Code-Example-008-t-distribution-scipy-functions.ipynb

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   "cell_type": "code",
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   "source": [
    "# upgrade scipy to the latest\n",
    "# ! pip install --upgrade scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.pythonfordatascience.org/independent-samples-t-test-python/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.7.1'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy\n",
    "scipy.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9745751901857019"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.cdf(2.76, df=4, loc=0, scale=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9745751901857019"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.cdf(2.76, df=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.760000000000005"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.ppf(0.9745751901857019, df=4, loc=0, scale=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One Sample t-test\n",
    "A scientist wishes to test the claim that great white sharks average 20 feet in length.\n",
    "\n",
    "The measurements are 18.1, 23.4, 23.8, 24.1, 22.5, 19, 25.4, 23.1, 16.5, 26.7.\n",
    "\n",
    "Are these data good evidence that great white sharks are longer than 20 feet in\n",
    "length at the $\\alpha=0.10$ level of significance?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "shark_len = np.array([18.1, 23.4, 23.8, 24.1, 22.5, 19, 25.4, 23.1, 16.5, 26.7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=2.1602437665312957, pvalue=0.02952201627710914)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "\n",
    "# scipy.__version__ 1.7.1 or higher\n",
    "stats.ttest_1samp(shark_len, 20, alternative='greater')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function ttest_1samp in module scipy.stats.stats:\n",
      "\n",
      "ttest_1samp(a, popmean, axis=0, nan_policy='propagate', alternative='two-sided')\n",
      "    Calculate the T-test for the mean of ONE group of scores.\n",
      "    \n",
      "    This is a two-sided test for the null hypothesis that the expected value\n",
      "    (mean) of a sample of independent observations `a` is equal to the given\n",
      "    population mean, `popmean`.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    a : array_like\n",
      "        Sample observation.\n",
      "    popmean : float or array_like\n",
      "        Expected value in null hypothesis. If array_like, then it must have the\n",
      "        same shape as `a` excluding the axis dimension.\n",
      "    axis : int or None, optional\n",
      "        Axis along which to compute test; default is 0. If None, compute over\n",
      "        the whole array `a`.\n",
      "    nan_policy : {'propagate', 'raise', 'omit'}, optional\n",
      "        Defines how to handle when input contains nan.\n",
      "        The following options are available (default is 'propagate'):\n",
      "    \n",
      "          * 'propagate': returns nan\n",
      "          * 'raise': throws an error\n",
      "          * 'omit': performs the calculations ignoring nan values\n",
      "    alternative : {'two-sided', 'less', 'greater'}, optional\n",
      "        Defines the alternative hypothesis.\n",
      "        The following options are available (default is 'two-sided'):\n",
      "    \n",
      "          * 'two-sided'\n",
      "          * 'less': one-sided\n",
      "          * 'greater': one-sided\n",
      "    \n",
      "        .. versionadded:: 1.6.0\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    statistic : float or array\n",
      "        t-statistic.\n",
      "    pvalue : float or array\n",
      "        Two-sided p-value.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> from scipy import stats\n",
      "    >>> rng = np.random.default_rng()\n",
      "    >>> rvs = stats.norm.rvs(loc=5, scale=10, size=(50, 2), random_state=rng)\n",
      "    \n",
      "    Test if mean of random sample is equal to true mean, and different mean.\n",
      "    We reject the null hypothesis in the second case and don't reject it in\n",
      "    the first case.\n",
      "    \n",
      "    >>> stats.ttest_1samp(rvs, 5.0)\n",
      "    Ttest_1sampResult(statistic=array([-2.09794637, -1.75977004]), pvalue=array([0.04108952, 0.08468867]))\n",
      "    >>> stats.ttest_1samp(rvs, 0.0)\n",
      "    Ttest_1sampResult(statistic=array([1.64495065, 1.62095307]), pvalue=array([0.10638103, 0.11144602]))\n",
      "    \n",
      "    Examples using axis and non-scalar dimension for population mean.\n",
      "    \n",
      "    >>> result = stats.ttest_1samp(rvs, [5.0, 0.0])\n",
      "    >>> result.statistic\n",
      "    array([-2.09794637,  1.62095307])\n",
      "    >>> result.pvalue\n",
      "    array([0.04108952, 0.11144602])\n",
      "    \n",
      "    >>> result = stats.ttest_1samp(rvs.T, [5.0, 0.0], axis=1)\n",
      "    >>> result.statistic\n",
      "    array([-2.09794637,  1.62095307])\n",
      "    >>> result.pvalue\n",
      "    array([0.04108952, 0.11144602])\n",
      "    \n",
      "    >>> result = stats.ttest_1samp(rvs, [[5.0], [0.0]])\n",
      "    >>> result.statistic\n",
      "    array([[-2.09794637, -1.75977004],\n",
      "           [ 1.64495065,  1.62095307]])\n",
      "    >>> result.pvalue\n",
      "    array([[0.04108952, 0.08468867],\n",
      "           [0.10638103, 0.11144602]])\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(stats.ttest_1samp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n"
   ]
  }
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