analysis/9.5_fragsys_RSA_clusters_annotator.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ANNOTATING BOXPLOTS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IMPORTING NECESSARY PACKAGES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import colorsys\n",
    "import itertools\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from fractions import Fraction\n",
    "import matplotlib.pyplot as plt\n",
    "from typing import Iterable, Tuple\n",
    "from statannotations.Annotator import Annotator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SOME FUNCTIONS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "### COLOURS ###\n",
    "\n",
    "# This code I did not write, I grabbed it from the following URL:\n",
    "\n",
    "# https://stackoverflow.com/questions/470690/how-to-automatically-generate-n-distinct-colors\n",
    "\n",
    "def zenos_dichotomy() -> Iterable[Fraction]:\n",
    "    \"\"\"\n",
    "    http://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%C2%B7_%C2%B7_%C2%B7\n",
    "    \"\"\"\n",
    "    for k in itertools.count():\n",
    "        yield Fraction(1,2**k)\n",
    "\n",
    "def fracs() -> Iterable[Fraction]:\n",
    "    \"\"\"\n",
    "    [Fraction(0, 1), Fraction(1, 2), Fraction(1, 4), Fraction(3, 4), Fraction(1, 8), Fraction(3, 8), Fraction(5, 8), Fraction(7, 8), Fraction(1, 16), Fraction(3, 16), ...]\n",
    "    [0.0, 0.5, 0.25, 0.75, 0.125, 0.375, 0.625, 0.875, 0.0625, 0.1875, ...]\n",
    "    \"\"\"\n",
    "    yield Fraction(0)\n",
    "    for k in zenos_dichotomy():\n",
    "        i = k.denominator # [1,2,4,8,16,...]\n",
    "        for j in range(1,i,2):\n",
    "            yield Fraction(j,i)\n",
    "\n",
    "# can be used for the v in hsv to map linear values 0..1 to something that looks equidistant\n",
    "# bias = lambda x: (math.sqrt(x/3)/Fraction(2,3)+Fraction(1,3))/Fraction(6,5)\n",
    "\n",
    "HSVTuple = Tuple[Fraction, Fraction, Fraction]\n",
    "RGBTuple = Tuple[float, float, float]\n",
    "\n",
    "def hue_to_tones(h: Fraction) -> Iterable[HSVTuple]:\n",
    "    for s in [Fraction(6,10)]: # optionally use range\n",
    "        for v in [Fraction(8,10),Fraction(5,10)]: # could use range too\n",
    "            yield (h, s, v) # use bias for v here if you use range\n",
    "\n",
    "def hsv_to_rgb(x: HSVTuple) -> RGBTuple:\n",
    "    return colorsys.hsv_to_rgb(*map(float, x))\n",
    "\n",
    "flatten = itertools.chain.from_iterable\n",
    "\n",
    "def hsvs() -> Iterable[HSVTuple]:\n",
    "    return flatten(map(hue_to_tones, fracs()))\n",
    "\n",
    "def rgbs() -> Iterable[RGBTuple]:\n",
    "    return map(hsv_to_rgb, hsvs())\n",
    "\n",
    "def plot_boxes(df, x, y, order, pairs, col_palette, flierprops, fsize = (5, 5), dpi = 100, annotate = False, ann_loc = \"inside\", ylab = None, out = None, show = True):\n",
    "    \"\"\"\n",
    "    customised boxplot plotting function\n",
    "    \"\"\"\n",
    "    plt.figure(figsize = fsize, dpi = dpi)\n",
    "    \n",
    "    ax = sns.boxplot(data = df, x = x, y = y, order = order, palette = col_palette, flierprops = flierprops)\n",
    "    if ylab != None:\n",
    "        plt.ylabel(ylab)\n",
    "    if annotate == True:\n",
    "        annotator = Annotator(ax, pairs, data = df, x = x, y = y, order = order)\n",
    "        annotator.configure(test = \"Mann-Whitney\", text_format = \"star\", loc = ann_loc)\n",
    "        annotator.apply_and_annotate()\n",
    "        \n",
    "    if show == False:\n",
    "        plt.close()\n",
    "        \n",
    "    if out != None:\n",
    "        plt.savefig(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## READING INPUT DATA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "main_dir = \"./../\"\n",
    "results_dir = os.path.join(main_dir, \"results\")\n",
    "figs_dir = os.path.join(main_dir, \"figs\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "rsa_df = pd.read_pickle(os.path.join(results_dir, \"clusters_rsa.pkl\"))\n",
    "shenk_df = pd.read_pickle(os.path.join(results_dir, \"clusters_shenkin.pkl\"))\n",
    "mess_df = pd.read_pickle(os.path.join(results_dir, \"clusters_mes.pkl\"))\n",
    "burial_df = pd.read_pickle(os.path.join(results_dir, \"clusters_burial_size.pkl\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "order = [1, 2, 3, 4]\n",
    "pairs = [(1, 2),(1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]\n",
    "flierprops = dict(marker = \"o\", markerfacecolor = \"black\", markersize = 4,\n",
    "                  markeredgecolor = \"none\")\n",
    "sample_colors = list(itertools.islice(rgbs(), 200)) # list of colours\n",
    "my_pal = {i: sample_colors[i-1] for i in order}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CHARACTERISING RSA-BASED CLUSTERS: RSA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "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>RSA</th>\n",
       "      <th>Cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>29.88</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>78.38</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>32.99</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     RSA  Cluster\n",
       "0  29.88        1\n",
       "1  78.38        1\n",
       "2  32.99        1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(rsa_df.head(3), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cluster\n",
       "1    20.09\n",
       "2    31.25\n",
       "3    41.27\n",
       "4    55.01\n",
       "Name: RSA, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rsa_df.groupby(\"Cluster\").RSA.mean().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value annotation legend:\n",
      "      ns: p <= 1.00e+00\n",
      "       *: 1.00e-02 < p <= 5.00e-02\n",
      "      **: 1.00e-03 < p <= 1.00e-02\n",
      "     ***: 1.00e-04 < p <= 1.00e-03\n",
      "    ****: p <= 1.00e-04\n",
      "\n",
      "1 vs. 2: Mann-Whitney-Wilcoxon test two-sided, P_val:5.288e-28 U_stat=3.725e+05\n",
      "2 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:4.524e-19 U_stat=4.365e+05\n",
      "3 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:1.302e-09 U_stat=3.842e+04\n",
      "1 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:1.741e-62 U_stat=1.396e+05\n",
      "2 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:7.928e-26 U_stat=4.988e+04\n",
      "1 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:2.371e-46 U_stat=1.292e+04\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boxes(\n",
    "    rsa_df, \"Cluster\", \"RSA\", order, pairs, my_pal, flierprops,\n",
    "    fsize = (5, 5), dpi = 100, annotate = True, ann_loc = \"inside\", ylab = \"RSA %\",\n",
    "    #out = os.path.join(figs_dir, \"RSA_clusters_size.png\"),\n",
    "    show = True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CHARACTERISING RSA-BASED CLUSTERS: SHENKIN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "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>Shenkin</th>\n",
       "      <th>Cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>30.12</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.16</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.24</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Shenkin  Cluster\n",
       "0    30.12        1\n",
       "1     1.16        1\n",
       "2    18.24        1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(shenk_df.head(3), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cluster\n",
       "1    22.27\n",
       "2    29.78\n",
       "3    34.95\n",
       "4    33.96\n",
       "Name: Shenkin, dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(shenk_df, 2).groupby(\"Cluster\").Shenkin.mean().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value annotation legend:\n",
      "      ns: p <= 1.00e+00\n",
      "       *: 1.00e-02 < p <= 5.00e-02\n",
      "      **: 1.00e-03 < p <= 1.00e-02\n",
      "     ***: 1.00e-04 < p <= 1.00e-03\n",
      "    ****: p <= 1.00e-04\n",
      "\n",
      "1 vs. 2: Mann-Whitney-Wilcoxon test two-sided, P_val:9.249e-13 U_stat=1.550e+05\n",
      "2 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:2.794e-06 U_stat=1.713e+05\n",
      "3 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:5.934e-01 U_stat=1.595e+04\n",
      "1 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:7.938e-24 U_stat=6.249e+04\n",
      "2 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:5.003e-02 U_stat=2.624e+04\n",
      "1 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:1.202e-07 U_stat=9.253e+03\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boxes(\n",
    "    shenk_df, \"Cluster\", \"Shenkin\", order, pairs, my_pal, flierprops,\n",
    "    fsize = (5, 5), dpi = 100, annotate = True, ann_loc = \"inside\", ylab = \"NShenkin\",\n",
    "    #out = os.path.join(figs_dir, \"RSA_clusters_size.png\"),\n",
    "    show = True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CHARACTERISING RSA-BASED CLUSTERS: MES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "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>MES</th>\n",
       "      <th>Cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.75</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.28</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.57</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    MES  Cluster\n",
       "0 -0.75        1\n",
       "1 -0.28        1\n",
       "2 -0.57        1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(mess_df.head(3), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cluster\n",
       "1   -0.17\n",
       "2   -0.07\n",
       "3   -0.02\n",
       "4    0.06\n",
       "Name: MES, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mess_df.groupby(\"Cluster\").MES.mean().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value annotation legend:\n",
      "      ns: p <= 1.00e+00\n",
      "       *: 1.00e-02 < p <= 5.00e-02\n",
      "      **: 1.00e-03 < p <= 1.00e-02\n",
      "     ***: 1.00e-04 < p <= 1.00e-03\n",
      "    ****: p <= 1.00e-04\n",
      "\n",
      "1 vs. 2: Mann-Whitney-Wilcoxon test two-sided, P_val:4.733e-04 U_stat=8.297e+04\n",
      "2 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:6.473e-02 U_stat=1.174e+05\n",
      "3 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:8.577e-02 U_stat=8.740e+03\n",
      "1 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:8.987e-07 U_stat=4.460e+04\n",
      "2 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:1.560e-02 U_stat=1.385e+04\n",
      "1 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:4.412e-05 U_stat=5.080e+03\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boxes(\n",
    "    mess_df, \"Cluster\", \"MES\", order, pairs, my_pal, flierprops,\n",
    "    fsize = (5, 5), dpi = 100, annotate = True, ann_loc = \"inside\",\n",
    "    #out = os.path.join(figs_dir, \"RSA_clusters_size.png\"),\n",
    "    show = True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CHARACTERISING RSA-BASED CLUSTERS: SITE SIZE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "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>cluster_id</th>\n",
       "      <th>prop_burial</th>\n",
       "      <th>bs_size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.67</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1.00</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0.67</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   cluster_id  prop_burial  bs_size\n",
       "0           1         0.67       24\n",
       "1           1         1.00        6\n",
       "2           1         0.67       12"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(burial_df.head(3), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value annotation legend:\n",
      "      ns: p <= 1.00e+00\n",
      "       *: 1.00e-02 < p <= 5.00e-02\n",
      "      **: 1.00e-03 < p <= 1.00e-02\n",
      "     ***: 1.00e-04 < p <= 1.00e-03\n",
      "    ****: p <= 1.00e-04\n",
      "\n",
      "1 vs. 2: Mann-Whitney-Wilcoxon test two-sided, P_val:2.111e-04 U_stat=3.997e+03\n",
      "2 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:3.288e-07 U_stat=8.114e+03\n",
      "3 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:1.826e-07 U_stat=2.165e+03\n",
      "1 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:1.344e-09 U_stat=3.419e+03\n",
      "2 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:2.547e-13 U_stat=3.443e+03\n",
      "1 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:4.910e-11 U_stat=1.270e+03\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boxes(\n",
    "    burial_df, \"cluster_id\", \"bs_size\", order, pairs, my_pal, flierprops,\n",
    "    fsize = (5, 5), dpi = 100, annotate = True, ann_loc = \"inside\", ylab = \"Binding site size\",\n",
    "    #out = os.path.join(figs_dir, \"RSA_clusters_size.png\"),\n",
    "    show = True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CHARACTERISING RSA-BASED CLUSTERS: BURIAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "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>cluster_id</th>\n",
       "      <th>prop_burial</th>\n",
       "      <th>bs_size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.67</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1.00</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0.67</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   cluster_id  prop_burial  bs_size\n",
       "0           1         0.67       24\n",
       "1           1         1.00        6\n",
       "2           1         0.67       12"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(burial_df.head(3), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cluster_id\n",
       "1    0.68\n",
       "2    0.47\n",
       "3    0.30\n",
       "4    0.10\n",
       "Name: prop_burial, dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "burial_df.groupby(\"cluster_id\").prop_burial.mean().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cluster_id\n",
       "1    15.61\n",
       "2    11.49\n",
       "3     8.53\n",
       "4     5.00\n",
       "Name: bs_size, dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "burial_df.groupby(\"cluster_id\").bs_size.mean().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value annotation legend:\n",
      "      ns: p <= 1.00e+00\n",
      "       *: 1.00e-02 < p <= 5.00e-02\n",
      "      **: 1.00e-03 < p <= 1.00e-02\n",
      "     ***: 1.00e-04 < p <= 1.00e-03\n",
      "    ****: p <= 1.00e-04\n",
      "\n",
      "1 vs. 2: Mann-Whitney-Wilcoxon test two-sided, P_val:7.213e-17 U_stat=5.344e+03\n",
      "2 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:1.139e-22 U_stat=1.027e+04\n",
      "3 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:1.095e-10 U_stat=2.368e+03\n",
      "1 vs. 3: Mann-Whitney-Wilcoxon test two-sided, P_val:4.278e-21 U_stat=4.158e+03\n",
      "2 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:8.333e-17 U_stat=3.664e+03\n",
      "1 vs. 4: Mann-Whitney-Wilcoxon test two-sided, P_val:3.237e-13 U_stat=1.334e+03\n"
     ]
    },
    {
     "data": {
      "image/png": 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hKCgII0aMwF/+8hf07dsXn332WYv3SklJQXV1tfZTVlbWFo9A1GbKy8sRHx+PqqoqDB06FDdv3kR8fPxDy1t7jsgRWc2iDYIgYPv27Zg4ceIj627ZsgUzZszA1q1b8eyzzz6y/iuvvILvv/8e+fn5BsXCRRvI3jR9ZxoVFQWlUtnsnemD5QBadY7vTMme2O2iDTk5OZg5cyZycnIMSqSiKKK4uBiDBg1qg+iIrJO+BNd08JAh5aacI7J3kibT2tpaXLx4UXt8+fJlFBcXw9PTEz169EBKSgrKy8vxxRdfALiXSKdOnYrMzEyEhYWhsrISwL0tlhQKBQBgyZIlCAsLQ58+faBSqZCVlYXi4mKsXLmy7R+QyAoplUqjyk05R+QoJH1neuzYMQQHB2tH2iYnJyM4OBgffPABAKCiogKlpaXa+mvWrMHdu3cxe/ZsdOvWTftJSkrS1qmqqsKrr76K/v37IyYmBuXl5SgsLMTw4cPb9uGIiMhhWM07U2vCd6ZERAQYng9sdjQvERGRtWAyJSIiMpHNjeYlshVN93MkadjyPppkW5hMiSxAFEUkJibi5MmTUofi0IKCgrBu3TomVLI4dvMSWYBGo2EitQIlJSXsHaA2wZYpkYUVFBRoVw2itqFWqxETEyN1GORATEqm169fx9GjR9HQ0IBhw4ahW7du5oqLyG64ubkxmRLZuVYn07y8PCQmJqJv3764c+cOzp8/j5UrV2LGjBnmjI+IiMjqGfzOtLa2Vud4yZIl+Oc//4l//vOfOHHiBLZu3YoFCxaYPUAiIiJrZ3AyDQkJwc6dO7XH7dq1w9WrV7XH//vf/+Dq6mre6IiIiGyAwcsJXrlyBW+88QZkMhlWrlyJS5cuIT4+Hg0NDbh79y6cnJyQnZ2N8ePHWzpmi+NygmSqpnNMOdex7fHnT+Zi9i3Yevbsid27d2Pz5s14+umnkZSUhIsXL+LixYtoaGhAv379IJfLzRI8ka0TBIGDjiTEnz+1NaPnmU6ePFn7njQqKgqNjY0YMmQIEykRETkso0bz5ufn48yZMwgKCsL69euhVCoxefJkjB8/Hh999BH/J0hERA7J4JbpO++8g+nTp+O7777Da6+9hqVLlyIqKgonTpyATCbDkCFDkJ+fb8lYyU5ERUUZVW7KOSKitmBwy/Tzzz/Hnj17EBISghs3biAsLAyLFi2Cq6srfvvb3+LFF1/Ea6+9htjYWEvGSzbq0KFDUKvViI6O1pbt27cPbm5uLZYDaNW5yMhISz8OEZEOg5Np+/btcfnyZYSEhKCsrKzZO9IBAwbgm2++MXuAZB969OiB5ORkbNu2DTU1NXjjjTdw48YNpKWlYf78+c3K09PT0djYqPeaR50jImprBnfzpqamYurUqfDx8cHTTz+NpUuXWjIusjN+fn7YunUrFAoFioqK4OHhgdzcXPj7++st9/X1bfGaR50jImprBifTKVOmoKysDDt37sSVK1fw/PPPWzIusjPl5eWIj49HVVUVhg4dips3byI+Pv6h5a09R0TU1gxetMGRcNEG82v6zjQqKgpKpbLZO9MHywG06hzfmRKRuZh90Yb6+nqd5QIvXbqEzz77DBcuXEC3bt3w+uuvIyQkxLSoyW7pS3BNBw8ZUm7KOSIiSzK4Zers7IyKigp06dIFxcXFiIyMRN++fTFs2DAUFxejpKQEBw8exPDhwy0ds8WxZUpERIDh+cDgZOrk5ITKykp06dIFEyZMgFwux1/+8hftmpczZ85ERUWFXcw1ZTIlIiLAAt28TRUXFyM3N1dn8eikpCSMGzeuNbcjIiKyaQaP5hUEQZs8nZ2dm2Vod3d3VFdXmzc6IiIiG2Bwy1QURfTt2xeCIKC2thanTp3CoEGDtOcvXLiArl27WiRIMl7TLahIOtz+i8gxGJxMN2zYoHPcu3dvneNvv/0WL7zwgnmiIpOIoojExEScPHlS6lAcXlBQENatW8eESmTnOM9UD1sfgKRWqzFixAipw6CfHDx4kDsqEdkoiw5AIttRUFDAf8gloFarERMTI3UYRNRGjEqmJSUl+PLLL+Hp6YlJkyahc+fO2nMqlQpz587F559/bvYgqfXc3NyYTImILMzg0bwFBQUYPnw4cnNzkZaWhv79+2P//v3a82q1Gn/6058sEiQREZE1MziZLl68GPPnz8e//vUvXLlyBe+88w6ee+45fPXVV5aMj4iIyOoZ3M17+vRpbNy4EcC9Oadvv/02unfvjl/96lfIycmxi2UEiYiIWsPgZCqTyVBVVaVT9uKLL8LJyQnx8fHclNmKyOVyHDx4UPs1tT3+Dogci8HJdMiQIdi/f3+znWHi4uLQ2NiIadOmmT04ah1BEDjoSGL8HRA5FoOT6euvv47CwkK951588UUAwNq1a80TFRERkQ3hog162PqiDUREZB6G5gODR/MSERGRfkYl07KyMoSEhOB///ufTnl1dTWGDRuGf//732YNjoiIyBYYlUz9/PwAADk5OTrlW7duRU1NDfr27Wu+yIiIiGyE0d28U6dObbbS0caNGzF16lSzBUVERGRLjE6mU6ZMwZkzZ3D69GkAwJUrV3DkyBEmUyIiclhGJ9POnTtj/Pjx2tbppk2b8PTTT6N79+5Gf/PCwkJMmDABPj4+EAQBO3bseOQ1Bw4cQEhICORyOX72s5/hD3/4Q7M6eXl5CAwMhEwmQ2BgILZv3250bERERIZq1WjeqVOnYvPmzRBFERs3bmz1gg23bt1CUFAQVqxYYVD9y5cvY/z48RgxYgROnDiB999/H3PmzEFeXp62zpEjRxAXF4eEhASUlJQgISEBkyZNwtGjR1sVIxER0aO0ap7pnTt34OPjgzlz5mD58uWorKw0ebUXQRCwfft2TJw4scU67777Lv72t7/h7Nmz2rJZs2ahpKQER44cAXBvRSaVSoX8/HxtnWeeeQaPP/54s4FTLWnreaaiKEKj0VjkfnK5HIIgmOW+5rwXEZEtsOjm4C4uLnjxxRexdOlSJCQktNmyaUeOHGm24fK4ceOwfv163LlzBy4uLjhy5AjmzZvXrE5GRkaL962rq0NdXZ32WKVSmTfwR9BoNIiKimrT79kaSqWSS+QREenR6kUbZsyYAV9fX8ycOdOc8TxUZWUlvL29dcq8vb1x9+5dXL9+/aF1KisrW7xvamoqFAqF9nN/ChAREZEhWtUyBYDg4GBcvnzZnLEY5MFuxvu91E3L9dV5WPdkSkoKkpOTtccqlapNE6pcLodSqTTb/dRqNWJjYwEA+fn5ZmtNcvcTIiL9Wp1MH9TQ0IAvv/zyoe88TdW1a9dmLcyrV6+iXbt26NSp00PrPNhabUomk0Emk5k/YANZcocRNzc3ds0SEVmYyWvznjt3Du+88w58fHwwadIkc8TUovDwcOzdu1enrKCgAE8++SRcXFweWiciIsKisRERkeNqVTK9desWPv/8c0RGRmLAgAEoKirCxx9/jB9++MGo+9TW1qK4uBjFxcUA7k19KS4uRmlpKYB73a9NF4OYNWsW/vvf/yI5ORlnz57F559/jvXr12P+/PnaOklJSSgoKEBaWhrOnTuHtLQ07Nu3D3Pnzm3NoxIRET2aaITDhw+LM2fOFDt06CAGBweLy5cvF52dncXTp08bcxut/fv3iwCafaZNmyaKoihOmzZNfPrpp3WuUSqVYnBwsOjq6ir27NlTXL16dbP7bt26VQwICBBdXFzEfv36iXl5eUbFVV1dLQIQq6urW/VcUrt9+7Y4fPhwcfjw4eLt27elDoeIyGYZmg8MnmcaGBiI27dvY/LkyXjppZcQGBgI4N40mZKSEu2xPbD1/UzVarV2qg2nsxARtZ7Z9zO9ePEiRo4ciVGjRqF///5mCZKIiMgeGJxML1++jICAALz++uvo3r075s+fjxMnTnBFHCIicngGJ1NfX18sWLAAFy9exMaNG1FZWYnIyEjcvXsX2dnZ3BiciIgcVqtG844ePRqbNm1CRUUFVqxYgX/84x/o168fBg8ebO74iIiIrJ5J80wVCgXeeOMNHDt2DEVFRTaxviwREZG5mbwC0t27d6HRaDBkyBBkZWWZIyYiIiKbYnDLdPfu3di4caNO2ccff4wOHTrAw8MDMTExuHnzptkDJCIisnYGJ9Ply5frbE12+PBhfPDBB1i0aBH+8pe/oKysDEuXLrVIkERERNbM4GT6r3/9S2d927/+9a8YO3YsFixYgF/84hdIT0/Hl19+aZEgiYiIrJnBybSmpka7MwsAfPPNNxg9erT2eMCAAUavzUtERGQPDE6mPj4+OHv2LIB7C9SXlJQgMjJSe/7HH39E+/btzR8hERGRlTM4mf7qV7/C3LlzsXHjRrzyyivo2rUrwsLCtOePHTuGgIAAiwRJRERkzQyeGvPhhx/ihx9+wJw5c9C1a1ds2rQJzs7O2vM5OTmYMGGCRYIkIiKyZgYn0/bt2zebGtPU/v37zRIQERGRrTFpBaSmNBoNli9fbq7bERER2Qyjkun169exa9cuFBQUoKGhAQBw584dZGZmomfPnli2bJlFgiQiIrJmBnfzHj58GM8++yyqq6shCAKefPJJbNiwARMnTkRjYyMWLlyImTNnWjJWIiIiq2Rwy3TRokUYN24cTp48iaSkJHz33Xf4+c9/joULF+LChQv4zW9+w6kxRETkkAxOpiUlJVi0aBEGDhyI3/72txAEAWlpaZg6dSo3CCciIodmcDK9ceMGvLy8ANwb2du+fXsEBwdbLDAiIiJbYfA7U0EQUFNTA7lcDlEUIQgCbt++rbP4PQC4u7ubPUgiIiJrZnAyFUURffv21Tlu2jK9n2Dvj/IlIiJyFAYnUy7KQEREpJ/ByfTpp5+2ZBxEREQ2y2wrIBERETkqJlMiIiITMZkSERGZiMmUiIjIREymREREJjJ4NO99t27dwrJly/D111/j6tWraGxs1Dn/n//8x2zBERER2QKjk+nLL7+MAwcOICEhAd26deO6vERE5PCMTqb5+fnYtWsXIiMjLREPERGRzTH6nenjjz8OT09PS8RCRERkk4xOpkuXLsUHH3yA27dvWyIeIiIim2N0N296ejouXboEb29v9OzZEy4uLjrni4qKzBYcERGRLTA6mU6cONEScRAREdkso5Pphx9+aIk4iIiIbJbRyfS+48eP4+zZsxAEAYGBgTp7mxIRETkSo5Pp1atXER8fD6VSCQ8PD4iiiOrqaowaNQq5ubnw8vKyRJxERERWy+jRvG+++SZUKhVOnz6NGzdu4ObNm/jXv/4FlUqFOXPmWCJGIiIiq2Z0y/Srr77Cvn370L9/f21ZYGAgVq5ciZiYGLMGR0REZAuMbpk2NjY2mw4DAC4uLs3W6SUiInIERifT0aNHIykpCT/88IO2rLy8HPPmzcOYMWPMGhwREZEtMDqZrlixAjU1NejZsyd69+6NJ554Ar169UJNTQ0+++wzowNYtWoVevXqBblcjpCQEBw8eLDFutOnT4cgCM0+AwYM0NbJzs7WW0ej0RgdGxERkSGMfmfq5+eHoqIi7N27F+fOnYMoiggMDER0dLTR33zLli2YO3cuVq1ahcjISKxZswaxsbE4c+YMevTo0ax+ZmYmli1bpj2+e/cugoKC8Otf/1qnnru7O86fP69TJpfLjY6PiIjIEK2eZzp27FiMHTvWpG/+u9/9DomJiXj55ZcBABkZGdizZw9Wr16N1NTUZvUVCgUUCoX2eMeOHbh58yZmzJihU08QBHTt2tWk2B5FFEWrbe2q1Wq9X1sTuVzO7fuIyG4YlEyzsrLw6quvQi6XIysr66F1DZ0eU19fj+PHj+O9997TKY+JicHhw4cNusf69esRHR0Nf39/nfLa2lr4+/ujoaEBQ4YMwdKlSx+6qERdXR3q6uq0xyqV6pHfW6PRICoqyqA4pRQbGyt1CHoplUq4ublJHQYRkVkYlEx///vfY8qUKZDL5fj973/fYj1BEAxOptevX0dDQwO8vb11yr29vVFZWfnI6ysqKpCfn4/NmzfrlPfr1w/Z2dkYNGgQVCoVMjMzERkZiZKSEvTp00fvvVJTU7FkyRKD4iYiInqQQcn08uXLer82hwe7+kRRNNvpiJEAACAASURBVKj7Lzs7Gx4eHs0W3g8LC0NYWJj2ODIyEkOHDsVnn33WYqs6JSUFycnJ2mOVSgU/Pz+Dn2FBQABcnYwey2UxoijijigCAFx+GoBlDeobG/HxA++yiYjsgdHvTD/66CPMnz8f7du31ylXq9X49NNP8cEHHxh0n86dO8PZ2blZK/Tq1avNWqsPEkURn3/+ORISEuDq6vrQuk5OThg2bBguXLjQYh2ZTAaZTGZQ3Pq4OjlZVTIFgNY/DRERGcvoDLBkyRLU1tY2K799+7ZRXaWurq4ICQnB3r17dcr37t2LiIiIh1574MABXLx4EYmJiY/8PqIoori4GN26dTM4NiIiImMY3TJtqRu2pKQEnp6eRt0rOTkZCQkJePLJJxEeHo61a9eitLQUs2bNAnCv+7W8vBxffPGFznXr169HaGgoBg4c2OyeS5YsQVhYGPr06QOVSoWsrCwUFxdj5cqVRsVGZKpr167h5MmTGDx4MDeAILJzBifTxx9/XLsAQt++fXUSakNDA2pra7VJ0FBxcXH48ccf8dFHH6GiogIDBw7E7t27taNzKyoqUFpaqnNNdXU18vLykJmZqfeeVVVVePXVV1FZWQmFQoHg4GAUFhZi+PDhRsVGZIo1a9Zgzpw5qK+vh6urK7KysvDaa69JHRYRWYggij+NVHmEP/3pTxBFETNnzkRGRobOfE9XV1f07NkT4eHhFgu0LalUKigUClRXV8Pd3V1vHbVarZ0as6R/f6t7Z2qN6hsb8eHZswDse2rMtWvX0L17d9TX12vLZDIZysrK2EIlsjGG5APAiJbptGnTcPfuXQBAdHQ0unfvbnqURHbo5MmTOokUuDeX+dSpUxg9erREURGRJRnVnGrXrh3eeOMNNDQ0WCoeIps3ePDgZqPMZTIZBg8eLFFERGRpRvdNhoaG4sSJE5aIhcgueHl5ISsrSzvdSiaTITMzE507d5Y4MiKyFKNH877xxht466238P333yMkJASPPfaYznn+75tskbnXWk5ISMCoUaNw5swZBAcHo0uXLmZZJ5lrGhNZJ6OTaVxcHADdNXgFQdBOmWEXMNkiW1lr2Z4HbhHZMqOTqbmXEyQiIrJ1RifTB3doIbIHcrkcSqXSbPdTq9XaHXvy8/PN1prkvrxE1qlV+5leunQJGRkZOHv2LARBQP/+/ZGUlITevXubOz6iNiEIgsW6T93c3Ng1S2TnjE6me/bswXPPPYchQ4YgMjISoiji8OHDGDBgAL788kuTNwy3FU3XuqhvbJQwEtvR9Odk4FohREQ2wehk+t5772HevHlYtmxZs/J3333XYZJp05Gf3FbMeBqNptnOQ0REtsroeaZnz57Vu1vLzJkzcebMGbMERUREZEuMbpl6eXmhuLgYffr00SkvLi5Gly5dzBaYtWs6EMTaNge3Vk03B+dAGiKyJ0Yn01deeQWvvvoq/vOf/yAiIgKCIOCbb75BWloa3nrrLUvEaJWaTpy3xs3BrR0XHiAie2J0Ml20aBE6duyI9PR0pKSkAAB8fHywePFinYUciIiIHIXRyVQQBMybNw/z5s1DTU0NAKBjx45mD4yIiMhWtGqeKQBcvXoV58+fhyAICAgI4D6NRETksIx+0adSqZCQkAAfHx88/fTTGDlyJHx8fPDSSy+hurraEjESERFZNaOT6csvv4yjR49i165dqKqqQnV1Nf7+97/j2LFjeOWVVywRIxERkVUzupt3165d2LNnD5566ilt2bhx4/DHP/4RzzzzjFmDIyIisgVGt0w7deoEhULRrFyhUODxxx83S1BERES2xOhkunDhQiQnJ6OiokJbVllZibfffhuLFi0ya3BERES2wOhu3tWrV+PixYvw9/dHjx49AAClpaWQyWS4du0a1qxZo61bVFRkvkiJiIislNHJdOLEiZaIg4iIyGYZnUw//PBDS8RBRERks1q9aMPx48e1m4MHBgYiODjYnHERERHZDKOT6dWrVxEfHw+lUgkPDw+Ioojq6mqMGjUKubm5XAmJiIgcjtHJ9M0334RKpcLp06fRv39/AMCZM2cwbdo0zJkzBzk5OWYP0trVNzZKHYIOURRxRxQBAC6CYDU7tFjbz4mIyFyMTqZfffUV9u3bp02kABAYGIiVK1ciJibGrMHZivt7dBIRkWMyep5pY2MjXFxcmpW7uLigkS0PIiJyQEa3TEePHo2kpCTk5OTAx8cHAFBeXo558+ZhzJgxZg/QWsnlciiVSqnD0EutViM2NhYAkJ+fDzc3N4kjak4ul0sdAhGR2RidTFesWIHnn38ePXv2hJ+fHwRBQGlpKQYNGoRNmzZZIkarJAiCVSapB7m5udlEnEREtszoZOrn54eioiLs3bsX586dgyiKCAwMRHR0tCXiIyJqlWvXruHkyZMYPHgwZxmQxRmVTO/evQu5XI7i4mKMHTsWY8eOtVRcRESttmbNGsyZMwf19fVwdXVFVlYWXnvtNanDIjtm1ACkdu3awd/fHw0NDZaKh4jIJNeuXdMmUgCor69HUlISrl27JnFkZM9atWtMSkoKbty4YYl4iIhMcvLkSW0iva+urg6nTp2SKCJyBEa/M83KysLFixfh4+MDf39/PPbYYzrnuVMMEUlp8ODBcHV11UmoMpkMgwcPljAqsndGJ9Pnn3/ealbUIccmiiI0Go3UYeilVqv1fm1N5HK5Xf5d9vLyQlZWFpKSklBXVweZTIbMzEx07txZ6tDIjgmi+NO6c6SlUqmgUChQXV0Nd3d3qcMxmlqtRlRUFABAqVTa7dSYps9JxrPnPxvAvXenp06dwqBBgzial1rN0Hxg8DvT27dvY/bs2fD19UWXLl0wefJkXL9+3SzBEhGZm5eXF0aPHs1ESm3C4G7eDz/8ENnZ2ZgyZQrkcjlycnLw+uuvY+vWrZaMj8ggEa6ucJY6iCZEUcT9xTWdAKvpTm0AcPiBwTlEZDqDk+m2bduwfv16xMfHAwBeeuklREZGoqGhAc7O1vTPGDkiZwDOVpKwAADWFEtTfKtDZBEGd/OWlZVhxIgR2uPhw4ejXbt2+OGHHywSGBERka0wOJk2NDTA1dVVp6xdu3a4e/euSQGsWrUKvXr1glwuR0hICA4ePNhiXaVSCeGn/Tmbfs6dO6dTLy8vD4GBgZDJZAgMDMT27dtNipGIiOhhDO7mFUUR06dPh0wm05ZpNBrMmjVLZ67ptm3bDP7mW7Zswdy5c7Fq1SpERkZizZo1iI2NxZkzZ9CjR48Wrzt//rzOqKqmAwyOHDmCuLg4LF26FC+88AK2b9+OSZMm4ZtvvkFoaKjBsRERERnK4KkxM2bMMOiGGzZsMPibh4aGYujQoVi9erW2rH///pg4cSJSU1Ob1VcqlRg1ahRu3rwJDw8PvfeMi4uDSqVCfn6+tuyZZ57B448/jpycHIPi4tQY29D0OUe4ulrXO1Mr1SCKOPjTACRr+7NhznnDTe9l7vm09jo/l/QzNB8Y3DI1Jkkaor6+HsePH8d7772nUx4TE4PDhw8/9Nrg4GBoNBoEBgZi4cKFGDVqlPbckSNHMG/ePJ3648aNQ0ZGRov3q6urQ11dnfZYpVIZ8yhEZAYajcYm5g1b239CyDoYvTavuVy/fh0NDQ3w9vbWKff29kZlZaXea7p164a1a9ciLy8P27ZtQ0BAAMaMGYPCwkJtncrKSqPuCQCpqalQKBTaj5+fnwlPRkREjsbo5QTN7cHuElEUW+xCCQgIQEBAgPY4PDwcZWVlWL58OUaOHNmqewJASkoKkpOTtccqlYoJlaiNyeVyKJVKs9xLrVYjNjYWAJCfn2/WlqRcLjfbvch+SJZMO3fuDGdn52YtxqtXrzZrWT5MWFgYNm3apD3u2rWr0feUyWQ6A6uIqO0JgmCR7lM3Nzd2y5LFSdbN6+rqipCQEOzdu1enfO/evYiIiDD4PidOnEC3bt20x+Hh4c3uWVBQYNQ9iYiIjCFpN29ycjISEhLw5JNPIjw8HGvXrkVpaSlmzZoF4F73a3l5Ob744gsAQEZGBnr27IkBAwagvr4emzZtQl5eHvLy8rT3TEpKwsiRI5GWlobnn38eO3fuxL59+/DNN99I8oxkOU0HojdwZR+DNP05cY8LIvORNJnGxcXhxx9/xEcffYSKigoMHDgQu3fvhr+/PwCgoqICpaWl2vr19fWYP38+ysvL4ebmhgEDBmDXrl0YP368tk5ERARyc3OxcOFCLFq0CL1798aWLVs4x9QONZ1GcfjOHQkjsU0ajQbt27eXOgwiu8At2PTgPFPbcOPGDe0gEzJefn4+PD09pQ7DIhzl7wBZntnnmRJZm6ajKiNcXLhogwEaRFHbiueoVCLzYTIlm9V0upOzIDCZGomr+BCZj2SjeYmIiOwFkykREZGJmEyJiIhMxGRKRERkIg5AIrvQAABWNMtLFEU0/vS1E6xnsE+D1AEQ2SkmU7ILh3/ao5OISArs5iUiIjIRW6Zks8y5ZZe5WXILMHPhog1E5sNkSjbLUlt2mRu3ACOyf+zmJSIiMhFbplZAFEWdHVBMpVar9X5tKrlcbjWjUomIrAmTqRXQaDTaHS7MzZy7qnD3DSIi/djNS0REZCK2TK2AuUelNu02NmfXLEd/EhHpx2RqBSwxKrV9+/ZmvR8REbWM3bxEREQmYjIlIiIyEbt5iajVzD2ty1wsNT3M3DjdzH4wmRJRq1lyWpe5mHN6mLlxupn9YDcvERGRidgyJSKzCFiwAE6urlKHAeBe97N45w4AQHBxsaqu1Mb6epz/+GOpwyAzYzIlIrNwcnW1mmQKAJDJpI6AHAi7eYmIiEzEZEpERGQiJlMiIiIT8Z0pEREBMO+8YUutEW6J+5kDkykREQGwjXnDgHXOz2U3LxERkYnYMiUiIgDm3Q5SrVZrV5/Kz883a0vSGreDZDIlIiIAltkOEgDc3NysrlvW3NjNS0REZCImUyIiIhMxmRIREZmIyZSIiMhETKZEREQm4mheIph35Rfg3rQAfV+bytpWfhFFUft1Y329hJHYjqY/p6Y/P7JtTKZEsOzKL/fn2pmDta380vQ/INyj03gajQbt27eXOgwyA3bzEhERmYgtUyKYd+UXwHKLfFvbyi9N4wlYsMC6Nge3Uo319dpWvLX9Pqn1mEyJYJmVXxyh+67pfxKcXF2ZTI1kTe+/yTTs5iUiIjKR5Ml01apV6NWrF+RyOUJCQnDw4MEW627btg1jx46Fl5cX3N3dER4ejj179ujUyc7OhiAIzT7mHKlJRETUlKTdvFu2bMHcuXOxatUqREZGYs2aNYiNjcWZM2fQo0ePZvULCwsxduxYfPLJJ/Dw8MCGDRswYcIEHD16FMHBwdp67u7uOH/+vM61fDdBZFnWNDVGFEWId+4AAAQXF6vqTrWmnxOZj6TJ9He/+x0SExPx8ssvAwAyMjKwZ88erF69Gqmpqc3qZ2Rk6Bx/8skn2LlzJ7788kudZCoIArp27WpwHHV1dairq9Meq1QqYx+FyOFxagw5Msm6eevr63H8+HHExMTolMfExODw4cMG3aOxsRE1NTXw9PTUKa+trYW/vz+6d++On//85zhx4sRD75OamgqFQqH9+Pn5GfcwRETk0CRrmV6/fh0NDQ3w9vbWKff29kZlZaVB90hPT8etW7cwadIkbVm/fv2QnZ2NQYMGQaVSITMzE5GRkSgpKUGfPn303iclJQXJycnaY5VKxYRKZABzTykyF0tuTG1OfP1kPySfGvPguwxRFA16v5GTk4PFixdj586d6NKli7Y8LCwMYWFh2uPIyEgMHToUn332GbKysvTeSyaTQSaTtfIJiByXpTaTNidH2JiapCdZMu3cuTOcnZ2btUKvXr3arLX6oC1btiAxMRFbt25FdHT0Q+s6OTlh2LBhuHDhgskxExER6SPZO1NXV1eEhIRg7969OuV79+5FREREi9fl5ORg+vTp2Lx5M5599tlHfh9RFFFcXIxu3bqZHDMREZE+knbzJicnIyEhAU8++STCw8Oxdu1alJaWYtasWQDuvcssLy/HF198AeBeIp06dSoyMzMRFhambdW6ublBoVAAAJYsWYKwsDD06dMHKpUKWVlZKC4uxsqVK6V5SCIisnuSJtO4uDj8+OOP+Oijj1BRUYGBAwdi9+7d8Pf3BwBUVFSgtLRUW3/NmjW4e/cuZs+ejdmzZ2vLp02bhuzsbABAVVUVXn31VVRWVkKhUCA4OBiFhYUYPnx4mz4bERE5DkHkhnrNqFQqKBQKVFdXw93dXepwiMhIarVau6WetW1b5yjs5XdgaD6QfDlBIiIiWyf51BgiImq9ptv9WRO1Wq33a2tjri0SmUyJiGyYRqPRdqdaq/sLaFgjc3VBs5uXiIjIRGyZEhHZCdeICMDZWeowANzrfkZj470DJyer2rkHDQ2oN3ANeEMxmRIR2QtnZwhWkkytKHU2Y4kpLOzmJSIiMhGTKZGFXLt2DV9//TWuXbsmdShEZGFMpkQWsGbNGnTv3h3R0dHo3r071qxZI3VIRGRBTKZEZnbt2jXMmTMH9fX1AID6+nokJSWxhUpkx5hMiczs5MmT2kR6X11dHU6dOiVRRERkaUymRGY2ePBguLq66pTJZDIMHjxYooiIyNKYTInMzMvLC1lZWZDJZADuJdLMzEx07txZ4siIyFI4z5TIAl577TX84he/wKlTpzBo0CB4eXlJHRIRWRCTKZGFeHl5YfTo0VKHQURtgN28REREJmIyJSIiMhGTKRERkYmYTImIiEzEZEpERGQiJlMiIiITMZkSERGZiMmUiIjIRFy0gYisgiiK0Gg0ZrmXWq3W+7U5yOVyCIJg1nuS7WMyJSKroNFoEBUVZfb7xsbGmvV+SqUSbm5uZr0n2T528xIREZmILVMisgpyuRxKpdIs92raZWzublm5XG62e5H9YDIlIqsgCIJZu0/bt29vtnsRPQq7eYmIiEzEZEpERGQiJlMiIiITMZkSERGZiMmUiIjIREymREREJmIyJSIiMhGTKRERkYmYTImIiEzEZEpERGQiJlMiIiITMZkSERGZiMmUiIjIREymREREJpI8ma5atQq9evWCXC5HSEgIDh48+ND6Bw4cQEhICORyOX72s5/hD3/4Q7M6eXl5CAwMhEwmQ2BgILZv326p8ImIiKRNplu2bMHcuXOxYMECnDhxAiNGjEBsbCxKS0v11r98+TLGjx+PESNG4MSJE3j//fcxZ84c5OXlaescOXIEcXFxSEhIQElJCRISEjBp0iQcPXq0rR6LiKzA2bNn8emnn+Ls2bNSh0IOQBBFUZTqm4eGhmLo0KFYvXq1tqx///6YOHEiUlNTm9V/99138be//U3nL8esWbNQUlKCI0eOAADi4uKgUqmQn5+vrfPMM8/g8ccfR05OjkFxqVQqKBQKVFdXw93dvbWPR0QSmTJlCjZv3qw9njx5Mv785z9LGJHl3L59G6NGjQIAuISGAs7Orb6XKIpAY6O5QrMcJycIgtD66xsacOenBtb+/fsfupG8ofmgXeujMU19fT2OHz+O9957T6c8JiYGhw8f1nvNkSNHEBMTo1M2btw4rF+/Hnfu3IGLiwuOHDmCefPmNauTkZHRYix1dXWoq6vTHqtUKmMfh4isxNmzZ3USKQBs3rwZCxcuRP/+/SWKynI0Go326zvsgTOaRqN5aDI1lGTdvNevX0dDQwO8vb11yr29vVFZWan3msrKSr317969i+vXrz+0Tkv3BIDU1FQoFArtx8/PrzWPRERW4O9//7ve8t27d7dxJORIJGuZ3vdgU10UxYc23/XVf7Dc2HumpKQgOTlZe6xSqZhQiWzUz3/+c7zzzjt6y+2Rh4eHzmstU4iiqNNLZ61kMplp3bxNeHh4mOU+kiXTzp07w9nZuVmL8erVq81alvd17dpVb/127dqhU6dOD63T0j2Be78YmUzWmscgIivTv39/TJ48udk704CAAAmjshwnJyd4enpKHYbDk6yb19XVFSEhIdi7d69O+d69exEREaH3mvDw8Gb1CwoK8OSTT8LFxeWhdVq6JxHZnz//+c84c+YMli9fjjNnztjt4COyIqKEcnNzRRcXF3H9+vXimTNnxLlz54qPPfaYeOXKFVEURfG9994TExIStPX/85//iO3btxfnzZsnnjlzRly/fr3o4uIi/vWvf9XWOXTokOjs7CwuW7ZMPHv2rLhs2TKxXbt24rfffmtwXNXV1SIAsbq62nwPS0RENsfQfCDpO9O4uDj8+OOP+Oijj1BRUYGBAwdi9+7d8Pf3BwBUVFTozDnt1asXdu/ejXnz5mHlypXw8fFBVlYWfvnLX2rrREREIDc3FwsXLsSiRYvQu3dvbNmyBaGhoW3+fERE5BgknWdqrTjPlIiIAMPzgeTLCRIREdk6JlMiIiITMZkSERGZSPJFG6zR/dfIXFaQiMix3c8DjxpexGSqR01NDQBwFSQiIgJwLy8oFIoWz3M0rx6NjY344Ycf0LFjR7MtWdXW7i+JWFZWxhHJEuHvQFr8+UvPHn4HoiiipqYGPj4+cHJq+c0oW6Z6ODk5oXv37lKHYRbu7u42+4fYXvB3IC3+/KVn67+Dh7VI7+MAJCIiIhMxmRIREZnIefHixYulDoIsw9nZGVFRUWjXjr35UuHvQFr8+UvPUX4HHIBERERkInbzEhERmYjJlIiIyERMpkRERCZiMiUiIjIRk6mdKSwsxIQJE+Dj4wNBELBjxw6pQ3IoqampGDZsGDp27IguXbpg4sSJOH/+vNRhOZTVq1dj8ODB2oUCwsPDkZ+fL3VYDi01NRWCIGDu3LlSh2IxTKZ25tatWwgKCsKKFSukDsUhHThwALNnz8a3336LvXv34u7du4iJicGtW7ekDs1hdO/eHcuWLcOxY8dw7NgxjB49Gs8//zxOnz4tdWgO6bvvvsPatWsxePBgqUOxKE6NsWOCIGD79u2YOHGi1KE4rGvXrqFLly44cOAARo4cKXU4DsvT0xOffvopEhMTpQ7FodTW1mLo0KFYtWoVfvvb32LIkCHIyMiQOiyLYMuUyIKqq6sB3PvHnNpeQ0MDcnNzcevWLYSHh0sdjsOZPXs2nn32WURHR0sdisXZ95IURBISRRHJycl46qmnMHDgQKnDcSinTp1CeHg4NBoNOnTogO3btyMwMFDqsBxKbm4uioqK8N1330kdSptgMiWykN/85jc4efIkvvnmG6lDcTgBAQEoLi5GVVUV8vLyMG3aNBw4cIAJtY2UlZUhKSkJBQUFkMvlUofTJvjO1I7xnal03nzzTezYsQOFhYXo1auX1OE4vOjoaPTu3Rtr1qyROhSHsGPHDrzwwgtwdnbWljU0NEAQBDg5OaGurk7nnD1gy5TIjERRxJtvvont27dDqVQykVoJURRRV1cndRgOY8yYMTh16pRO2YwZM9CvXz+8++67dpdIASZTu1NbW4uLFy9qjy9fvozi4mJ4enqiR48eEkbmGGbPno3Nmzdj586d6NixIyorKwHc21zYzc1N4ugcw/vvv4/Y2Fj4+fmhpqYGubm5UCqV+Oqrr6QOzWF07Nix2TiBxx57DJ06dbLb8QNMpnbm2LFjGDVqlPY4OTkZADBt2jRkZ2dLFJXjWL16NQAgKipKp3zDhg2YPn162wfkgP73v/8hISEBFRUVUCgUGDx4ML766iuMHTtW6tDIjvGdKRERkYk4z5SIiMhETKZEREQmYjIlIiIyEZMpERGRiZhMiYiITMRkSkREZCImUyIiIhMxmRIREZmIyZTIBl25cgWCIKC4uFjqUIw2ffr0R26+EBUVhblz57ZRRESmYzIlImRnZ8PDw6NNvldmZiaXtiS7w7V5ichsmm6z1RKFQtGGERG1DbZMiaxYY2Mj0tLS8MQTT0Amk6FHjx74+OOPm9XT17LcsWMHBEHQHpeUlGDUqFHo2LEj3N3dERISgmPHjkGpVGLGjBmorq6GIAgQBAGLFy8GANTX1+Odd96Br68vHnvsMYSGhkKpVDb7vn//+98RGBgImUyG//73vw99pge7eW/duoWpU6eiQ4cO6NatG9LT01vxkyKSFlumRFYsJSUFf/zjH/H73/8eTz31FCoqKnDu3LlW3WvKlCkIDg7G6tWr4ezsjOLiYri4uCAiIgIZGRn44IMPcP78eQBAhw4dANzbg/LKlSvIzc2Fj48Ptm/fjmeeeQanTp1Cnz59AAC3b99Gamoq1q1bh06dOqFLly5GxfX2229j//792L59O7p27Yr3338fx48fx5AhQ1r1nERSYDIlslI1NTXIzMzEihUrMG3aNABA79698dRTT+HKlStG36+0tBRvv/02+vXrBwDaZAjc63oVBAFdu3bVll26dAk5OTn4/vvv4ePjAwCYP38+vvrqK2zYsAGffPIJAODOnTtYtWoVgoKCjI6ptrYW69evxxdffKHdIu1Pf/oTunfvbvS9iKTEZEpkpc6ePYu6ujqMGTPGLPdLTk7Gyy+/jI0bNyI6Ohq//vWv0bt37xbrFxUVQRRF9O3bV6e8rq4OnTp10h67urpi8ODBrYrp0qVLqK+vR3h4uLbM09MTAQEBrbofkVSYTImslJubm8F1nZyc8ODWxHfu3NE5Xrx4MSZPnoxdu3YhPz8fH374IXJzc/HCCy/ovWdjYyOcnZ1x/PhxODs765y73w18P86m72aNwe2UyV5wABKRlerTpw/c3Nzw9ddfP7Kul5cXampqcOvWLW2Zvjmoffv2xbx581BQUIBf/OIX2LBhA4B7rcuGhgadusHBwWhoaMDVq1fxxBNP6Hyadgeb4oknnoCLiwu+/fZbbdnNmzfx73//2yz3J2orbJkSWSm5XI53330X77zzDlxdXREZGYlr167h9OnTzbp+Q0ND0b59e7z//vt488038c9//lNnLqdarcbbvQ1bGQAAAXdJREFUb7+NX/3qV+jVqxe+//57fPfdd/jlL38JAOjZsydqa2vx9ddfIygoCO3bt0ffvn0xZcoUTJ06Fenp6QgODsb169fxj3/8A4MGDcL48eNNfsYOHTogMTERb7/9Njp16gRvb28sWLDgoVNriKwR/8QSWbFFixbhrbfewgcffID+/fsjLi4OV69ebVbP09MTmzZtwu7duzFo0CDk5ORop7cAgLOzM3788UdMnToVffv2xaRJkxAbG4slS5YAACIiIjBr1izExcXBy8sL//d//wcA2LBhA6ZOnYq33noLAQEBeO6553D06FH4+fmZ7Rk//fRTjBw5Es899xyio6Px1FNPISQkxGz3J2oLgsiXFkRERCZhy5SIiMhETKZEZFYdOnRo8XPw4EGpwyOyCHbzEpFZXbx4scVzvr6+Rk35IbIVTKZEREQmYjcvERGRiZhMiYiITMRkSkREZCImUyIiIhMxmRIREZmIyZSIiMhETKZEREQm+n8qcfWhrApQdgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boxes(\n",
    "    burial_df, \"cluster_id\", \"prop_burial\", order, pairs, my_pal, flierprops,\n",
    "    fsize = (5, 5), dpi = 100, annotate = True, ann_loc = \"inside\", ylab = \"Proportion RSA<25%\",\n",
    "    #out = os.path.join(figs_dir, \"RSA_clusters_prop_burial.png\"),\n",
    "    show = True\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:stats]",
   "language": "python",
   "name": "conda-env-stats-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}