paired_t_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6579e0f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# paired t-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ee4dc717",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d4f1249c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test for normality: ShapiroResult(statistic=0.9562923908233643, pvalue=0.7429129481315613)\n",
      "do not reject the null\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha: 0.05\n",
      "sample size: 10\n",
      "mean diff: 3.6\n",
      "std of diff: 4.971027168615266\n",
      "paired t-statistic: 2.290110110135922\n",
      "DoF: 9\n",
      "p-value: 0.047766050110303535\n",
      "critical value: 2.262\n",
      "p-value: 0.047766050110303535\n",
      "ME: 3.555811558561561\n",
      "CI: (0.04418844143843925, 7.155811558561561)\n"
     ]
    }
   ],
   "source": [
    "# Do the mean age of married men differ than married women\n",
    "# sample size of 10 married couples\n",
    "# the array provides the difference in ages\n",
    "# two-tailed test\n",
    "\n",
    "# Hypotheses:\n",
    "# H0: μ1 = μ2 (the means are equal)\n",
    "# H1: μ1 ≠ μ2 (the means are not equal, two-tailed test)\n",
    "\n",
    "# Differences data\n",
    "differences = np.array([6, -1, -3, 4, 6, -2, 1, 4, 13, 8])\n",
    "\n",
    "## test for normality \n",
    "\n",
    "# test for normality\n",
    "# Ho: data is normally distributued\n",
    "# Ha: data is not normally distributed\n",
    "\n",
    "shapiro_test = stats.shapiro(differences)\n",
    "print(f'test for normality: {shapiro_test}')\n",
    "\n",
    "if (round(shapiro_test[1],2)) < alpha:\n",
    "    print(\"reject the null hypotheses\")\n",
    "else:\n",
    "    print(\"do not reject the null\")\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "stats.probplot(differences, dist=\"norm\", plot=ax)\n",
    "plt.title(\"Normal Probability Plot\")\n",
    "plt.xlabel('Theoretical Quantiles')\n",
    "plt.ylabel('Ordered Values')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# define the threshold\n",
    "alpha = 0.05\n",
    "print(f'alpha: {alpha}')\n",
    "\n",
    "# Sample size\n",
    "n = len(differences)\n",
    "print(f'sample size: {n}')\n",
    "\n",
    "# mean difference\n",
    "mean_diff = np.mean(differences)\n",
    "print(f'mean diff: {mean_diff}')\n",
    "\n",
    "# Standard deviation of differences\n",
    "std_diff = np.std(differences, ddof=1)\n",
    "print(f'std of diff: {std_diff}')\n",
    "\n",
    "# t-statistic \n",
    "t_statistic = mean_diff / (std_diff / np.sqrt(n))\n",
    "print(f'paired t-statistic: {t_statistic}')\n",
    "\n",
    "# Degrees of freedom\n",
    "df = n - 1\n",
    "print(f'DoF: {df}')\n",
    "\n",
    "# Determine critical t-value for 95% confidence level (two-tailed test)\n",
    "t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "t_critical = round(t_critical,3)\n",
    "print(f'critical value: {t_critical}')\n",
    "\n",
    "# p-value\n",
    "# Multiplying by 2 accounts for both tails of the distribution\n",
    "p_value = stats.t.sf(np.abs(t_statistic), df) * 2  # two-tailed test\n",
    "print(f'p-value: {p_value}')\n",
    "\n",
    "\n",
    "# Confidence interval calculation\n",
    "confidence_level = 0.95\n",
    "margin_of_error = t_critical * (std_diff / np.sqrt(n))\n",
    "print(f'ME: {margin_of_error}')\n",
    "\n",
    "# Lower and upper bounds of the confidence interval\n",
    "confidence_interval = (mean_diff - margin_of_error, mean_diff + margin_of_error)\n",
    "print(f'CI: {confidence_interval}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a1c8065",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4da2a641",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "diff: [ 4 -1  1  5  3  0 -5 -6]\n",
      "alpha: 0.1\n",
      "sample size: 8\n",
      "test for normality: ShapiroResult(statistic=0.932479739189148, pvalue=0.5389149785041809)\n",
      "do not reject the null\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean diff: 0.125\n",
      "std of diff: 4.0155946010522525\n",
      "paired t-statistic: 0.0880450906325624\n",
      "DoF: 7\n",
      "critical value: 1.415\n",
      "p-value: 0.4661533601711949\n"
     ]
    }
   ],
   "source": [
    "# paired t-test (left-tailed)\n",
    "# all you have to do is change the differences values in each array\n",
    "\n",
    "# Data \n",
    "pop1 = np.array([7, 4, 9, 7, 19, 12, 13, 5])\n",
    "pop2 = np.array([3, 5, 8, 2, 16, 12, 18, 11])\n",
    "\n",
    "# Calculate the differences\n",
    "differences = pop1 - pop2\n",
    "differences_array = np.array(differences)\n",
    "print(f'diff: {differences}')\n",
    "\n",
    "# alpha\n",
    "alpha = 0.10\n",
    "print(f'alpha: {alpha}')\n",
    "\n",
    "# Sample size\n",
    "n = len(differences)\n",
    "print(f'sample size: {n}')\n",
    "\n",
    "# test for normality\n",
    "# Ho: data is normally distributued\n",
    "# Ha: data is not normally distributed\n",
    "\n",
    "shapiro_test = stats.shapiro(differences)\n",
    "print(f'test for normality: {shapiro_test}')\n",
    "\n",
    "if (round(shapiro_test[1],2)) < alpha:\n",
    "    print(\"reject the null hypotheses\")\n",
    "else:\n",
    "    print(\"do not reject the null\")\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "stats.probplot(differences, dist=\"norm\", plot=ax)\n",
    "plt.title(\"Normal Probability Plot\")\n",
    "plt.xlabel('Theoretical Quantiles')\n",
    "plt.ylabel('Ordered Values')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# mean difference\n",
    "mean_diff = np.mean(differences)\n",
    "print(f'mean diff: {mean_diff}')\n",
    "\n",
    "# Standard deviation of differences\n",
    "std_diff = np.std(differences, ddof=1)\n",
    "print(f'std of diff: {std_diff}')\n",
    "\n",
    "# t-statistic \n",
    "t_statistic = mean_diff / (std_diff / np.sqrt(n))\n",
    "print(f'paired t-statistic: {t_statistic}')\n",
    "\n",
    "# Degrees of freedom\n",
    "df = n - 1\n",
    "print(f'DoF: {df}')\n",
    "\n",
    "# Determine critical t-value for 95% confidence level (left-tailed test)\n",
    "t_critical = stats.t.ppf(alpha, df)\n",
    "t_critical = round(t_critical,3)\n",
    "print(f'critical value: {t_critical}')\n",
    "\n",
    "# Conduct the right-tailed paired t-test\n",
    "# stats.ttest_rel() by default returns a two-tailed p-value\n",
    "t_statistic, p_value = stats.ttest_rel(pop1, pop2)\n",
    "\n",
    "# Since we are performing a right-tailed test, we adjust the p-value\n",
    "# If the t-statistic is positive, we divide by 2 for the right tail\n",
    "if t_statistic > 0:\n",
    "    p_value /= 2\n",
    "    print(f'p-value: {p_value}')\n",
    "else:\n",
    "    p_value = 1 - p_value / 2\n",
    "    print(f'p-value: {p_value}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0886d137",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b10965bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# paired t-test (right-tailed)\n",
    "# all you have to do is change the differences values in each array\n",
    "\n",
    "# Data \n",
    "pop1 = np.array([15, 22, 15, 27, 24, 23, 8, 20, 2])\n",
    "pop2 = np.array([18, 25, 17, 24, 30, 23, 10, 27, 3])\n",
    "\n",
    "# Calculate the differences\n",
    "differences = pop1 - pop2\n",
    "differences_array = np.array(differences)\n",
    "print(f'diff: {differences}')\n",
    "\n",
    "# alpha\n",
    "alpha = 0.10\n",
    "print(f'alpha: {alpha}')\n",
    "\n",
    "# Sample size\n",
    "n = len(differences)\n",
    "print(f'sample size: {n}')\n",
    "\n",
    "# test for normality\n",
    "# Ho: data is normally distributued\n",
    "# Ha: data is not normally distributed\n",
    "\n",
    "shapiro_test = stats.shapiro(differences)\n",
    "print(f'test for normality: {shapiro_test}')\n",
    "\n",
    "if (round(shapiro_test[1],2)) < alpha:\n",
    "    print(\"reject the null hypotheses\")\n",
    "else:\n",
    "    print(\"do not reject the null\")\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "stats.probplot(differences, dist=\"norm\", plot=ax)\n",
    "plt.title(\"Normal Probability Plot\")\n",
    "plt.xlabel('Theoretical Quantiles')\n",
    "plt.ylabel('Ordered Values')\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# mean difference\n",
    "mean_diff = np.mean(differences)\n",
    "print(f'mean diff: {mean_diff}')\n",
    "\n",
    "# Standard deviation of differences\n",
    "std_diff = np.std(differences, ddof=1)\n",
    "print(f'std of diff: {std_diff}')\n",
    "\n",
    "# t-statistic \n",
    "t_statistic = mean_diff / (std_diff / np.sqrt(n))\n",
    "print(f'paired t-statistic: {t_statistic}')\n",
    "\n",
    "# Degrees of freedom\n",
    "df = n - 1\n",
    "print(f'DoF: {df}')\n",
    "\n",
    "# Determine critical t-value for 95% confidence level (right-tailed test)\n",
    "t_critical = stats.t.ppf(1 - alpha, df)\n",
    "t_critical = round(t_critical,3)\n",
    "print(f'critical value: {t_critical}')\n",
    "\n",
    "# Conduct the right-tailed paired t-test\n",
    "# stats.ttest_rel() by default returns a two-tailed p-value\n",
    "t_statistic, p_value = stats.ttest_rel(pop1, pop2)\n",
    "\n",
    "# Since we are performing a right-tailed test, we adjust the p-value\n",
    "# If the t-statistic is positive, we divide by 2 for the right tail\n",
    "if t_statistic < 0:\n",
    "    p_value /= 2\n",
    "    print(f'p-value: {p_value}')\n",
    "else:\n",
    "    p_value = 1 - p_value / 2\n",
    "    print(f'p-value: {p_value}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08bc7920",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6ad265b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# paired-t-test (two-tailed)\n",
    "# quick method\n",
    "\n",
    "# Array of differences\n",
    "differences = [49, -67, 8, 16, 6, 23, 28, 41, 14, 29, 56, 24, 75, 60, -48]\n",
    "\n",
    "# Perform a paired t-test\n",
    "# Pass the differences array and the value 0 \n",
    "# Test if the average of these differences is non-zero\n",
    "t_statistic, p_value = stats.ttest_1samp(differences, 0)\n",
    "\n",
    "# Check significance at both the 5% and 1% levels\n",
    "alpha_5_percent = 0.05\n",
    "alpha_1_percent = 0.01\n",
    "\n",
    "# Prepare the conclusion based on p-value\n",
    "significance_5_percent = p_value < alpha_5_percent\n",
    "significance_1_percent = p_value < alpha_1_percent\n",
    "\n",
    "t_statistic, p_value, significance_5_percent, significance_1_percent\n"
   ]
  }
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