correlation_confidence_interval.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "38109fab",
   "metadata": {},
   "source": [
    "# Confidence interval for Pearson's correlation\n",
    "\n",
    "With a given correlation $\\rho$, the transformed $z$ following is approximately normally distributed with variance of $\\frac{1}{n-3}$ where $n$ is the sample size.\n",
    "\n",
    "$$\n",
    "z = \\frac{1}{2} {\\rm ln}\\left( \\frac{1 + \\rho}{1 - \\rho} \\right)\n",
    "$$\n",
    "\n",
    "This is just an `arctanh` function to map from (-1, 1) to (-inf, inf), or if you fancy so-called Fisher transformation (https://en.wikipedia.org/wiki/Fisher_transformation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "169b8419",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:14.962878Z",
     "iopub.status.busy": "2021-09-12T14:27:14.962626Z",
     "iopub.status.idle": "2021-09-12T14:27:15.335590Z",
     "shell.execute_reply": "2021-09-12T14:27:15.335182Z",
     "shell.execute_reply.started": "2021-09-12T14:27:14.962815Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('bmh')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9465973e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.336252Z",
     "iopub.status.busy": "2021-09-12T14:27:15.336116Z",
     "iopub.status.idle": "2021-09-12T14:27:15.338765Z",
     "shell.execute_reply": "2021-09-12T14:27:15.338410Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.336220Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def to_z(corr):\n",
    "    \"\"\" Convert a Pearson correlation to $z$ which is approximately normally distributed \"\"\"\n",
    "    return 0.5 * np.log((1 + corr) / (1 - corr))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bcbb5ca",
   "metadata": {},
   "source": [
    "$z$ goes to `inf` when $\\rho$ is 1 or -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4816b00a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.339702Z",
     "iopub.status.busy": "2021-09-12T14:27:15.339571Z",
     "iopub.status.idle": "2021-09-12T14:27:15.360149Z",
     "shell.execute_reply": "2021-09-12T14:27:15.359645Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.339685Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-2-b383a178c785>:3: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return 0.5 * np.log((1 + corr) / (1 - corr))\n",
      "<ipython-input-2-b383a178c785>:3: RuntimeWarning: divide by zero encountered in log\n",
      "  return 0.5 * np.log((1 + corr) / (1 - corr))\n"
     ]
    }
   ],
   "source": [
    "corr = np.linspace(-1, 1, 1000)\n",
    "z = to_z(corr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "463cb439",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.361269Z",
     "iopub.status.busy": "2021-09-12T14:27:15.361117Z",
     "iopub.status.idle": "2021-09-12T14:27:15.507246Z",
     "shell.execute_reply": "2021-09-12T14:27:15.506757Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.361248Z"
    },
    "tags": []
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(corr, z)\n",
    "ax.set_xlabel('Pearson correlation')\n",
    "ax.set_ylabel('z');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72645943",
   "metadata": {},
   "source": [
    "# Two-sided confidence interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4e4ef3b8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.507983Z",
     "iopub.status.busy": "2021-09-12T14:27:15.507849Z",
     "iopub.status.idle": "2021-09-12T14:27:15.511668Z",
     "shell.execute_reply": "2021-09-12T14:27:15.511095Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.507966Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def corr_ci(corr, alpha: float, n: int):\n",
    "    \"\"\" Compute the two-sided confidence interva for a Pearson correlation \"\"\"\n",
    "    sigma = norm.ppf(alpha + (1 - alpha) / 2, 0, 1)\n",
    "    z = to_z(corr)\n",
    "    var = 1.0 / (n - 3)\n",
    "    \n",
    "    z_lower = z - sigma * var ** 0.5\n",
    "    z_upper = z + sigma * var ** 0.5\n",
    "    \n",
    "    corr_lower = (np.exp(2 * z_lower) - 1) / (np.exp(2 * z_lower) + 1)\n",
    "    corr_upper = (np.exp(2 * z_upper) - 1) / (np.exp(2 * z_upper) + 1)\n",
    "    \n",
    "    return corr_lower, corr_upper"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf8ebea9",
   "metadata": {},
   "source": [
    "Symmetric when the base correlation is 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f60c03fa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.512386Z",
     "iopub.status.busy": "2021-09-12T14:27:15.512254Z",
     "iopub.status.idle": "2021-09-12T14:27:15.531418Z",
     "shell.execute_reply": "2021-09-12T14:27:15.530873Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.512369Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.19641811768205933, 0.19641811768205936)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corr_ci(0, alpha=0.95, n=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e04cfc59",
   "metadata": {},
   "source": [
    "Otherwise it's asymmetric. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "37c533fb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.532281Z",
     "iopub.status.busy": "2021-09-12T14:27:15.532069Z",
     "iopub.status.idle": "2021-09-12T14:27:15.544508Z",
     "shell.execute_reply": "2021-09-12T14:27:15.543995Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.532263Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.3366433044090918, 0.6341398407485443)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corr_ci(0.5, alpha=0.95, n=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9980c9c2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.545253Z",
     "iopub.status.busy": "2021-09-12T14:27:15.545113Z",
     "iopub.status.idle": "2021-09-12T14:27:15.556694Z",
     "shell.execute_reply": "2021-09-12T14:27:15.556317Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.545235Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-2-b383a178c785>:3: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return 0.5 * np.log((1 + corr) / (1 - corr))\n",
      "<ipython-input-2-b383a178c785>:3: RuntimeWarning: divide by zero encountered in log\n",
      "  return 0.5 * np.log((1 + corr) / (1 - corr))\n",
      "<ipython-input-5-38ed633e41fe>:10: RuntimeWarning: invalid value encountered in true_divide\n",
      "  corr_lower = (np.exp(2 * z_lower) - 1) / (np.exp(2 * z_lower) + 1)\n",
      "<ipython-input-5-38ed633e41fe>:11: RuntimeWarning: invalid value encountered in true_divide\n",
      "  corr_upper = (np.exp(2 * z_upper) - 1) / (np.exp(2 * z_upper) + 1)\n"
     ]
    }
   ],
   "source": [
    "corr_lower, corr_upper = corr_ci(corr, alpha=0.95, n=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e3577c1e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.557900Z",
     "iopub.status.busy": "2021-09-12T14:27:15.557760Z",
     "iopub.status.idle": "2021-09-12T14:27:15.740691Z",
     "shell.execute_reply": "2021-09-12T14:27:15.740209Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.557882Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(corr, corr, label='Base correlation')\n",
    "ax.plot(corr, corr_lower, label='lower 95% CI', color='black', lw=1, ls='--')\n",
    "ax.plot(corr, corr_upper, label='upper 95% CI', color='black', lw=1, ls='--')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "14b6a19f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.741561Z",
     "iopub.status.busy": "2021-09-12T14:27:15.741416Z",
     "iopub.status.idle": "2021-09-12T14:27:15.744976Z",
     "shell.execute_reply": "2021-09-12T14:27:15.744553Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.741543Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-2-b383a178c785>:3: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return 0.5 * np.log((1 + corr) / (1 - corr))\n",
      "<ipython-input-2-b383a178c785>:3: RuntimeWarning: divide by zero encountered in log\n",
      "  return 0.5 * np.log((1 + corr) / (1 - corr))\n",
      "<ipython-input-5-38ed633e41fe>:10: RuntimeWarning: invalid value encountered in true_divide\n",
      "  corr_lower = (np.exp(2 * z_lower) - 1) / (np.exp(2 * z_lower) + 1)\n",
      "<ipython-input-5-38ed633e41fe>:11: RuntimeWarning: invalid value encountered in true_divide\n",
      "  corr_upper = (np.exp(2 * z_upper) - 1) / (np.exp(2 * z_upper) + 1)\n"
     ]
    }
   ],
   "source": [
    "corr_lower2, corr_upper2 = corr_ci(corr, alpha=0.95, n=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a745761",
   "metadata": {},
   "source": [
    "The band becomes narrower as the sample size increases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "026bae9a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-09-12T14:27:15.745703Z",
     "iopub.status.busy": "2021-09-12T14:27:15.745567Z",
     "iopub.status.idle": "2021-09-12T14:27:15.953311Z",
     "shell.execute_reply": "2021-09-12T14:27:15.952808Z",
     "shell.execute_reply.started": "2021-09-12T14:27:15.745685Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(corr, corr, label='Base correlation')\n",
    "ax.plot(corr, corr_lower, label='lower 95% CI (n=100)', color='black', lw=1, ls='--')\n",
    "ax.plot(corr, corr_upper, label='upper 95% CI (n=100)', color='black', lw=1, ls='--')\n",
    "ax.plot(corr, corr_lower2, label='lower 95% CI (n=1000)', color='red', lw=1, ls='--')\n",
    "ax.plot(corr, corr_upper2, label='upper 95% CI (n=1000)', color='red', lw=1, ls='--')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a00ae957",
   "metadata": {},
   "source": [
    "# Reference\n",
    "- Confidence Intervals for Pearson’s Correlation https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/PASS/Confidence_Intervals_for_Pearsons_Correlation.pdf"
   ]
  }
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