{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "630839fb",
   "metadata": {},
   "source": [
    "# Lesson 14: Advanced statistics demonstration\n",
    "\n",
    "This notebook demonstrates key concepts in advanced statistics including hypothesis testing, confidence intervals, and statistical inference.\n",
    "\n",
    "We'll explore:\n",
    "\n",
    "**1. Confidence intervals**\n",
    "\n",
    "- Constructing confidence intervals for sample means\n",
    "- Interpreting confidence interval coverage\n",
    "- Visualizing multiple confidence intervals\n",
    "\n",
    "**2. Hypothesis testing**\n",
    "\n",
    "- Comparing two samples with t-tests\n",
    "- Understanding null and alternative hypotheses\n",
    "- Interpreting p-values and significance levels\n",
    "\n",
    "**3. Type I errors through repeated testing**\n",
    "\n",
    "- Understanding false positive rates\n",
    "- Empirically demonstrating Type I error rates\n",
    "- Visualizing distributions of p-values and t-statistics\n",
    "\n",
    "**4. Multiple testing correction**\n",
    "\n",
    "- Controlling family-wise error rate\n",
    "- Applying Bonferroni correction\n",
    "- Comparing corrected and uncorrected significance levels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86aaf35a",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5c784930",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec797e2a",
   "metadata": {},
   "source": [
    "### Population distribution\n",
    "\n",
    "Generate a large sample to represent our population and visualize its characteristics. We'll create 10,000 data points from a normal distribution with mean 100 and standard deviation 15."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "796bdb87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate population data\n",
    "np.random.seed(42)\n",
    "population = np.random.normal(loc=100, scale=15, size=10000)\n",
    "\n",
    "# Calculate population parameters\n",
    "pop_mean = population.mean()\n",
    "pop_std = population.std()\n",
    "\n",
    "# Plot population distribution\n",
    "plt.title('Population Distribution')\n",
    "plt.hist(population, bins=50, edgecolor='black', color='skyblue')\n",
    "plt.axvline(pop_mean, color='red', linestyle='--', label=f'Mean: {pop_mean:.2f}')\n",
    "plt.axvline(pop_mean - pop_std, color='orange', label=f'±1 SD: {pop_std:.2f}')\n",
    "plt.axvline(pop_mean + pop_std, color='orange')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a22c0f3",
   "metadata": {},
   "source": [
    "## 1. Confidence interval for sample mean\n",
    "\n",
    "Draw a sample of 100 observations from the population and construct a 95% confidence interval around the sample mean. The confidence interval gives us a range of plausible values for the true population mean based on our sample.\n",
    "\n",
    "### 1.1. Construct 95% confidence interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c14d9796",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Draw a sample of 100 data points\n",
    "sample_size = 100\n",
    "sample = np.random.choice(population, size=sample_size, replace=False)\n",
    "\n",
    "# Calculate sample statistics\n",
    "sample_mean = sample.mean()\n",
    "sample_std = sample.std(ddof=1)\n",
    "sample_se = sample_std / np.sqrt(sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c203ae9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Construct 95% confidence interval\n",
    "confidence_level = 0.95\n",
    "alpha = 1 - confidence_level\n",
    "df = sample_size - 1\n",
    "\n",
    "# Use t-distribution for confidence interval\n",
    "t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "margin_of_error = t_critical * sample_se\n",
    "\n",
    "ci_lower = sample_mean - margin_of_error\n",
    "ci_upper = sample_mean + margin_of_error\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "15887ad4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample mean: 100.18\n",
      "\n",
      "95% Confidence Interval: [97.46, 102.90]\n",
      "Margin of error: ±2.72\n"
     ]
    }
   ],
   "source": [
    "print(f\"Sample mean: {sample_mean:.2f}\")\n",
    "print(f\"\\n95% Confidence Interval: [{ci_lower:.2f}, {ci_upper:.2f}]\")\n",
    "print(f\"Margin of error: ±{margin_of_error:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daad4709",
   "metadata": {},
   "source": [
    "### 1.2. Sample distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ad87f493",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the confidence interval\n",
    "plt.title('Sample distribution with 95% confidence interval')\n",
    "plt.hist(sample, bins=20, edgecolor='black', color='skyblue', label='Sample')\n",
    "plt.axvline(sample_mean, color='blue', label=f'Sample Mean: {sample_mean:.2f}')\n",
    "plt.axvline(ci_lower, color='orange', label=f'95% CI: [{ci_lower:.2f}, {ci_upper:.2f}]')\n",
    "plt.axvline(ci_upper, color='orange')\n",
    "plt.axvline(pop_mean, color='red', linestyle='--', label=f'Population Mean: {pop_mean:.2f}')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a0b67d0",
   "metadata": {},
   "source": [
    "### 1.3. Confidence intervals with reapeated samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b8f5390c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of CIs containing population mean: 96/100\n",
      "Actual coverage: 96.0%\n",
      "Expected coverage: 95%\n",
      "\n",
      "Interpretation: About 95% of confidence intervals should contain the true population mean.\n"
     ]
    }
   ],
   "source": [
    "# Draw 100 samples and calculate confidence intervals\n",
    "num_samples = 100\n",
    "sample_size = 100\n",
    "confidence_level = 0.95\n",
    "alpha = 1 - confidence_level\n",
    "\n",
    "# Store results\n",
    "ci_results = []\n",
    "contains_pop_mean = []\n",
    "\n",
    "for i in range(num_samples):\n",
    "    # Draw sample\n",
    "    sample = np.random.choice(population, size=sample_size, replace=False)\n",
    "    \n",
    "    # Calculate statistics\n",
    "    sample_mean = sample.mean()\n",
    "    sample_std = sample.std(ddof=1)\n",
    "    sample_se = sample_std / np.sqrt(sample_size)\n",
    "    \n",
    "    # Calculate confidence interval\n",
    "    df = sample_size - 1\n",
    "    t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "    margin_of_error = t_critical * sample_se\n",
    "    \n",
    "    ci_lower = sample_mean - margin_of_error\n",
    "    ci_upper = sample_mean + margin_of_error\n",
    "    \n",
    "    # Check if CI contains population mean\n",
    "    contains = ci_lower <= pop_mean <= ci_upper\n",
    "    \n",
    "    ci_results.append((ci_lower, ci_upper, sample_mean))\n",
    "    contains_pop_mean.append(contains)\n",
    "\n",
    "# Calculate coverage\n",
    "coverage = sum(contains_pop_mean) / num_samples * 100\n",
    "\n",
    "print(f\"Number of CIs containing population mean: {sum(contains_pop_mean)}/{num_samples}\")\n",
    "print(f\"Actual coverage: {coverage:.1f}%\")\n",
    "print(f\"Expected coverage: {confidence_level*100:.0f}%\")\n",
    "print(f\"\\nInterpretation: About 95% of confidence intervals should contain the true population mean.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "78436d9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the confidence intervals\n",
    "plt.figure(figsize=(6, 8))\n",
    "\n",
    "plt.title(f'95% confidence intervals from {num_samples} samples\\n{sum(contains_pop_mean)} intervals contain population mean ({coverage:.1f}%)')\n",
    "\n",
    "for i, (ci_lower, ci_upper, sample_mean) in enumerate(ci_results):\n",
    "\n",
    "    if contains_pop_mean[i]:\n",
    "        color = 'black'\n",
    "        label = 'Pop mean in CI'\n",
    "\n",
    "    else:\n",
    "        color = 'red'\n",
    "        label = 'Pop mean not in CI'\n",
    "\n",
    "    plt.plot([ci_lower, ci_upper], [i, i], color=color, linewidth=1, label=label)\n",
    "    plt.plot(sample_mean, i, 'o', color=color, markersize=2)\n",
    "\n",
    "plt.axvline(pop_mean, color='blue', linestyle='--', linewidth=2, label=f'Population Mean: {pop_mean:.2f}')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Sample Number')\n",
    "\n",
    "ax = plt.gca()\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "unique = [(h, l) for i, (h, l) in enumerate(zip(handles, labels)) if l not in labels[:i]]\n",
    "ax.legend(*zip(*unique), loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b449226",
   "metadata": {},
   "source": [
    "## 2. Comparing two samples with hypothesis testing\n",
    "\n",
    "Draw two random samples from the same population and compare their distributions. We'll use an independent samples t-test to determine if the two samples have significantly different means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "020ea6a3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 1 - Mean: 101.82, SD: 13.44\n",
      "Sample 2 - Mean: 99.05, SD: 15.23\n",
      "Difference in means: 2.77\n"
     ]
    }
   ],
   "source": [
    "# Draw two samples of size 50\n",
    "sample_size = 50\n",
    "sample1 = np.random.choice(population, size=sample_size, replace=False)\n",
    "sample2 = np.random.choice(population, size=sample_size, replace=False)\n",
    "\n",
    "# Calculate statistics for both samples\n",
    "mean1 = sample1.mean()\n",
    "mean2 = sample2.mean()\n",
    "std1 = sample1.std(ddof=1)\n",
    "std2 = sample2.std(ddof=1)\n",
    "\n",
    "print(f\"Sample 1 - Mean: {mean1:.2f}, SD: {std1:.2f}\")\n",
    "print(f\"Sample 2 - Mean: {mean2:.2f}, SD: {std2:.2f}\")\n",
    "print(f\"Difference in means: {abs(mean1 - mean2):.2f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "50f1c756",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create boxplot comparison\n",
    "plt.title('Comparison of two samples (n=50 each)')\n",
    "plt.boxplot([sample1, sample2], tick_labels=['Sample 1', 'Sample 2'])\n",
    "plt.ylabel('Value')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4f7b1c4",
   "metadata": {},
   "source": [
    "### 2.1. Hypothesis formulation\n",
    "\n",
    "1. **Null hypothesis (H₀)**: The means of the two samples are equal (μ₁ = μ₂).\n",
    "2. **Alternative hypothesis (H₁)**: The means of the two samples are different (μ₁ ≠ μ₂).\n",
    "\n",
    "This is a two-tailed test because we're checking for any difference, not a specific direction."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1c84902",
   "metadata": {},
   "source": [
    "### 2.2. t-test for differences in means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "09aef357",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Independent Samples t-test:\n",
      " - t-statistic: 0.9627\n",
      " - p-value: 0.3381\n"
     ]
    }
   ],
   "source": [
    "# Perform independent samples t-test\n",
    "t_statistic, p_value = stats.ttest_ind(sample1, sample2)\n",
    "\n",
    "print(f\"\\nIndependent Samples t-test:\")\n",
    "print(f\" - t-statistic: {t_statistic:.4f}\")\n",
    "print(f\" - p-value: {p_value:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ab712ed",
   "metadata": {},
   "source": [
    "**Result**: The p-value (0.1034) is above the significance level of α = 0.05 so we do not reject the null hypothesis and conclude there is no significant difference between the two sample means."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe8c75b0",
   "metadata": {},
   "source": [
    "### 2.3. Test statistic distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2c853d37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize t-distribution with rejection regions\n",
    "df = 2 * sample_size - 2  # Degrees of freedom for two-sample t-test\n",
    "t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "\n",
    "# Generate t-distribution\n",
    "t_values = np.linspace(-4, 4, 1000)\n",
    "t_pdf = stats.t.pdf(t_values, df)\n",
    "\n",
    "plt.title(f't-distribution (df={df}) with rejection regions (α={alpha:0.2f})')\n",
    "\n",
    "plt.plot(t_values, t_pdf, color='black', label='t-distribution')\n",
    "\n",
    "# Shade rejection regions\n",
    "rejection_left = t_values[t_values <= -t_critical]\n",
    "rejection_right = t_values[t_values >= t_critical]\n",
    "plt.fill_between(rejection_left, stats.t.pdf(rejection_left, df), alpha=0.3, color='red', label='Rejection region')\n",
    "plt.fill_between(rejection_right, stats.t.pdf(rejection_right, df), alpha=0.3, color='red')\n",
    "\n",
    "# Mark critical values\n",
    "plt.axvline(-t_critical, color='red', label=f'Critical values: ±{t_critical:.3f}')\n",
    "plt.axvline(t_critical, color='red')\n",
    "\n",
    "# Mark observed t-statistic\n",
    "plt.axvline(t_statistic, color='green', label=f'Observed t: {t_statistic:.3f}')\n",
    "\n",
    "plt.xlabel('t-value')\n",
    "plt.ylabel('Probability density')\n",
    "plt.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "235f8d74",
   "metadata": {},
   "source": [
    "**Decision rules**\n",
    "\n",
    "- **Fail to reject H₀** if p-value ≥ α (evidence is not strong enough to conclude a difference exists)\n",
    "- **Reject H₀** if p-value < α (evidence suggests a significant difference exists)\n",
    "\n",
    "Since both samples are drawn from the same population, any rejection of the null hypothesis would be a Type I error.\n",
    "\n",
    "**Type I error**\n",
    "\n",
    "When using α = 0.05, we will incorrectly reject the null hypothesis (false positive) on average 5% of the time, even when the null hypothesis is true. This is known as a **Type I error** or false positive."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f851e073",
   "metadata": {},
   "source": [
    "## 3. Understanding Type I errors through repeated testing\n",
    "\n",
    "Repeat the sampling and t-test process multiple times to empirically demonstrate the Type I error rate. Since both samples come from the same population, the null hypothesis is always true, so any rejections are Type I errors (false positives)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "caf838f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_tests = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcb937a5",
   "metadata": {},
   "source": [
    "### 3.1. T-test with repeated sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c1942101",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from 100 independent t-tests:\n",
      " - Null hypothesis rejected: 6 times (incorrect conclusion)\n",
      " - Null hypothesis accepted: 94 times (correct conclusion)\n",
      " - Errors: 6.0% (expected ~5.0%)\n"
     ]
    }
   ],
   "source": [
    "# Repeat sampling and t-test 100 times\n",
    "sample_size = 50\n",
    "alpha = 0.05\n",
    "\n",
    "rejections = []\n",
    "p_values = []\n",
    "t_statistics = []\n",
    "\n",
    "for i in range(num_tests):\n",
    "\n",
    "    # Draw two samples from the same population\n",
    "    sample1 = np.random.choice(population, size=sample_size, replace=False)\n",
    "    sample2 = np.random.choice(population, size=sample_size, replace=False)\n",
    "    \n",
    "    # Perform t-test\n",
    "    t_statistic, p_value = stats.ttest_ind(sample1, sample2)\n",
    "    t_statistics.append(t_statistic)\n",
    "    p_values.append(p_value)\n",
    "    \n",
    "    # Check if null hypothesis is rejected\n",
    "    reject = p_value < alpha\n",
    "    rejections.append(reject)\n",
    "\n",
    "# Count results\n",
    "num_rejections = sum(rejections)\n",
    "num_acceptances = num_tests - num_rejections\n",
    "\n",
    "print(f'Results from {num_tests} independent t-tests:')\n",
    "print(f' - Null hypothesis rejected: {num_rejections} times (incorrect conclusion)')\n",
    "print(f' - Null hypothesis accepted: {num_acceptances} times (correct conclusion)')\n",
    "print(f' - Errors: {num_rejections/num_tests*100:.1f}% (expected ~{alpha*100:.1f}%)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c0ea131",
   "metadata": {},
   "source": [
    "### 3.2. Distribution of p-values & t-statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "4c78b869",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the distribution of p-values and t-statistics\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "# Plot p-values distribution\n",
    "ax1.set_title(f'Distribution of p-values from {num_tests} t-tests\\n{num_rejections} rejections (p < {alpha})')\n",
    "ax1.hist(p_values, bins=20, density=True, edgecolor='black', color='purple')\n",
    "ax1.axvline(alpha, color='red', label=f'α = {alpha}')\n",
    "ax1.set_xlabel('p-value')\n",
    "ax1.set_ylabel('Frequency')\n",
    "ax1.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "# Plot t-statistics distribution\n",
    "ax2.set_title(f'Distribution of t-statistics from {num_tests} t-tests\\n{num_rejections} beyond critical values')\n",
    "ax2.hist(t_statistics, bins=30, density=True, edgecolor='black', color='teal')\n",
    "ax2.axvline(-t_critical, color='red', label=f'Critical values: ±{t_critical:.3f}')\n",
    "ax2.axvline(t_critical, color='red')\n",
    "ax2.set_xlabel('t-statistic')\n",
    "ax2.set_ylabel('Frequency')\n",
    "ax2.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52eddd7b",
   "metadata": {},
   "source": [
    "**Interpretation**: When conducting a large number of tests, we will falsely reject the null hypothesis approximately 5% of the time, even when it is true."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2b4e9c0",
   "metadata": {},
   "source": [
    "## 4. Multiple testing correction\n",
    "\n",
    "When performing multiple hypothesis tests, the probability of making at least one Type I error increases. The Bonferroni correction adjusts the significance level to control the family-wise error rate.\n",
    "\n",
    "**Bonferroni correction**: Divide the desired α by the number of tests.\n",
    "\n",
    "- Original α = 0.05\n",
    "- Bonferroni-corrected α = 0.05 / number of tests\n",
    "\n",
    "This ensures the overall probability of making any Type I error across all tests remains at approximately 5%.\n",
    "\n",
    "### 4.1. T-test with repeated sampling and Bonferroni correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "ddcc7bd7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results from 100 independent t-tests:\n",
      "\n",
      "Bonferroni correction (α = 0.000500):\n",
      " - Null hypothesis rejected: 0 times\n",
      " - Null hypothesis accepted: 100 times\n",
      " - Error rate: 0.00%\n",
      "\n",
      "Uncorrected (α = 0.05):\n",
      " - Expected error rate: ~5.0%\n"
     ]
    }
   ],
   "source": [
    "# Repeat sampling and t-test with Bonferroni correction\n",
    "sample_size = 50\n",
    "alpha = 0.05\n",
    "alpha_bonferroni = alpha / num_tests  # Bonferroni correction\n",
    "\n",
    "rejections_bonferroni = []\n",
    "p_values_bonferroni = []\n",
    "t_statistics_bonferroni = []\n",
    "\n",
    "for i in range(num_tests):\n",
    "\n",
    "    # Draw two samples from the same population\n",
    "    sample1 = np.random.choice(population, size=sample_size, replace=False)\n",
    "    sample2 = np.random.choice(population, size=sample_size, replace=False)\n",
    "    \n",
    "    # Perform t-test\n",
    "    t_statistic, p_value = stats.ttest_ind(sample1, sample2)\n",
    "    t_statistics_bonferroni.append(t_statistic)\n",
    "    p_values_bonferroni.append(p_value)\n",
    "    \n",
    "    # Check if null hypothesis is rejected using Bonferroni correction\n",
    "    reject = p_value < alpha_bonferroni\n",
    "    rejections_bonferroni.append(reject)\n",
    "\n",
    "# Count results\n",
    "num_rejections_bonf = sum(rejections_bonferroni)\n",
    "num_acceptances_bonf = num_tests - num_rejections_bonf\n",
    "\n",
    "print(f'Results from {num_tests} independent t-tests:')\n",
    "print(f'\\nBonferroni correction (α = {alpha_bonferroni:.6f}):')\n",
    "print(f' - Null hypothesis rejected: {num_rejections_bonf} times')\n",
    "print(f' - Null hypothesis accepted: {num_acceptances_bonf} times')\n",
    "print(f' - Error rate: {num_rejections_bonf/num_tests*100:.2f}%')\n",
    "print(f'\\nUncorrected (α = {alpha}):')\n",
    "print(f' - Expected error rate: ~{alpha*100:.1f}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9a81ff9",
   "metadata": {},
   "source": [
    "### 4.2. Distribution of p-values and t-statistics with Bonferroni correction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5745b400",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the distribution of p-values and t-statistics with Bonferroni correction\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "# Plot p-values distribution\n",
    "ax1.set_title(f'Distribution of p-values from {num_tests} t-tests\\n{num_rejections_bonf} rejections (p < {alpha_bonferroni:.6f})')\n",
    "ax1.hist(p_values_bonferroni, bins=20, density=True, edgecolor='black', color='purple')\n",
    "ax1.axvline(alpha_bonferroni, color='red', label=f'α Bonf = {alpha_bonferroni:.6f}')\n",
    "ax1.axvline(alpha, color='orange', label=f'α uncorrected = {alpha}')\n",
    "ax1.set_xlabel('p-value')\n",
    "ax1.set_ylabel('Frequency')\n",
    "ax1.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "# Plot t-statistics distribution\n",
    "df = 2 * sample_size - 2\n",
    "t_critical = stats.t.ppf(1 - alpha/2, df)\n",
    "\n",
    "df = 2 * sample_size - 2\n",
    "t_critical_bonferroni = stats.t.ppf(1 - alpha_bonferroni/2, df)\n",
    "\n",
    "ax2.set_title(f'Distribution of t-statistics from {num_tests} t-tests\\n{num_rejections_bonf} beyond critical values')\n",
    "ax2.hist(t_statistics_bonferroni, bins=30, density=True, edgecolor='black', color='teal')\n",
    "ax2.axvline(-t_critical_bonferroni, color='red', label=f'Critical Bonf: ±{t_critical_bonferroni:.3f}')\n",
    "ax2.axvline(t_critical_bonferroni, color='red')\n",
    "ax2.axvline(-t_critical, color='orange', label=f'Critical uncorrected: ±{t_critical:.3f}')\n",
    "ax2.axvline(t_critical, color='orange')\n",
    "ax2.set_xlabel('t-statistic')\n",
    "ax2.set_ylabel('Frequency')\n",
    "ax2.legend(loc='best', framealpha=1, edgecolor='black')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
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