One-Way-ANOVA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "datafile = \"PlantGrowth.csv\"\n",
    "data = pd.read_csv(datafile, index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>weight</th>\n",
       "      <th>group</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.17</td>\n",
       "      <td>ctrl</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.58</td>\n",
       "      <td>ctrl</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.18</td>\n",
       "      <td>ctrl</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.11</td>\n",
       "      <td>ctrl</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4.50</td>\n",
       "      <td>ctrl</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   weight group\n",
       "1    4.17  ctrl\n",
       "2    5.58  ctrl\n",
       "3    5.18  ctrl\n",
       "4    6.11  ctrl\n",
       "5    4.50  ctrl"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11aef9e8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Create a boxplot\n",
    "data.boxplot('weight', by='group', figsize=(12, 8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "ctrl = data['weight'][data.group == 'ctrl']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1     4.17\n",
       "2     5.58\n",
       "3     5.18\n",
       "4     6.11\n",
       "5     4.50\n",
       "6     4.61\n",
       "7     5.17\n",
       "8     4.53\n",
       "9     5.33\n",
       "10    5.14\n",
       "Name: weight, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ctrl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "grps = pd.unique(data.group.values)\n",
    "d_data = {grp:data['weight'][data.group == grp] for grp in grps}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = len(pd.unique(data.group))  # number of conditions\n",
    "N = len(data.values)  # conditions times participants\n",
    "n = data.groupby('group').size()[0] # Participants in each condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 30, 10)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k, N, n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "\n",
    "F, p = stats.f_oneway(d_data['ctrl'], d_data['trt1'], d_data['trt2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.846087862380136, 0.0159099583256229)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F, p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "DFbetween = k - 1\n",
    "DFwithin = N - k\n",
    "DFtotal = N - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 27, 29)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DFbetween, DFwithin, DFtotal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            sum_sq    df         F   PR(>F)\n",
      "group      3.76634   2.0  4.846088  0.01591\n",
      "Residual  10.49209  27.0       NaN      NaN\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "\n",
    "mod = ols('weight ~ group',\n",
    "                data=data).fit()\n",
    "                \n",
    "aov_table = sm.stats.anova_lm(mod, typ=2)\n",
    "print(aov_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>coef</th>\n",
       "      <th>std err</th>\n",
       "      <th>t</th>\n",
       "      <th>P&gt;|t|</th>\n",
       "      <th>Conf. Int. Low</th>\n",
       "      <th>Conf. Int. Upp.</th>\n",
       "      <th>pvalue-hs</th>\n",
       "      <th>reject-hs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>trt1-ctrl</th>\n",
       "      <td>-0.371</td>\n",
       "      <td>0.278782</td>\n",
       "      <td>-1.330791</td>\n",
       "      <td>0.194388</td>\n",
       "      <td>-0.943013</td>\n",
       "      <td>0.201013</td>\n",
       "      <td>0.194388</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>trt2-ctrl</th>\n",
       "      <td>0.494</td>\n",
       "      <td>0.278782</td>\n",
       "      <td>1.771996</td>\n",
       "      <td>0.087682</td>\n",
       "      <td>-0.078013</td>\n",
       "      <td>1.066013</td>\n",
       "      <td>0.167675</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>trt2-trt1</th>\n",
       "      <td>0.865</td>\n",
       "      <td>0.278782</td>\n",
       "      <td>3.102787</td>\n",
       "      <td>0.004459</td>\n",
       "      <td>0.292987</td>\n",
       "      <td>1.437013</td>\n",
       "      <td>0.013318</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            coef   std err         t     P>|t|  Conf. Int. Low  \\\n",
       "trt1-ctrl -0.371  0.278782 -1.330791  0.194388       -0.943013   \n",
       "trt2-ctrl  0.494  0.278782  1.771996  0.087682       -0.078013   \n",
       "trt2-trt1  0.865  0.278782  3.102787  0.004459        0.292987   \n",
       "\n",
       "           Conf. Int. Upp.  pvalue-hs  reject-hs  \n",
       "trt1-ctrl         0.201013   0.194388      False  \n",
       "trt2-ctrl         1.066013   0.167675      False  \n",
       "trt2-trt1         1.437013   0.013318       True  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pair_t = mod.t_test_pairwise('group')\n",
    "pair_t.result_frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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