{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b63k23jwy8p",
   "metadata": {},
   "source": [
    "# Statistical Significance and Error Bars\n",
    "\n",
    "Lecture 13 | CMU ANLP Spring 2026 | Instructor: Sean Welleck\n",
    "\n",
    "Basics of evaluating model performance with confidence intervals and statistical significance testing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0a1e7ad8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "307fdda7",
   "metadata": {},
   "source": [
    "### Setup\n",
    "\n",
    "- $q_i$: question $i$\n",
    "- $s_i$: score on question $i$\n",
    "- $n$: number of evaluation questions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbf3b4a9",
   "metadata": {},
   "source": [
    "#### Scenario\n",
    "\n",
    "Suppose we evaluate model A and model B on HumanEval. In this case, \n",
    "\n",
    "- $s_i$ is either 0 or 1 (incorrect or correct, based on test cases passing)\n",
    "- $n$ is 164"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "606fe939",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1,\n",
       "        0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,\n",
       "        1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1,\n",
       "        0, 1, 1, 0, 0, 1, 1, 1, 1, 1]),\n",
       " array([1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,\n",
       "        1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1,\n",
       "        1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu_A = 0.86\n",
    "mu_B = 0.86\n",
    "\n",
    "n = 164\n",
    "\n",
    "scores_A = np.random.binomial(1, mu_A, n)\n",
    "scores_B = np.random.binomial(1, mu_B, n)\n",
    "\n",
    "scores_A, scores_B"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19507c93",
   "metadata": {},
   "source": [
    "### Standard error and confidence intervals\n",
    "\n",
    "$$SE_{Bernoulli}=\\sqrt{\\bar s(1-\\bar s)/n}$$\n",
    "\n",
    "$$CI_{95\\%}=\\bar s \\pm 1.96\\times SE$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0b795a3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.8414634146341463), np.float64(0.8902439024390244))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_A = np.mean(scores_A)\n",
    "mean_B = np.mean(scores_B)\n",
    "\n",
    "mean_A, mean_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e8527ba8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.02852071738082699), np.float64(0.024408826948108142))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "se_A = np.sqrt(mean_A*(1.0-mean_A)/n)\n",
    "se_B = np.sqrt(mean_B*(1.0-mean_B)/n)\n",
    "se_A, se_B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b0df235a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((np.float64(0.7855628085677254), np.float64(0.8973640207005672)),\n",
       " (np.float64(0.8424026016207324), np.float64(0.9380852032573164)))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ci_95_A = (mean_A-1.96*se_A, mean_A+1.96*se_A)\n",
    "ci_95_B = (mean_B-1.96*se_B, mean_B+1.96*se_B)\n",
    "\n",
    "ci_95_A, ci_95_B"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ee4190e",
   "metadata": {},
   "source": [
    "Look at the confidence intervals above; intuitively, do you think that we can conclude that one model is better than the other?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75ef7e80",
   "metadata": {},
   "source": [
    "### Comparing models: unpaired analysis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6275c15d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.299440529053058)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_BA = mean_B - mean_A\n",
    "se_BA = np.sqrt(se_A**2 +se_B**2)\n",
    "\n",
    "z = mean_BA/se_BA\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f88ebce",
   "metadata": {},
   "source": [
    "<img src=\"https://www.ztable.net/wp-content/uploads/2018/11/positiveztable.png\" height=500px>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "dd8c702d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.9031036047966683)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy\n",
    "scipy.stats.norm.cdf(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5a770ed",
   "metadata": {},
   "source": [
    "Interpretation: the observed difference is `z` standard errors away from 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2da72605",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19379999999999997"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_z = 0.9031\n",
    "\n",
    "p = 2*(1-p_z)\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c1fa727",
   "metadata": {},
   "source": [
    "Interpretation: if the two models truly have equal performance, then there is a `p`*100\\% chance that we'd see the observed difference just due to sampling variability.\n",
    "\n",
    "Example decision rule:\n",
    "- `p < 0.05`: result is rare enough; reject the null hypothesis that the two models are equal. We say that the result is statistically significant (p = 0.05).\n",
    "- `p > 0.05`: result isn't that rare; don't reject the null hypothesis that the two models' performances are equal. The difference could be noise.\n",
    "\n",
    "In other words, `p=0.194` means that we do not have evidence that model B is actually better than model A."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62cfa0ad",
   "metadata": {},
   "source": [
    "### Comparing models: paired analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "569ee5f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.037539607788304036), np.float64(0.03438704414581275))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_AB = mean_A - mean_B\n",
    "\n",
    "temp = 0\n",
    "for sa, sb in zip(scores_A, scores_B):\n",
    "    sab = sa - sb\n",
    "    temp += ((sab - mean_AB)**2)\n",
    "\n",
    "se_paired = np.sqrt(((1/(n-1))*temp)/n)\n",
    "se_BA, se_paired"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d392a5ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(1.8439760797588902)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z_paired = mean_AB/se_paired\n",
    "p_z_paired = scipy.stats.norm.cdf(z_paired)\n",
    "p_paired = 2*(1-p_z_paired)\n",
    "p_paired\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94b75367",
   "metadata": {},
   "source": [
    "### Effect of dataset size on standard error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "925fdcd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=  100: SE=0.0347\n",
      "n=  156: SE=0.0278\n",
      "n=  500: SE=0.0155\n",
      "n= 1000: SE=0.0110\n",
      "n= 2000: SE=0.0078\n",
      "n= 5000: SE=0.0049\n"
     ]
    }
   ],
   "source": [
    "observed_accuracy = 0.86\n",
    "\n",
    "dataset_sizes = [100, 156, 500, 1000, 2000, 5000]\n",
    "\n",
    "ses = [np.sqrt(observed_accuracy * (1-observed_accuracy)/n) for n in dataset_sizes]\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))\n",
    "\n",
    "# Linear scale\n",
    "ax1.plot(dataset_sizes, ses, 'o-', linewidth=2, markersize=8)\n",
    "ax1.set_xlabel('Number of questions (n)')\n",
    "ax1.set_ylabel('Standard Error')\n",
    "ax1.set_title(f'SE vs dataset size (observed accuracy = {observed_accuracy})')\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Log-log scale\n",
    "ax2.plot(dataset_sizes, ses, 'o-', linewidth=2, markersize=8)\n",
    "ax2.set_xlabel('Number of questions (n)')\n",
    "ax2.set_ylabel('Standard Error')\n",
    "ax2.set_title('Log-log: SE ∝ 1/√n')\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_yscale('log')\n",
    "ax2.grid(True, alpha=0.3, which='both')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "for n, se in zip(dataset_sizes, ses):\n",
    "    print(f\"n={n:5d}: SE={se:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "jvngazi7zg",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope from data: -0.5000\n",
      "\n",
      "Interpretation: doubling n reduces SE by a factor of 1.414\n"
     ]
    }
   ],
   "source": [
    "# Check the slope\n",
    "log_n = np.log(dataset_sizes)\n",
    "log_se = np.log(ses)\n",
    "\n",
    "# Fit a line: log(SE) = a + b*log(n)\n",
    "slope, intercept = np.polyfit(log_n, log_se, 1)\n",
    "\n",
    "print(f\"Slope from data: {slope:.4f}\")\n",
    "print(f\"\\nInterpretation: doubling n reduces SE by a factor of {2**(-slope):.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a3d9219",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "anlp",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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