test_significance_t_u_shapiro.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a5975753",
   "metadata": {},
   "source": [
    "## Three steps that will cover the majority of cases:\n",
    "\n",
    "### 1) are my data normally distributed? shapiro test\n",
    "### 2) if yes: t-test\n",
    "### 3) if no: u-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3fe379a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats #the only import you actually need for this\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%config InlineBackend.print_figure_kwargs={'facecolor' : \"w\"}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74cbab56",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24acca47",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "06d7bc02",
   "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": [
    "#generate normally distributed values\n",
    "group_a = np.random.normal(4, 1,  5) #mu, sigma, n\n",
    "group_b = np.random.normal(5, 1,  5) #mu, sigma, n\n",
    "df = pd.DataFrame(np.concatenate((np.vstack((group_a, np.array(['a']*len(group_a)))).T,\n",
    "                                  np.vstack((group_b, np.array(['b']*len(group_a)))).T)), columns = ['value', 'group'])\n",
    "df['value'] = df['value'].astype('float')\n",
    "ax = sns.swarmplot(data = df, x = 'group', y = 'value', s = 8)\n",
    "plt.ylim(bottom = 0, top = df.value.max() + 2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0db544c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-2.141696254533902, pvalue=0.0646055063603198)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(group_a, group_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "52f5d905",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-4.273273869671518, pvalue=0.0016285682897101618)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind([1,3,4,3,2], [4,5,6,6,5,4,5]) #input can just be list of numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d23231ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.9919436573982239, pvalue=0.9807631969451904)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#shapiro test for normal distribution\n",
    "stats.shapiro(np.random.normal(10, 1,  50) ) #p value > 0.05 if it is normally distributed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "90f0bc0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEGCAYAAAB/+QKOAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAigUlEQVR4nO3df1TUdaL/8ecA/kJ+qCgKjokKiIpCMJheFTXDH3ijbCt13dQvFse+tdXd2u/tbqdbu93ddU+7e63cq9HXutZ+F3ezdm1d9Grkj9VUdlJLJYlMFAH5oaKIAgLz/WNqaOSDrJszH2Jej3M4Z96fHzMvPJ558fltcTgcDkRERK7hZ3YAERHpnFQQIiJiSAUhIiKGVBAiImJIBSEiIoYCzA5wM/Xv35+oqCizY4iIfGsUFxdTXV1tOK9LFURUVBR2u93sGCIi3xo2m63dedrFJCIihlQQIiJiyGO7mDIzM9m0aRPh4eEcOXIEgPnz51NYWAhATU0Nffr04dChQ23WjYqKIjg4GH9/fwICArTbSETEBB4riKVLl/Loo4+yePFi17Tf//73rtdPPvkkoaGh7a6/fft2+vfv76l4IiLSAY8VRGpqKsXFxYbzHA4Hf/jDH/jggw889fEiIvINmXIM4q9//SsDBw4kJibGcL7FYmHmzJkkJyeTnZ193ffKzs7GZrNhs9moqqryRFwREZ9kymmuOTk5LFy4sN35e/bsITIyksrKStLS0oiLiyM1NdVw2aysLLKysoDrn64lIiI3xutbEE1NTbz77rvMnz+/3WUiIyMBCA8PZ968eeTn53srnoiIfMnrBfH+++8TFxeH1Wo1nF9XV0dtba3r9datW4mPj/dmRBERwYMFsXDhQiZOnEhhYSFWq5W1a9cCsH79+ja7l8rKykhPTwegoqKCyZMnk5CQwPjx45k7dy6zZ8/2VEwREWmHpSs9Uc5ms+maCRGRG3C9701dSS0iIoZUECIiYkgFISIihlQQIiJiSAUhIiKGVBAiImJIBSEiIoZUECIiYkgFIW00tzi41NBkdgwRMZkpd3OVzmvz4XKe3XiU6ksNTI0dwMsLbiU0sJvZsUTEBNqCEJeL9Vd58u2Pqb7UAMDOz6pYmfeZyalExCwqCHE5UVXH5cZmt2lHyy6alEZEzKaCEJe4iGDCend3mzZphJ4LLuKrVBA+7njVJTZ8dJovqi7RI8CftUtTSInqy6CQnmROGsbD00aYHVFETKKD1D7sD38r4V/f/QSHAywW+OW9CXwn2cov70ug9PwVkob2pXuA/oYQ8VUqCB/24tZCvnoaiMMBv9payMlzl3nlgyIcDhgY0oOchyYwfECQuUFFxBT689CH1V1zrUNtQxO/2f65qzQqLjbwygefG65bVFHLxyU1dKHnTYnINVQQPux7E4a6jWePGURzi/sX/kcnz3Pbz95nxq92kHu4HIfDwWM5B0n7z13c9Zs93P2bPdTWX/VmbBHxEhWED8tIiCSwu79rHBHag7hBwW7LnDp3mYqLDRyvquP7OQfZeKiM9z4uc83/+PQF1ueXeC2ziHiPCsKHvfJBkdt1D6t3fsHiCUMJ6RmABeh/zSmvzS0O9p842+Z9yi/UezqqiJhABeHDzl5qdBtfbXbw09xPuVjfhAOormtss869yVaCe7ae2+BngX9OiPB0VBExgccKIjMzk/DwcOLj413Tnn/+eQYPHkxiYiKJiYnk5uYarrtlyxZGjhxJdHQ0K1as8FREn/edZKvbeOSgYOquuZI6PLgH3f396BPYjRfuGkPy0H68vXwi9yQNZk78INZljifplr7ejC0iXmJxeOg0lF27dhEUFMTixYs5cuQI4CyIoKAgnnrqqXbXa25uJjY2lm3btmG1WklJSSEnJ4fRo0d3+Jk2mw273X7Tfgdf8N7HZWw9eoaosN4suu0WZq3cxcX61rObHpk+gifuiMXfYsHPz2JiUhHxhOt9b3psCyI1NZV+/frd8Hr5+flER0czfPhwunfvzoIFC9i4caMHEgo4D1Sv+m4ST80aSUSfXrx4bwL9enfH38/CxOFhPDo9hm7+fioHER/k9WMQq1atYty4cWRmZnL+/Pk280tLSxkyZIhrbLVaKS0tbff9srOzsdls2Gw2qqqqPJLZl6za/jnn6hppbnGw94uzbC04Y3YkETGJVwvi4Ycf5vjx4xw6dIiIiAiefPLJNssY7fGyWNr/6zUrKwu73Y7dbmfAgAE3Na+v+bT8IodLL7hNe9t+2qQ0ImI2rxbEwIED8ff3x8/Pj4ceeoj8/Pw2y1itVkpKWs+rP336NJGRkd6M6bP6BHbj2j1J/a451VVEfIdXC6K8vNz1+o9//KPbGU5fSUlJoaioiBMnTtDY2Mj69evJyMjwZkyfFRHai4emDHeN+/XuzqO3R5uYSETM5LGb9S1cuJAdO3ZQXV2N1Wrlxz/+MTt27ODQoUNYLBaioqJ49dVXASgrK+PBBx8kNzeXgIAAVq1axaxZs2hubiYzM5MxY8Z4KqZcY1b8IHZ9VkXphSvMiR9EVFhvsyOJL2tqcN5JsltPs5P4JI+d5moGneb6zdRfbWbSig84+7UL5J64I4Yn7og1MZX4rB0rYM9L0NIEtkyYvcJ5X3q5qa73vanbfYtL4Zlat3IA+PD4WZ64w6RA4rtOfgg7ft463r8GhoyHc1/AsVwIi4YZz0KfW8zL6ANUEOIyfEBvArv7u92fKT4y1MRE4rPKP247Lf//wqkPna/LDsCZw/C/92qrwoN0LyZxCe7ZjV/fn8jAkB5YLHB7XDiP3xFjdizxRVGTgWu++C9VuI+rPoWzx70WyRdpC0LczI4fxMzRA2loaqHX124FLuJVX+wAvnZ4NPQWGDQWzn2tELr1guBB3k7mU7QFIW34+VlUDmKuwxvcxxdO0WaLwr+nsyTEY1QQItL5hAx2Hwf0gurP3KfVn9cuJg9TQYhI53P7MxA00PnaLwDueB6sye7L9Oqrs5g8TMcgRKTzGTgGnjgMpR9B32EQEgF7XnFfJmSwLqDzMG1BiEjnFNADhv6TsxwAPr3mtv8VR+B8sddj+RIVhIh8O/S65vkyft2gR4g5WXyECkJEvh2m/Sv0+NqFm6lPQeCNP5RM/n46BiFt1FxupOJiA7EDg677LA4RrxqcDP9yGIp3O2+1MWCk2Ym6PBWEuPnvPSf42eZjNDa1EBMexLrM8UT20bnm0kl0D3KeuRQUbnYSn6BdTOJy9lIDP839lMamFgCKKi/xcl6RyalEvnT2OLySDGsmw6/i4KN1Zifq8lQQ4lJ+oZ6rze53fy8+W2dSGpFrfPACnD/hfN1UD1v+DRpqzc3UxakgxGVURAi39At0mzYnPsKkNCLXOHfCfXy1Di5VmpPFR+gYhLj4+1l4a9l4Vr5fRMm5y6SPjWDxxKFmxxJxGp0B5YdaxwPjIWyEaXF8gQpC3AwN681/zk80O4YIXDkPH/031FXD2Hth0r84b7txLBf6R8O0H0HlMefDhJqvQsoyGJxkduouRQUhIp1PSzO8MRcqjzrH+9fA0r/AxEdhxAwItTqPQ6xNg4aLzmUOvw3L/6rTX28iFYSIdD4n97SWAzifS/3hK1Bx1HmgOqAnjMpoLQeA5gY48g5M/5H383ZROkgtIp1P995tp31VDuDceijY2HaZ3gM8m8vHeKwgMjMzCQ8PJz4+3jXthz/8IXFxcYwbN4558+ZRU1NjuG5UVBRjx44lMTERm83mqYgi0lkNTobYOa3jXv2cN+/7uuYGsI5vHUckQsJCr8TzFR4riKVLl7Jlyxa3aWlpaRw5coRPPvmE2NhYfv7zn7e7/vbt2zl06BB2u91TEUWkM1vwO/jeuzDvVfj+R3DLBPf5gWHw4DZYts15fOKh7dAjyJysXZTHjkGkpqZSXFzsNm3mzJmu1xMmTGDDhmseKygi8hU/P4ie0To+f8p9/pUa5xlOQ8YjnmHaMYjXX3+dOXPmGM6zWCzMnDmT5ORksrOzr/s+2dnZ2Gw2bDYbVVVVnogqIp3B1Wuu6nc0w9Ur5mTxEaacxfTTn/6UgIAAFi1aZDh/z549REZGUllZSVpaGnFxcaSmphoum5WVRVZWFoCOV4h0ZbZMKNnfOo5Ogz5DzMvjA7xeEOvWrWPTpk3k5eW1eyvpyMhIAMLDw5k3bx75+fntFoTcfGU1VyiruULCkD5089eJbtJJJCyA3v2/vFAuBpKWmJ2oy/NqQWzZsoVf/OIX7Ny5k8DAQMNl6urqaGlpITg4mLq6OrZu3cq///u/ezOmT1v1QRG/3vYZLQ4Y3KcXv3voNoaGGZxyKGKG6DucP+IVHvvzcOHChUycOJHCwkKsVitr167l0Ucfpba2lrS0NBITE1m+fDkAZWVlpKenA1BRUcHkyZNJSEhg/PjxzJ07l9mzZ3sqpnxNZW09K98vouXLG7qW1lzh5bzPzQ0lIqbx2BZETk5Om2nLli0zXDYyMpLc3FwAhg8fzscff+ypWHIdlRcbaGpxv913+QUdBJROorkJdr0Ix/7ivBfTjOeg3zCzU3Vp2sEs/K34HH/4Wwn9encnJtz9PPJjZ2qZ+uJ21uefamdtES/Z9SLsXAEVh+HoH+F394PD0fF68g/TvZh83PPvHeW/PywGoEeAHy8tSOTD42c5XHqBg6dqOFfXyLm6Rp5+9zCxg4JJuqWvuYHFd3222X1c/ZnzKXP9o83J4wO0BeHDqmobeHNvsWvc0NTCW3tP0q93dxqutrRZfu/xs15MJ3KN/rHu4+5BEKIHWnmStiB8WENTM9cccuBQSQ172imCcdZQL6QSaUfYNVsKQeHGN/WTm0ZbED7M2jeQ2+PC3abVNTa7jf0s0KubP9+/PZopMbpTppioaKv7+NwXbR9DKjeVtiB83H8tSuJtewlfVNeRdEtfHlt/0O2435z4CFYuSNQFc2K+oEHuY/8e0KuPKVF8hQrCx/Xs5s8DE6Nc41d3HedIqfMhLBbgzoRIlYN0DtP/DUr2weWzYPGD25+BXjppwpNUEOJSfuEKBWWtT+hyALmHy5kdP6j9lUS8ZdBYeOKI835MYSOgzy1mJ+ryVBDiUnP5apuD1ucvN5oTRsRI90AYMd3sFD5D+w7EZVRESJszle6z6W6ZIr5KWxDi5s3M8by+p5jT5y6TPjaCO0YPNDuSiJhEBSFu+gR25wdpsR0vKOJpJz+EPS9DcyPcthxiZ3a8jtxUKggR6XzOF8Obd0Nzg3P8xXZ46APnvZc+2wJhMTBmHvjrK8yT9K8rIp3PZ//TWg4AjhbYvRI+fc/5Gpz3Zrr3dVPi+QodpBaRzqdvVNtpFUdaywHgyLtwscxrkXyRCkJEOp/oNBg3v3UcMwuCr7kex2IBi793c/kY7WISkc7Hzw/uyYbpz0BLk/PCuM/fh1P7nGOAxEUQrLPsPEkFISKdV9+hra+j74CH9zpv2tc/xrmVIR6lgpA2KmvrOXOhnjGRofj7WcyOI9JqQKzzR7xCBSFuXt15nBf/p5CmFgdDwwL57bLbGNIv0OxYImICHaQWl6raBlc5AJw8e5mX84pMTiUiZvFYQWRmZhIeHk58fLxr2rlz50hLSyMmJoa0tDTOnz9vuO6WLVsYOXIk0dHRrFixwlMR5RoVF+td5fCV0+evmJRGRMzmsYJYunQpW7ZscZu2YsUKZsyYQVFRETNmzDD88m9ubuaRRx5h8+bNFBQUkJOTQ0FBgadi+rzDpy/w0cnzOBwORkeEMLy/+yMc547TM39FfJXHCiI1NZV+/fq5Tdu4cSNLliwBYMmSJfzpT39qs15+fj7R0dEMHz6c7t27s2DBAjZu3OipmD6rqbmF//VGPneu2s13Vn/IPas/pL6pmUemjyCoh/Pc8vjBIcy7dbDJSUXELF49BlFRUUFEhPMv0oiICCorK9ssU1paypAhrbeYtlqtlJaWtvue2dnZ2Gw2bDYbVVVVNz90F5V3rJLtha3/XgdP1fC7/ad4/r0CLjU4n0t9pPQiL3+gYxAivqrTHaR2OBxtplks7Z9qmZWVhd1ux263M2DAAE9G61IqaxvaTPusopbahia3aQdP1XgpkYh0Nh0WREVFBcuWLWPOnDkAFBQUsHbt2n/owwYOHEh5eTkA5eXlhIeHt1nGarVSUlLiGp8+fZrIyMh/6POkfTNHDySoR+tZzt38LSy6bSihvbq5LTc+qt+1q4qY58g7sCETtv8c6i+YnabL67Agli5dyqxZsygrc94UKzY2lpUrV/5DH5aRkcG6desAWLduHXfddVebZVJSUigqKuLEiRM0Njayfv16MjIy/qHPk/YNDOnJ28sncl+ylbsTI1mfNYGEIX1Y8k9D8f9yiy08uAffm6Dn/konYX/dWQ5H3oGdKyBnodmJurwOC6K6upr7778fPz/nogEBAfj7d3yDrIULFzJx4kQKCwuxWq2sXbuWp59+mm3bthETE8O2bdt4+umnASgrKyM9Pd31/qtWrWLWrFmMGjWK+++/nzFjxnyT31HaMSoihBfvS2DlgltJHtqPi/VXeW3XCZq/3M1XWdvAmp1fmJxS5EsH/5/7+OQe53MjxGM6vJK6d+/enD171nUcYN++fYSGhnawFuTk5BhOz8vLazMtMjKS3Nxc1zg9Pd1VGOI9xdV1XLna7DatoPyiSWlErtG7v/vYvzv0CDEni4/osCB+/etfk5GRwfHjx5k0aRJVVVVs2LDBG9nEy0YOCqZ/UA+qL7UewE6N6X+dNUS8aNrTcGpv67GH1P8DgTpG5kkWh9FpQ9doamqisLAQh8PByJEj6datW0ermMJms2G3282O8a12+PQFXvhLAafOXSYjIZIfzhpJN/9Od7Kb+Kr6i85nVYdFQ/9os9N0Cdf73uxwC+LNN990Gx84cACAxYsX34Ro0tkUVtTyadlFahuasBef48KVq/QP6mF2LPE1tWfgvceg+K8QeSvc+bKzEK5egfoa5494XIcF8be//c31ur6+nry8PJKSklQQXVDN5Uae+eNhGpqcj3U8cKqGl94v4oW74ztYU+Qm2/QDKPof5+uTe+DdB2HWz+G398DVy87p//R9mPkf5mX0AR0WxCuvvOI2vnDhAg888IDHAol5Tp277CqHr3xWUWtSGvFpJ/e4j8sOwo4VreUAsPe/YNITbQ9ey01zwzuXAwMDKSrS7Re6olERIQwK6ek27fa4thczinicNcV9PDAemq65s7Cj2bnLSTymwy2IO++803WKa0tLCwUFBdx///0eDybe183fj3WZ4/nFlmOUnLtM+tgIHpwy3OxY4ov++T/hj8vh5G6ISIC7V8OZw1Cyv3WZ6DToM6T995BvrMOzmHbu3Ol6HRAQwNChQ7FarR4P9o/QWUwiXUxLC/h9bUfH53lQmOs8iyl5KXTrZVq0ruIbncU0derUmx5IROTv4nfNXvDoGc4f8Yp2CyI4ONjwLqoOhwOLxcLFi7rCVkSkK2u3IGprdfaKiIgv63AX01cqKyupr693jW+5RXf5FBHpyjo8zfW9994jJiaGYcOGMXXqVKKiolzPhhAR8aqLZXDwt3Bqf8fLyjfWYUE8++yz7Nu3j9jYWE6cOEFeXh6TJk3yRjYRkVbFe+DlJNj4CLw+E7b8yOxEXV6HBdGtWzfCwsJoaWmhpaWF6dOnc+jQIS9EExH5mr/+0v1iuf1roK7avDw+oMNjEH369OHSpUtMmTKFRYsWER4eTkDA333oQkTk5mi87D7WldQe1+EWRGpqKjU1Nbz00kvMnj2bESNG8Oc//9kb2UREWqU86D6Ona0rqT2sw00Bh8PBrFmz6NevHwsWLGD+/PmEhYV5I5uISKtx90HQADiWC/1j4FbdNNTTOtyCeO655zh69Ci/+c1vKCsrY+rUqdxxxx3eyCYi4q6x7sufS9DSZHaaLu/vPpgQHh7OoEGDCAsLo7Ky0pOZRETaOvAWvPdo6/iLHbB4o2lxfEGHWxCrV69m2rRpzJgxg+rqal577TU++eQTb2QTEWl1YJ37+IsdcP6kKVF8RYcFcfLkSVauXMnRo0f58Y9/zOjRo7/RBxYWFpKYmOj6CQkJYeXKlW7L7Nixg9DQUNcyP/nJT77RZ4pIF9Czj/vYrxv0CDYliq/ocBfTihUrbuoHjhw50nUdRXNzM4MHD2bevHltlpsyZQqbNm26qZ8tIt9iU/8VTu11Hn8AmPQ4BPYzN1MXZ+oFDXl5eYwYMYKhQ4eaGUNEvg2GpMATh+HETgiLgUF6Vrqn3fAjR2+m9evXs3DhQsN5e/fuJSEhgTlz5nD06FEvJxORTuns51D+MZQfgqZGs9N0eR0+Uc5TGhsbiYyM5OjRowwcONBt3sWLF/Hz8yMoKIjc3Fwef/zxdp+DnZ2dTXZ2NgBVVVWcPKmDViJd0tE/wdtLgS+/skZlwPy3TAzUNVzviXKmbUFs3ryZpKSkNuUAEBISQlBQEADp6elcvXqV6mrje65kZWVht9ux2+0MGDDAo5lFxET7X8VVDgCfvgcXSk2L4wtMK4icnJx2dy+dOXOGrzZs8vPzaWlp0dXbIr7Ov5v72OLXdprcVKYcpL58+TLbtm3j1VdfdU1bs2YNAMuXL2fDhg2sXr2agIAAevXqxfr16w0ffyoiPmTyvzjPYmr+8thD8lIICjc1Uldn2jEIT7jevjQR6QLOnYDP34ewETB8OugPx2/set+bum+3iHx79BsG4x8yO4XPMPU0VxER6bxUECIiYkgFISIihlQQIiJiSAUhIiKGVBAiImJIBSEiIoZUECIiYkgFISIihlQQIiJiSAUhIiKGVBAiImJIBSEiIoZUECIiYkgFISIihlQQIiJiSAUhIiKGVBAiImJIBSEiIoZUECIiYsiUgoiKimLs2LEkJiZis9nazHc4HDz22GNER0czbtw4Dhw4YEJKERHfFmDWB2/fvp3+/fsbztu8eTNFRUUUFRWxf/9+Hn74Yfbv3+/lhCIivq1T7mLauHEjixcvxmKxMGHCBGpqaigvLzc7loiITzGlICwWCzNnziQ5OZns7Ow280tLSxkyZIhrbLVaKS0t9WZEERGfZ8oupj179hAZGUllZSVpaWnExcWRmprqmu9wONqsY7FYDN8rOzvbVTJVVVWeCSwi4oNM2YKIjIwEIDw8nHnz5pGfn+8232q1UlJS4hqfPn3atc61srKysNvt2O12BgwY4LnQIiI+xusFUVdXR21trev11q1biY+Pd1smIyODN998E4fDwb59+wgNDSUiIsLbUUVEfJrXdzFVVFQwb948AJqamvjud7/L7NmzWbNmDQDLly8nPT2d3NxcoqOjCQwM5I033vB2TBERn2dxGO3w/5ay2WzY7XazY4iIfGtc73uzU57mKiIi5lNBiIiIIRWEiIgYUkGIiIghFYSIiBhSQYiIiCEVhIiIGFJBiIiIIRWEiIgYUkGIiIghFYSIiBhSQYiIiCEVhIiIGFJBiIiIIRWEiIgYUkGIiIghFYSIiBhSQYiIiCEVhIiIGFJBiIiIIRWEiIgYUkGIiIghrxdESUkJ06dPZ9SoUYwZM4aXXnqpzTI7duwgNDSUxMREEhMT+clPfuLtmCIiPi/A6x8YEMCvfvUrkpKSqK2tJTk5mbS0NEaPHu223JQpU9i0aZO344mIyJe8vgURERFBUlISAMHBwYwaNYrS0lJvxxARkQ6YegyiuLiYgwcPctttt7WZt3fvXhISEpgzZw5Hjx5t9z2ys7Ox2WzYbDaqqqo8GVdExKdYHA6Hw4wPvnTpElOnTuWZZ57hnnvucZt38eJF/Pz8CAoKIjc3l8cff5yioqIO39Nms2G32z0VWUSky7ne96YpWxBXr17lO9/5DosWLWpTDgAhISEEBQUBkJ6eztWrV6murvZ2TBERn+b1gnA4HCxbtoxRo0bxgx/8wHCZM2fO8NWGTX5+Pi0tLYSFhXkzpoiIz/P6WUx79uzhrbfeYuzYsSQmJgLws5/9jFOnTgGwfPlyNmzYwOrVqwkICKBXr16sX78ei8Xi7agiIj7NtGMQnqBjECIiN6bTHYMQEZHOTwUhIiKGVBAiImJIBSEiIoZUECIiYkgFISIihlQQIiJiSAUhIiKGVBAiImJIBSEiIoZUECIiYkgFISIihlQQIiJiSAUhIiKGVBAiImJIBSEiIoZUECIiYkgFISIihlQQIiJiSAUhIiKGVBAiImLIlILYsmULI0eOJDo6mhUrVrSZ73A4eOyxx4iOjmbcuHEcOHDAhJQiIr7N6wXR3NzMI488wubNmykoKCAnJ4eCggK3ZTZv3kxRURFFRUVkZ2fz8MMPezumiIjP83pB5OfnEx0dzfDhw+nevTsLFixg48aNbsts3LiRxYsXY7FYmDBhAjU1NZSXl3s7qoiITwvw9geWlpYyZMgQ19hqtbJ///4OlyktLSUiIqLN+2VnZ5OdnQ3AsWPHsNlsHkruW6qqqhgwYIDZMUQM6f/nzVNcXNzuPK8XhMPhaDPNYrHc8DJfycrKIisr6+aEExebzYbdbjc7hogh/f/0Dq/vYrJarZSUlLjGp0+fJjIy8oaXERERz/J6QaSkpFBUVMSJEydobGxk/fr1ZGRkuC2TkZHBm2++icPhYN++fYSGhhruXhIREc/x+i6mgIAAVq1axaxZs2hubiYzM5MxY8awZs0aAJYvX056ejq5ublER0cTGBjIG2+84e2YPk+77aQz0/9P77A4jHb4i4iIz9OV1CIiYkgFISIihlQQIvKtUFxcTHx8vNkxfIoKQkREDKkgpI27776b5ORkxowZ47pKXaQzaGpqYsmSJYwbN457772Xy5cvmx2pS9NZTNLGuXPn6NevH1euXCElJYWdO3cSFhZmdizxccXFxQwbNozdu3czadIkMjMzGT16NE899ZTZ0bosbUFIGy+//DIJCQlMmDCBkpISioqKzI4kAsCQIUOYNGkSAN/73vfYvXu3yYm6Nq9fKCed244dO3j//ffZu3cvgYGBTJs2jfr6erNjiQBt78nW3j3a5ObQFoS4uXDhAn379iUwMJBjx46xb98+syOJuJw6dYq9e/cCkJOTw+TJk01O1LWpIMTN7NmzaWpqYty4cTz77LNMmDDB7EgiLqNGjWLdunWMGzeOc+fO6WFiHqaD1CIiYkhbECIiYkgFISIihlQQIiJiSAUhIiKGVBAiImJIBSEiIoZUECI3WVNTk9kRRG4KFYTIDXrhhReIi4sjLS2NhQsX8stf/pJp06bxox/9iKlTp/LSSy+Rl5fHrbfeytixY8nMzKShoQGAqKgoqqurAbDb7UybNg2A559/ngceeIDbb7+dmJgYXnvtNbN+PREX3YtJ5AbY7XbeeecdDh48SFNTE0lJSSQnJwNQU1PDzp07qa+vJyYmhry8PGJjY1m8eDGrV6/miSeeuO57f/LJJ+zbt4+6ujpuvfVW5s6dS2RkpBd+KxFj2oIQuQG7d+/mrrvuolevXgQHB3PnnXe65s2fPx+AwsJChg0bRmxsLABLlixh165dHb73V+/bv39/pk+fTn5+vmd+CZG/kwpC5AZc7840vXv37nCZgIAAWlpaANrcJVd3KpXORgUhcgMmT57Mn//8Z+rr67l06RJ/+ctf2iwTFxdHcXExn3/+OQBvvfUWU6dOBZzHID766CMA3nnnHbf1Nm7cSH19PWfPnmXHjh2kpKR4+LcRuT4VhMgNSElJISMjg4SEBO655x5sNhuhoaFuy/Ts2ZM33niD++67j7Fjx+Ln58fy5csBeO6553j88ceZMmUK/v7+buuNHz+euXPnMmHCBJ599lkdfxDT6W6uIjfo0qVLBAUFcfnyZVJTU8nOziYpKekbvefzzz9PUFCQHp8pnYrOYhK5QVlZWRQUFFBfX8+SJUu+cTmIdFbaghAREUM6BiEiIoZUECIiYkgFISIihlQQIiJiSAUhIiKG/j9OoRMXxp6IigAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#generate random distribution of numbers, i.e., not normally distributed\n",
    "group_a = np.random.uniform(low=9, high=17, size=(20,))\n",
    "group_b = np.random.uniform(low=7, high=15, size=(20,))\n",
    "df = pd.DataFrame(np.concatenate((np.vstack((group_a, np.array(['a']*len(group_a)))).T,\n",
    "                                  np.vstack((group_b, np.array(['b']*len(group_a)))).T)), columns = ['value', 'group'])\n",
    "df['value'] = df['value'].astype('float')\n",
    "ax = sns.swarmplot(data = df, x = 'group', y = 'value')\n",
    "plt.ylim(bottom = 0, top = df.value.max() + 2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e41b85da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.8799253702163696, pvalue=0.017637841403484344)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.shapiro(group_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "212ccb52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.9161470532417297, pvalue=0.08355055004358292)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.shapiro(group_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "000c02b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=267.0, pvalue=0.0720454304673439)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu(group_a, group_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f40c3e62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.8577129244804382, pvalue=0.14439702033996582)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.shapiro([4,5,6,6,5,4,5]) #example from value list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9386650d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=1.0, pvalue=0.008167958654692957)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.mannwhitneyu([1,3,4,3,2], [4,5,6,6,5,4,5]) #example from value list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4aec45f5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f558a08c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#example function that tests distribution then picks test accordingly\n",
    "def test_sig(x, y):\n",
    "    if stats.shapiro(x).pvalue >= 0.05 and stats.shapiro(y).pvalue >= 0.05: #if they are normally distriuted\n",
    "        print(\"t-test\")\n",
    "        return stats.ttest_ind(x,y)\n",
    "    else:\n",
    "        print(\"mann-whitney\")\n",
    "        return stats.mannwhitneyu(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "752d96d8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-test\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-10.808567545708417, pvalue=8.002021519806372e-18)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_sig(np.random.normal(10, 1,  50), np.random.normal(13, 2,  40))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4540acbf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mann-whitney\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "MannwhitneyuResult(statistic=7075.0, pvalue=4.0031006370913845e-07)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_sig(np.random.random(100)*1.4,np.random.random(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e348816",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}