{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bc6f073d-3176-4aac-9e59-171eafb0733b",
   "metadata": {},
   "source": [
    "# Lab 3-2: Rank-Sum Test Example\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02ac0f40-5029-49f4-a033-5a3e527df715",
   "metadata": {},
   "source": [
    "Note that the [scipy.stats.ranksums](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ranksums.html) function should only be used to compare two samples from continuous distributions (i.e. theoretical distributions). It does not handle ties between measurements nor does it apply the continuity correction. For a rank sum test function that can compare discontinuous distribution (i.e. empirical data), handle ties, and apply a continuity correction, use [scipy.stats.mannwhitneyu](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e053f7b5-85f6-48ba-9c2d-0c754c210cb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import libraries we'll need\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ddc5986a-03e3-43a9-89bf-a278188319e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.10/site-packages/openpyxl/worksheet/_read_only.py:79: UserWarning: Unknown extension is not supported and will be removed\n",
      "  for idx, row in parser.parse():\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date of peak</th>\n",
       "      <th>water year</th>\n",
       "      <th>peak value (cfs)</th>\n",
       "      <th>gage_ht (feet)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1928-10-09</td>\n",
       "      <td>1929</td>\n",
       "      <td>18800</td>\n",
       "      <td>10.55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1930-02-05</td>\n",
       "      <td>1930</td>\n",
       "      <td>15800</td>\n",
       "      <td>10.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1931-01-28</td>\n",
       "      <td>1931</td>\n",
       "      <td>35100</td>\n",
       "      <td>14.08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  date of peak  water year  peak value (cfs)  gage_ht (feet)\n",
       "0   1928-10-09        1929             18800           10.55\n",
       "1   1930-02-05        1930             15800           10.44\n",
       "2   1931-01-28        1931             35100           14.08"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read the excel file\n",
    "skykomish_data_file = '../data/Skykomish_peak_flow_12134500_skykomish_river_near_gold_bar.xlsx'\n",
    "skykomish_data = pd.read_excel(skykomish_data_file)\n",
    "# Preview our data\n",
    "skykomish_data.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "971f2d36-72d0-4bed-a511-a0956e8622ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set our alpha and confidence from our prior z-tests\n",
    "alpha = 0.05\n",
    "conf = 1 - alpha\n",
    "\n",
    "# Calculate z_alpha from a normal distribution (from our prior z-tests)\n",
    "z_alpha = stats.norm.ppf(conf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f85190f6-3bf6-4b69-858e-9858d670a87d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Divide the data into the early period (before 1975) and late period (after and including 1975).\n",
    "skykomish_before = skykomish_data[ skykomish_data['water year'] < 1975 ] \n",
    "skykomish_after = skykomish_data[ skykomish_data['water year'] >= 1975 ] "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a778ec8a-e9e4-4041-b0ca-0d41df5a9e72",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "In this example, we will test the significance of the change in the mean between the two sample periods using the two-sample Rank-Sum test. Read the documentation for [scipy.stats.mannwhitneyu](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2d3d1262-2bb1-44ee-b0ff-5ec92f1ff75c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U from stats.mannwhitneyu: 1394.5\n",
      "P from stats.mannwhitneyu: 0.0022\n",
      "Z from looking up (1-P): 2.8498\n"
     ]
    }
   ],
   "source": [
    "u_rs, p_rs = stats.mannwhitneyu(skykomish_after['peak value (cfs)'], \n",
    "                                skykomish_before['peak value (cfs)'],\n",
    "                                use_continuity=True,\n",
    "                                alternative=\"greater\")\n",
    "\n",
    "print(\"U from stats.mannwhitneyu: {}\".format(np.round(u_rs,4)))\n",
    "print(\"P from stats.mannwhitneyu: {}\".format(np.round(p_rs,4)))\n",
    "\n",
    "z_rs = stats.norm.ppf(1-p_rs)\n",
    "print(\"Z from looking up (1-P): {}\".format(np.round(z_rs,4)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a2521e1-61fd-43ca-87e8-6989c29fe46c",
   "metadata": {},
   "source": [
    "This returns u_mannwhitneyu, the test statistic U presuming this is a large enough sample that this is normally distributed, and p_mannwhitneyu, the one-sided p-value of the test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "08b62b8f-e5b9-4f8b-89c1-999e1390bd35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make a plot\n",
    "plt.figure(figsize=(10,6))\n",
    "\n",
    "# Create values for z\n",
    "z = np.linspace(-4, 4, num=160)\n",
    "\n",
    "# Plot the Null PDF\n",
    "plt.plot(z, stats.norm.pdf(z), label='Null PDF: ($\\overline{x}$ - $\\overline{y}$)')\n",
    "\n",
    "# Plot where z_alpha is\n",
    "plt.axvline(z_alpha, color='black', label=r'z$_\\alpha$')\n",
    "# Add label here with alpha value\n",
    "plt.text(z_alpha+0.05, 0.2, r'$z_{\\alpha}$ = ' + str(round(z_alpha,2)),fontsize=12, color='k')\n",
    "\n",
    "# Plot z_test by looking up p-value from MannWhitneyU test\n",
    "plt.axvline(z_rs, color='r', label=r'z$_{rs}$')\n",
    "# Add label here with z value (by looking up p-value from MannWhitneyU test)\n",
    "plt.text(z_rs+0.05, 0.3, r'$z_{rs}$ = ' + str(round(z_rs,2)),fontsize=12, color='r')\n",
    "\n",
    "# Add title, legend, and labels\n",
    "plt.title('Rank-Sum Test',fontsize=20)\n",
    "plt.xlabel('Z', fontsize=15)\n",
    "plt.ylabel('Probability',fontsize=15)\n",
    "plt.ylim(0, 0.5)\n",
    "plt.legend(loc='upper left',fontsize=12);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3b36f60-8418-475d-a9bb-821b536e5ef0",
   "metadata": {},
   "source": [
    "**How does our conclusions from the Rank-Sum test compare to our prior two-sample Z-test of the same hypothesis in [Lab 2-1](https://mountain-hydrology-research-group.github.io/data-analysis/modules/module2/lab2-1.html#two-sample-z-test)?** (i.e. compare p-value for the two tests) Only consider the case where the null hypothesis is that no change has occurred."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dbed0f45-eb29-4f7f-af82-08bcf01e4e86",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}