{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d6714b52",
   "metadata": {},
   "source": [
    "# One sample t-test"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "741220b6",
   "metadata": {},
   "source": [
    "### Set up Python libraries\n",
    "\n",
    "As usual, run the code cell below to import the relevant Python libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "692abf91",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set-up Python libraries - you need to run this but you don't need to change it\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "import pandas \n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54180c0e",
   "metadata": {},
   "source": [
    "## Example\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/images/rowingTeam.png\" width=50% >\n",
    "\n",
    "Here are the heights in cm of eight men on a rowing team"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cbac3239",
   "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>height</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>180.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>185.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>198.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>175.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>181.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>179.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>166.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>176.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   height\n",
       "0   180.7\n",
       "1   185.1\n",
       "2   198.1\n",
       "3   175.3\n",
       "4   181.3\n",
       "5   179.4\n",
       "6   166.5\n",
       "7   176.9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "heights = pandas.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/data/rowersHeights.csv')\n",
    "display(heights)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ee2764d",
   "metadata": {},
   "source": [
    "An observer notes that the men seem quite tall, and hypothesises that rowers are generally tall as tall people can row faster.\n",
    "\n",
    "Use a one-sample t-test to determine whether the mean height of the rowing team is \n",
    "significantly greater than the average height of men in the UK (175 cm)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf65d4b7",
   "metadata": {},
   "source": [
    "### Plot the data\n",
    "\n",
    "First we plot the data to check if they are roughly normally distributed and check for outliers. \n",
    "As before, a KDE plot is useful to show the shape of the distribution, and a rug plot to show individual values, \n",
    "as the sample size is so small \n",
    "                                                                                                                       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b5c48b94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot = sns.kdeplot(data = heights)\n",
    "sns.rugplot(data = heights, height=0.1)\n",
    "plt.xlabel(\"height (cm)\", fontsize = 12)\n",
    "plt.ylabel(\"density\", fontsize = 12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac06a0ef",
   "metadata": {},
   "source": [
    "As usual, it's difficult to say if the data are normally distributed from a plot of a small sample - \n",
    "they don't look too bad although there is one very tall outlier.\n",
    "\n",
    "However, height is generally normally distributed so let's go ahead and use the t-test."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82caf902",
   "metadata": {},
   "source": [
    "### Hypotheses\n",
    "\n",
    "\n",
    "Ho: the mean height of rowers is greater than the population average of 175cm\n",
    "\n",
    "Ha: the mean higher of rowers is not different from the populaation average of 175cm\n",
    "    \n",
    "This is a one tailed test as the observer's hypothesis (described above) is directional - \n",
    "she thinks taller people are more likely to be good rowers\n",
    "\n",
    "We will test at the $\\alpha = 0.05$ significance level"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88e5cc3d",
   "metadata": {},
   "source": [
    "### Descriptive Statistics\n",
    "\n",
    "First, we obtain the relevant desriptive statistics. By relevant, I mean the ones that go into the equation for the t-test:\n",
    "\n",
    "$$ t = \\frac{\\bar{x}}{\\frac{s}{\\sqrt{n}}} $$\n",
    "\n",
    "This would be the sample mean $\\bar{x}$, the standard deviation $s$, and the sample size $n$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "11eeb386",
   "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>height</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>180.412500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.013868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>166.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>176.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>180.050000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>182.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>198.100000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           height\n",
       "count    8.000000\n",
       "mean   180.412500\n",
       "std      9.013868\n",
       "min    166.500000\n",
       "25%    176.500000\n",
       "50%    180.050000\n",
       "75%    182.250000\n",
       "max    198.100000"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heights.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad893005",
   "metadata": {},
   "source": [
    "It looks like the mean height of rowers (180.4cm) is above the population mean of 175cm.\n",
    "\n",
    "Is this a big difference? It is less than one standard deviation above the mean: s=8.4 and (180.4-175)=5.4. \n",
    "It turns out (from the normal distribution) that if the average rower was an actual person, they would be taller than about 75% of others, so tall but not remarkably so. \n",
    "\n",
    "However, another key element is the variability in the dataset - if the rowers are consistently quite tall (that is most of them are tall), they may as a group be significantly taller than average."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5118a55a",
   "metadata": {},
   "source": [
    "### Carry out the test\n",
    "\n",
    "To do the t-test itself we use a one-sample t-test using the function <tt>ttest_1samp</tt> (that's <tt>1samp</tt> for one sample) from \n",
    "<tt>scipy.stats</tt>, here loaded as <tt>stats</tt>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "fc50b0c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=1.6983675966357161, pvalue=0.06662234508287802)"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(heights, 175, alternative='greater')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56a0749d",
   "metadata": {},
   "source": [
    "The inputs to stats.ttest_1samp are the sample (from our Pandas data frame <tt>heights</tt>) and the value to which they are to be compared (the average height of british men, 175cm),\n",
    "and the argument <tt>alternative='greater'</tt>, which tells the computer to run a one tailed test \n",
    "that mean of the first input <tt>heights</tt> is greater than the reference value <tt>175</tt>.\n",
    "\n",
    "The outputs are <tt>statistic</tt> ($t=1.70$) and <tt>pvalue</tt> ($p=0.067$) - if this is less than our $\\alpha$ value 0.5, there is a significant difference.\n",
    "\n",
    "### Degrees of freedom\n",
    "\n",
    "In a scientific write-up we also need to report the degrees of freedom of the test. This tells us how many observations (data-points) the test was based on, corrected for the number of means we had to estimate from the data in order to do the test.\n",
    "\n",
    "In the case of the one sample t-test $df = n-1$ so in this case, df=7 and we can report out test results as:\n",
    "\n",
    "$t(7) = 1.70, p=0.067$ (one-tailed)\n",
    "\n",
    "### Interpretation\n",
    "\n",
    "Our t value of 1.67 means that the difference between the mean height of the rowers and the standard value (175cm, the mean height of British men) is 1.67 times the standard error (where $ SE = \\frac{s}{\\sqrt{n}}$).\n",
    "\n",
    "Such a large difference (in the expected direction) would occur 0.067 (6.7%) of the time due to chance if the null hypothesis were true (rowers were no taller than other men), hence the p value of 0.067. This is higher than our alpha value (0.05) so the test is not significant.\n",
    "\n",
    "This diagram shows the expected distribution of t-values if the null were true, with our obtained t-value marked:\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/images/ttestRowing.png\" width=50% alt=\"There should be a picture of the t-distribution here\" >"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1746c632",
   "metadata": {},
   "source": [
    "### Draw conclusions\n",
    "\n",
    "As p>0.05 the test is not significant and we fail to reject the null hypothesis. There is not sufficient evidence to support the hypothesis that rowers are taller than average."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2309a35d",
   "metadata": {},
   "source": [
    "## Write-up \n",
    "<br>\n",
    "\n",
    "<div style = \"    padding-top: 10px;\n",
    "    padding-bottom: 10px;\n",
    "    padding-left: 10px;\n",
    "    padding-right: 10px;\n",
    "    box-shadow: 0px 8px 16px 0px rgba(0,0,0,0.2);\n",
    "    vertical-align: middle;\">\n",
    "    \n",
    "Above, I walked you through how to run the t-test and why we make different choices. \n",
    "    \n",
    "In this section we practice writing up our analysis in the correct style for a scientific report. \n",
    "    \n",
    "Replace the XXXs with the correct values!    \n",
    "\n",
    "</div>\n",
    "\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb2962b0",
   "metadata": {},
   "source": [
    "To test the hypothesis that rowers are taller than average, we measaured the heights of 8 male rowers and compared to the natinoal value for mean height of British men (obtained from Wikipedia): 175cm.\n",
    "\n",
    "The data are shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "513809b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot = sns.kdeplot(data = heights)\n",
    "sns.rugplot(data = heights, height=0.1)\n",
    "plt.xlabel(\"height (cm)\", fontsize = 12)\n",
    "plt.ylabel(\"density\", fontsize = 12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b88dc33",
   "metadata": {},
   "source": [
    "The mean height of the rowers was XXX.X cm and the standard deviation was X.XX cm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2e3ee40e",
   "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>height</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>180.412500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.013868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>166.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>176.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>180.050000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>182.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>198.100000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           height\n",
       "count    8.000000\n",
       "mean   180.412500\n",
       "std      9.013868\n",
       "min    166.500000\n",
       "25%    176.500000\n",
       "50%    180.050000\n",
       "75%    182.250000\n",
       "max    198.100000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heights = pandas.read_csv('data/rowersHeights.csv')\n",
    "heights.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cac7ffd1",
   "metadata": {},
   "source": [
    "We used a one-sample t-test (alpha = X, XX tailed). The use of the t-test (assumption of normality) was justified theoretically on the grounds that heights are typically normally distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9b8270ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=array([1.6983676]), pvalue=array([0.06662235]))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(heights, 175, alternative='greater')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ad7dd7",
   "metadata": {},
   "source": [
    "The results of the t-test $t(XX) =$ X.XX, $p=$X.XX (XX-tailed) suggest that there is insufficient evidence ot reject the null and we cannot conclude that rowers are taller than average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fd282232",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}