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Confidence_Interval.ipynb

@@ -0,0 +1,192 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "410cdd47",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "f769b682",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.01390952774409444"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# T-Multiplier\n",
+    "tstar = 1.96\n",
+    "# P hat value\n",
+    "p = .85\n",
+    "# Number of observations\n",
+    "n = 659\n",
+    "\n",
+    "# Calculate Standard Error\n",
+    "se = np.sqrt((p * (1 - p))/n)\n",
+    "se"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "d77c95f1",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0.8227373256215749, 0.8772626743784251)"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Lower confidence band\n",
+    "lcb = p - tstar * se\n",
+    "# Upper confidence band\n",
+    "ucb = p + tstar * se\n",
+    "# Show confidence bands\n",
+    "(lcb, ucb)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "1d08b43b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Same process, using statsmodels library\n",
+    "import statsmodels.api as sm"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "41cb97c9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0.8227378265796143, 0.8772621734203857)"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Get confidence bands\n",
+    "# n = observations\n",
+    "# p = result of a survey \n",
+    "sm.stats.proportion_confint(n * p, n)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4234b441",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Try to import dataset\n",
+    "import pandas as pd\n",
+    "\n",
+    "df = pd.read_csv(\"Cartwheeldata.csv\")\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d03c3d4f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Mean of a column\n",
+    "mean = df[\"CWDistance\"].mean()\n",
+    "# Standard deviation of a column\n",
+    "sd = df[\"CWDistance\"].std()\n",
+    "# Rows of the dataframe\n",
+    "n = len(df)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c52dddd2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "tstar = 2.064\n",
+    "\n",
+    "se = sd/np.sqrt(n)\n",
+    "\n",
+    "se"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2dfbab7d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "lcb = mean - tstar * se\n",
+    "ucb = mean + tstar * se\n",
+    "(lcb, ucb)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "649c18b1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#..OR use statsmodels instead\n",
+    "sm.stats.DescrStatsW(df[\"#ColumnName\"]).zconfint_mean()"
+   ]
+  }
+ ],
+ "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": "3.9.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}