probs_n_stats_-_hypothesis testing.ipynb

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    "# Hypothesis testing\n",
    "\n",
    "Table of contents\n",
    "- [independent sample t-test](#samplet)\n",
    "- [one sample t-test](#onesample)\n",
    "- [Chi-Square](#chisquare)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "from sklearn.datasets import fetch_openml\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"samplet\"></a>\n",
    "## independent sample t-test  \n",
    "Comparison of the mean of two samples.  \n",
    "  \n",
    "Calculation of the t-statistics with $2(N-1)$ degrees of freedom:\n",
    "$$\n",
    "t = \\frac{M_x - M_y}{\\sqrt{\\frac{S_x^2}{n_x} + \\frac{S_y^2}{n_y}}}\n",
    "$$\n",
    "with\n",
    "$$\n",
    "S^2=\\frac{\\sum (x - \\mu)}{n-1}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create normally distributed data with same standard deviation\n",
    "N = 100\n",
    "mu_a = 3\n",
    "sigma_a=4\n",
    "data_a = np.random.normal(loc=mu_a, scale=sigma_a, size=100)\n",
    "#create data b \n",
    "mu_b = 5\n",
    "sigma_b = 4\n",
    "data_b = np.random.normal(loc=mu_b, scale=sigma_b, size=100)"
   ]
  },
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   "execution_count": 3,
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     },
     "metadata": {}
    }
   ],
   "source": [
    "#Visualization\n",
    "fig, ax = plt.subplots(1, 2, figsize=[15,5])\n",
    "sns.distplot(data_b, ax=ax[1])\n",
    "range_a = np.linspace(stats.norm.ppf(0.001, mu_a, sigma_a), stats.norm.ppf(0.999, mu_a, sigma_a))\n",
    "range_b = np.linspace(stats.norm.ppf(0.001, mu_b, sigma_b), stats.norm.ppf(0.999, mu_b, sigma_b))\n",
    "ax[1].plot(range_b, stats.norm.pdf(range_b, loc=mu_b, scale=sigma_b))\n",
    "ax[0].plot(range_a, stats.norm.pdf(range_a, loc=mu_a, scale=sigma_a), color='C1')\n",
    "ax[0].set_title(\"sample 1\")\n",
    "ax[1].set_title(\"sample 2\")\n",
    "sns.distplot(data_a, ax=ax[0], color='C2' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "t: -3.7863969131446638, pvalue: 0.00020259998339248079\n"
     ]
    }
   ],
   "source": [
    "#calculate t-statistics\n",
    "\n",
    "#from scratch\n",
    "var1 = np.var(data_a, ddof=1)\n",
    "var2 = np.var(data_b, ddof=1)\n",
    "mean1 = np.mean(data_a)\n",
    "mean2 = np.mean(data_b)\n",
    "t = (mean1 - mean2)/(np.sqrt(var1/N + var2/N))\n",
    "pval =stats.t.cdf(t, df=2*N-2) * 2\n",
    "print(\"t: {}, pvalue: {}\".format(t, pval))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-3.7863969131446638, pvalue=0.00020259998339248079)"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "#calculate with scipy stats\n",
    "stats.ttest_ind(data_a,data_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x1a4d5ccf3c8>"
      ]
     },
     "metadata": {},
     "execution_count": 6
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "#Visualization\n",
    "fig, ax = plt.subplots(1, 1, figsize=[10,5])\n",
    "\n",
    "range_a = np.linspace(stats.t.ppf(0.0001, df=2*(N-1)), stats.t.ppf(0.9999, df=2*(N-1)))\n",
    "\n",
    "ax.plot(range_a, stats.t.pdf(range_a, df=2*(N-1)), color='C1')\n",
    "ax.axvline(t)\n",
    "ax.axvline(-t)\n",
    "range_fill_l = np.linspace(stats.t.ppf(0.0001, df=2*(N-1)), stats.t.ppf(0.025, df=2*(N-1)))\n",
    "range_fill_r = np.linspace(stats.t.ppf(0.975, df=2*(N-1)), stats.t.ppf(0.9999, df=2*(N-1)))\n",
    "ax.fill_between(range_fill_l,stats.t.pdf(range_fill_l, df=2*(N-1)),color='r', alpha=0.3)\n",
    "ax.fill_between(range_fill_r,stats.t.pdf(range_fill_r, df=2*(N-1)),color='r', alpha=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"onesample\"></a>\n",
    "## One sample t-test\n",
    "Comparison of mean of one sample to a known value. (population mean with null hypothesis)  \n",
    "Calculation of t-statistics:\n",
    "$$\n",
    "t = \\frac{x-\\mu}{\\frac{S}{\\sqrt{n}}}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create normally distributed data with same standard deviation\n",
    "N = 100\n",
    "mu_a = 3\n",
    "sigma_a=4\n",
    "data_a = np.random.normal(loc=mu_a, scale=sigma_a, size=100)\n",
    "\n",
    "#define known value\n",
    "mu = 3.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a4d5d2a148>"
      ]
     },
     "metadata": {},
     "execution_count": 8
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 720x360 with 1 Axes>",
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     },
     "metadata": {}
    }
   ],
   "source": [
    "#Visualization\n",
    "fig, ax = plt.subplots(1, 1, figsize=[10,5])\n",
    "\n",
    "range_a = np.linspace(stats.norm.ppf(0.001, mu_a, sigma_a), stats.norm.ppf(0.999, mu_a, sigma_a))\n",
    "\n",
    "ax.plot(range_a, stats.norm.pdf(range_a, loc=mu_a, scale=sigma_a), color='C1')\n",
    "ax.set_title(\"sample 1\")\n",
    "\n",
    "sns.distplot(data_a, ax=ax, color='C2' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "t: 0.7743647197424448, pvalue: 1.5594394239402942\n"
     ]
    }
   ],
   "source": [
    "#calculate t-statistics from scratch\n",
    "t = (np.mean(data_a) - mu)/(np.sqrt(np.var(data_a,ddof=1)/N)) \n",
    "pvalue = stats.t.cdf(t, df=(N-1))*2\n",
    "print(\"t: {}, pvalue: {}\".format(t, pvalue))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=0.7743647197424448, pvalue=0.44056057605970567)"
      ]
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "#calculate with scipy stats\n",
    "stats.ttest_1samp(data_a,popmean=mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x1a4d5dd6288>"
      ]
     },
     "metadata": {},
     "execution_count": 11
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "#Visualization\n",
    "fig, ax = plt.subplots(1, 1, figsize=[10,5])\n",
    "\n",
    "range_a = np.linspace(stats.t.ppf(0.0001, df=N-1), stats.t.ppf(0.9999, df=N-1))\n",
    "\n",
    "ax.plot(range_a, stats.t.pdf(range_a, df=N-1), color='C1')\n",
    "ax.axvline(t)\n",
    "ax.axvline(-t)\n",
    "range_fill_l = np.linspace(stats.t.ppf(0.0001, df=N-1), stats.t.ppf(0.025, df=N-1))\n",
    "range_fill_r = np.linspace(stats.t.ppf(0.975, df=N-1), stats.t.ppf(0.9999, df=N-1))\n",
    "ax.fill_between(range_fill_l,stats.t.pdf(range_fill_l, df=N-1),color='r', alpha=0.3)\n",
    "ax.fill_between(range_fill_r,stats.t.pdf(range_fill_r, df=N-1),color='r', alpha=0.3)\n"
   ]
  },
  {
   "source": [
    "<a id='chi-square'></a> $\\chi^2$"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}