFmNTrEs9IdmcCLBfcwv/xTriv7hKHHl2C67CeYl9/vmE3OT+kE4AOsNjsfHjzOs19UsLOyjZhwCz+8ehb3nZdLlB7K+VR9bbDzafjidzDYA8v/ES5+GKJGTkKneVtkmJXz5lcxJ6eRPaUZ7CtPo7hyKtMzmpmd3UhCTJ/RIZ4xu8nEvumXUjFlHquObGTexh8z8OXvCL3sEWTRHWDyvyseUX7UalNQUKAKCwuNDsMjlFLsr+3g7T11vLuvjqauAbISI7j33FxuW55FbHgA9arwlJYy2P4n2PM3GOqFmavgyn+DlJlGR+azdtTu4E+FfyI7LtuQ43d0h3OgcipltUnYlYmk2B5mZDaRM6XNv68KlGLK8UOsqtpGXl8Hg9FTsKx4ANPSeyHa92YuFJFdSqmCU5brBOA9/UM2tpW3sOVIE5sPN1Ld2kuo2cSls1O4ZVkWl81O1ZO2j9R1HA6+Dftfh5qdYAqBBbfCud+BqQuMjs7nGZ0AhvUPWiivS6SkNoW2rkhAkRrfTfaUdtKTO0iI7vPLdlVlt5NRv5fz6w8wr7sZu8mCbcaVhMy7GWZeDeG+MZ+CTgBeppSipq2Pg/Wd7K5uo7Cyjf01HQza7ISHmDhvWjJXzZ3C6vlpxEXqs/0T+jugdheUb4GyzdCw37F8ygJYcAssuiOoJ2+fKF9JAMOUgrauCKobE6g+Hk9rVxQAYSFDTE3sIiW+h6TYHpLiegi1+NdduBFt1SypLWJFey3x1n7sphDs2Sux5F8CeRdB2mKwGDOY3lgJwK0KZhFZBfwOMAN/UUr9YsT6MOB5HJO8tAC3K6Uqnet+DNwP2IDvKqU2urNPf6CUorVnkLr2fmrb+6hs6aGiqYeK5h4ONXTS1e+4xA0xCwsy4rjv/FzOnZbEuflJetC2wV7H+DwtJY4bt5qOQN1uaCl1rDeFQNY5jhm7Zl8HqXOMjVfzCBFIjO0jMbaPxdPr6O4LpaE1xvmIpep44omy0REDxEX1ER/dT0xkP9ERA8REDBIVMYjF7HvJoS8hmy8TsvncZiWu6QjzWsqY17CXrMqtAI6EkDobc9oSZOp8SJwGSfkQlw1mY9r6xr0CEBEzcBS4EqjBMUfwnUqpgy5lvgMsVEo9KCJ3ADcppW4XkbnAyzgmfE8HPgKGK2xPu8/RnO0VgFIKu3KMpeN4KIZsdgaG7AxYbQxY7fQO2ugbstE7YKV7+NFvpb1viPbeIdp7B2nuGaS5a4Dm7gEGrCf/IyZHh5KbFMWsqTHMTY9lTlosc9NiA+sL324H2+DfH0N9jn74Q72ORtnBHhjsgr526G93NNr2tEBPI3Qfh44a6G05eZ+xGZC2CDKWQvpSx5d/WLQR7y6g+NoVwHj6By00d0TS0hlFe1cE7T0RdPaEY7Of3AsuxGIlMmyI8NAhwkOthIVYCQuxERJiJdRiI9Riw2K2Y7HYsJjsmM12LCaF2WzHZLJjFoXJ5HyImrTqJ6UUqqeJqS1l5PW0kt3XTk5fB9HWv98nocSEPSoFYtMxxaYjkckQlezo2RYW66hGCouFzOVn/Jk4myuAFUCpUqrcuaNXgDWA65f1GuBnztdrgT+IY4yCNcArSqkBoMI5Z/AKZ7nx9ukxW379DTI6djNeZVeo8xE/yjqTCGaTnHi2mARzjOM5xGxyPFtMmEXADtQ5H+46q6o4l21P2s9oy5Xzteuzy3Jld3nYHOOgKLvj2W51PNQEx0Yxh0JUiuOfOirV8QUflwlxWZA8w/HQQzRPGpvdxqBt0Ogw3GIyD5Ka2EtqYvOJZUpB30Ao3X1h9PSF0zsQSp/zMTAYQnt3OANDFgaGLCh1Zt2lBYWI6wPHM87XAKJOfnZsiIz4Zhk9mVx24jhKKRLoIJsGcjhOlmoitbuDqd1tpNTtIYFu4unGwsknl0due49Zcz07oKE7CSADOObycw1wzlhllFJWEekAkpzLt43YNsP5erx9AiAiDwAPAGRnn9lZTGJGPraQHkwiJ/6YJhFMAmISzOL4YjeZwGIyYTaBWUxYzI4veIvZhHfaZs/iICf918npl4s4Xo/2LCbnQ0DMjq5tw88mC5hDnM+hf3+EhIMlwvEcGu18REFEPITHQUhkwNw56W9iQmOID4+na6DL6FDOjkBEpOMxFqXAZjdhtYZgtVmw2szYbGasdjN2uwm73YzNbnK8VsPPglKCsptQOF7blTjPixw/O/b999fDP8PwKZZz+YhzOHWaz7MVoZw0ykk76ZxNOROEKDtRDBCt+olRfUTRz30hnh+C2+c7mSulngKeAkcV0JnsY+Edj3k0Jk3zF3NS5vC71b8zOgzNR7lzvVQLZLn8nOlcNmoZEbEAcTgag8fa1p19apqmaZPInQSwE5ghInkiEgrcAawbUWYdcK/z9S3AZuVoXV4H3CEiYSKSB8wAdri5T03TNG0SjVsF5KzTfwjYiKPL5jNKqWIReQwoVEqtA54GXnA28rbi+ELHWe41HI27VuCflHK0II62T8+/PU3TNG0s+kYwTdO0ADdWN1A9xKSmaVqQ0glA0zQtSOkEoGmaFqR0AtA0TQtSftUILCJNQNUZbp4MNI9byvt0XBOj45oYHdfEBGpcOUqpUyYq8KsEcDZEpHC0VnCj6bgmRsc1MTquiQm2uHQVkKZpWpDSCUDTNC1IBVMCeMroAMag45oYHdfE6LgmJqjiCpo2AE3TNO1kwXQFoGmaprnQCUDTNC1IBWwCEJGfiUitiBQ5H9eMUW6ViBwRkVIRedgLcf2niBwWkX0i8paIxI9RrlJE9jtjn7QR8MZ7/86hvF91rt8uIrmTFYvLMbNE5BMROSgixSLyv0Ypc4mIdLj8fR+Z7Licxz3t30UcHnf+vvaJyFIvxDTL5fdQJCKdIvK9EWW88vsSkWdEpFFEDrgsSxSRTSJS4nxOGGPbe51lSkTk3tHKeDguwz+LY8Tlve8upVRAPnDMUfyDccqYgTIgH8d0wHuBuZMc11WAxfn6l8AvxyhXCSRPcizjvn/gO8CfnK/vAF71wt8uDVjqfB0DHB0lrkuA9Qb8X5327wJcA7yPY57AlcB2L8dnBhpw3Pjj9d8XcBGwFDjgsuz/AQ87Xz882v88kAiUO58TnK8TJjkuwz+LY8Tlte+ugL0CcNOJCe+VUoPA8OT0k0Yp9aFSyur8cRuO2dCM4s77XwP81fl6LXC5yORO8KuUqldK7Xa+7gIO8fe5pH3dGuB55bANiBeRNC8e/3KgTCl1pnfMnxWl1Gc45gRx5fo/9FfgxlE2vRrYpJRqVUq1AZuAVZMZly98Fsf4fbnDI99dgZ4AHnJe3j0zxmXnaBPee/OL5h9wnC2ORgEfisguEXlgko7vzvs/Ucb5YekAkiYpnlM4q5yWANtHWX2uiOwVkfdFZJ6XQhrv72L0/9QdwMtjrDPi9wUwRSlV73zdAEwZpYzRvzejP4sjeeW7y68TgIh8JCIHRnmsAf4ITAMWA/XAr30kruEy/4pjlrQXx9jNBUqppcBq4J9E5CIvhO5TRCQaeAP4nlKqc8Tq3TiqORYBvwfe9lJYPvt3Ecf0qjcAr4+y2qjf10mUo/7Cp/qe++Bn0WvfXeNOCenLlFJXuFNORP4MrB9l1aRMTj9eXCJyH3AdcLnzAzHaPmqdz40i8haOS77Pzja2Edx5/8NlakTEAsQBLR6O4xQiEoLjy/9FpdSbI9e7JgSl1AYR+W8RSVZKTepAXm78XSblf8pNq4HdSqnjI1cY9ftyOi4iaUqpemd1WOMoZWpxtFMMywS2THZgPvRZdD3eib/fZH93+fUVwOmMqHe9CTgwSjGvT04vIquAfwFuUEr1jlEmSkRihl/jaKwaLf6z5c77XwcM98i4Bdg81gfFU5xtDE8Dh5RS/zVGmanDbREisgLH//KkJiY3/y7rgHvEYSXQ4VL9MdnuZIzqHyN+Xy5c/4fuBd4ZpcxG4CoRSXBWeVzlXDZpfOyz6HpM7313TUbLti88gBeA/cA+5y8mzbk8HdjgUu4aHL1MyoB/9UJcpTjq7oqcjz+NjAtHy/5e56N4MuMa7f0Dj+H4UACE46hSKAV2APle+B1dgKOaYJ/L7+ka4EHgQWeZh5y/m704GvDO80Jco/5dRsQlwBPO3+d+oGCy43IeNwrHF3qcyzKv/75wJKB6YAhHvfT9ONqMPgZKgI+ARGfZAuAvLtv+g/P/rBT4phfiMvyzOEZcXvvu0kNBaJqmBamArQLSNE3TTk8nAE3TtCClE4CmaVqQ0glA0zQtSOkEoGmaFqR0AtA0TQtSOgFomqYFqf8feROMzJUkrFEAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Generate a grid of possible means\n",
"x = np.linspace(-5, 15, 100)\n",
"\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, dist_of_mean_1.pdf(x), label='Dist 1')\n",
"ax.plot(x, dist_of_mean_2.pdf(x), label='Dist 2');\n",
"\n",
"start_of_fill = dist_of_mean_1.ppf(.95)\n",
"fill_x = np.linspace(sig_threshold, 15) \n",
"ax.fill_between(fill_x, dist_of_mean_2.pdf(fill_x), color=\"g\", alpha=.5 )\n",
"ax.legend()"
]
},
{
"cell_type": "markdown",
"id": "threaded-rotation",
"metadata": {},
"source": [
"### Our power is 59%\n",
"Which means we might reject the null hypothesis but be wrong proably more than 60% of the time"
]
},
{
"cell_type": "code",
"execution_count": 61,
"id": "least-actress",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.5948157390930016"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"power = 1 - dist_of_mean_2.cdf(sig_threshold)\n",
"power"
]
}
],
"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": "3.9.1"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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