Distributions and Hypothesis Testing.ipynb

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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "_You are currently looking at **version 1.0** of this notebook. To download notebooks and datafiles, as well as get help on Jupyter notebooks in the Coursera platform, visit the [Jupyter Notebook FAQ](https://www.coursera.org/learn/python-data-analysis/resources/0dhYG) course resource._\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distributions in Pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.binomial(1, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.binomial(1000, 0.5)/1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "chance_of_tornado = 0.01/100\n",
    "np.random.binomial(100000, chance_of_tornado)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "chance_of_tornado = 0.01\n",
    "\n",
    "tornado_events = np.random.binomial(1, chance_of_tornado, 1000000)\n",
    "    \n",
    "two_days_in_a_row = 0\n",
    "for j in range(1,len(tornado_events)-1):\n",
    "    if tornado_events[j]==1 and tornado_events[j-1]==1:\n",
    "        two_days_in_a_row+=1\n",
    "\n",
    "print('{} tornadoes back to back in {} years'.format(two_days_in_a_row, 1000000/365))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.uniform(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.normal(0.75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Formula for standard deviation\n",
    "$$\\sqrt{\\frac{1}{N} \\sum_{i=1}^N (x_i - \\overline{x})^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "distribution = np.random.normal(0.75,size=1000)\n",
    "\n",
    "np.sqrt(np.sum((np.mean(distribution)-distribution)**2)/len(distribution))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "np.std(distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats\n",
    "stats.kurtosis(distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "stats.skew(distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi_squared_df2 = np.random.chisquare(2, size=10000)\n",
    "stats.skew(chi_squared_df2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi_squared_df5 = np.random.chisquare(5, size=10000)\n",
    "stats.skew(chi_squared_df5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "output = plt.hist([chi_squared_df2,chi_squared_df5], bins=50, histtype='step', \n",
    "                  label=['2 degrees of freedom','5 degrees of freedom'])\n",
    "plt.legend(loc='upper right')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hypothesis Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('grades.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "early = df[df['assignment1_submission'] <= '2015-12-31']\n",
    "late = df[df['assignment1_submission'] > '2015-12-31']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "early.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "late.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "stats.ttest_ind?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "stats.ttest_ind(early['assignment1_grade'], late['assignment1_grade'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "stats.ttest_ind(early['assignment2_grade'], late['assignment2_grade'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "stats.ttest_ind(early['assignment3_grade'], late['assignment3_grade'])"
   ]
  }
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