Z-Score

zScoreCalculation.ipynb

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   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as st\n",
    "\n",
    "# Population\n",
    "n_control = 80000\n",
    "n_variant = 80000\n",
    "\n",
    "# Conversion rate\n",
    "crv_control = 0.02\n",
    "crv_variant = 0.0219"
   ]
  },
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   "cell_type": "code",
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   "id": "streaming-yahoo",
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     "text": [
      "N - Control: 80000 , Variant: 80000\n",
      "CRV - Control: 0.0200 , Variant: 0.0219\n",
      "Conversions -  Control: 1600 , Variant: 1752\n",
      "Var -  Control: 0.0196 , Variant: 0.0214\n",
      "------------\n",
      "Z-score: 2.6534\n"
     ]
    }
   ],
   "source": [
    "# Variance\n",
    "var_control = crv_control * (1-crv_control) \n",
    "var_variant = crv_variant * (1-crv_variant)\n",
    "\n",
    "conversions_control = crv_control * n_control\n",
    "conversions_variant = crv_variant * n_variant\n",
    "\n",
    "print('N - Control: {:0.0f} , Variant: {:0.0f}'.format(n_control, n_variant))\n",
    "print('CRV - Control: {:0.4f} , Variant: {:0.4f}'.format(crv_control, crv_variant))\n",
    "print('Conversions -  Control: {:0.0f} , Variant: {:0.0f}'.format(conversions_control, conversions_variant))\n",
    "print('Var -  Control: {:0.4f} , Variant: {:0.4f}'.format(var_control, var_variant))\n",
    "\n",
    "# Create combined random variable S\n",
    "mean_control = crv_control\n",
    "mean_variant = crv_variant\n",
    "S_mean = mean_variant - mean_control\n",
    "S_var = (var_control/n_control) + (var_variant/n_variant)\n",
    "\n",
    "print('------------')\n",
    "Z_score = S_mean / np.sqrt(S_var)\n",
    "print('Z-score: {:0.4f}'.format(Z_score))"
   ]
  }
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