UM6P_SCI_Data_Science_Lab_Project_Data_Distribution_&_Stat_Tests.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "UM6P SCI Data Science Lab Project Data Distribution & Stat Tests.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "igzrd-ZrQbG6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "2be4a8ba-ca9c-4e98-ba59-0892575538ae"
      },
      "source": [
        "# Package import\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Normal Distribution\n",
        "x = np.random.normal(5.0, 1.0, 100000)\n",
        "\n",
        "# Plot histogram\n",
        "plt.hist(x, 100)\n",
        "plt.show()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# The Shapiro Wilk Normality Test\n",
        "from scipy.stats import shapiro\n",
        "sample_data = [0, 0, 3, 1, 1, 2, 2, 1, 2, 0]\n",
        "stat, p = shapiro(sample_data)\n",
        "print(\"stat=%.3f, p=%.3f\" % (stat, p))\n",
        "alpha = 0.05\n",
        "if (p > alpha):\n",
        "  print(\"Sample data look Guassian (fail to reject H0)\")\n",
        "else:\n",
        "  Print(\"Sample doesn't look Guassian (reject H0)\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "T9ZnUav6Cjcm",
        "outputId": "1960f751-8392-4418-d781-68227ebbb96e"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "stat=0.895, p=0.191\n",
            "Sample data look Guassian (fail to reject H0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# The Pearson's Corelation tests\n",
        "from scipy.stats import pearsonr\n",
        "sample_data1 = [0, 0, 3, 1, 1, 2, 2, 1, 2, 0]\n",
        "sample_data2 = [0, 0, 3, 1, 1, 2, 2, 1, 2, 0]\n",
        "stat, p = pearsonr(sample_data1, sample_data2)\n",
        "print(\"stat=%.3f, p=%.3f\" % (stat, p))\n",
        "alpha = 0.005\n",
        "if (p > alpha):\n",
        "  print(\"Probably independent\")\n",
        "else:\n",
        "  print(\"Probably dependent\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6VgBVaPfG1Bs",
        "outputId": "70f562d6-2466-4b84-8828-5a3626ab11a6"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "stat=1.000, p=0.000\n",
            "Probably dependent\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Example of Chi-square Test\n",
        "from scipy.stats import chi2_contingency\n",
        "table = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 0]]\n",
        "stat, p, dof, expected = chi2_contingency(table)\n",
        "print('stat=%.3f, p=%.3f' % (stat, p))\n",
        "alpha = 0.005\n",
        "if (p > alpha):\n",
        "    print(\"Probably independent\")\n",
        "else:\n",
        "    print(\"Probably dependent\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jqQ2hJGEI6hQ",
        "outputId": "17c3f860-b591-471a-f44d-eb2dd706a50b"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "stat=11.863, p=0.018\n",
            "Probably independent\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Example of student's t-test\n",
        "from scipy.stats import ttest_ind\n",
        "sample_data1 = [0, 0, 3, 1, 1, 2, 2, 1, 2, 0]\n",
        "sample_data2 = [0, 0, 3, 1, 1, 2, 2, 1, 2, 0]\n",
        "stat, p = ttest_ind(sample_data1, sample_data2)\n",
        "print('stat=%.3f, p=%.3f' % (stat, p))\n",
        "if (p > 0.005):\n",
        "  print(\"Probably thesame distribution\")\n",
        "else:\n",
        "  print(\"Probably different distribution\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nurK3cinKOse",
        "outputId": "5456e249-e431-45fc-f7c6-50c9b6f59800"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "stat=0.000, p=1.000\n",
            "Probably thesame distribution\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Example Bernouli distribution\n",
        "from scipy.stats import bernoulli\n",
        "import seaborn as sb\n",
        "data_bern = bernoulli.rvs(size = 100, p = 0.8)\n",
        "ax = sb.distplot(data_bern,\n",
        "                 kde=True, \n",
        "                 color='crimson', \n",
        "                 hist_kws={\"linewidth\":25, 'alpha':1})\n",
        "ax.set(xlabel=\"Bernoulli\", ylabel=\"Frequency\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "id": "bixNwQF8NB5T",
        "outputId": "1307f111-2cd4-4fdb-ea92-e7b738b89ed2"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
            "  warnings.warn(msg, FutureWarning)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Text(0, 0.5, 'Frequency'), Text(0.5, 0, 'Bernoulli')]"
            ]
          },
          "metadata": {},
          "execution_count": 56
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Example of Binomial distribution\n",
        "import seaborn as sb, numpy as np\n",
        "from scipy.stats import binom\n",
        "data_binom = binom.rvs(size = 100, n = 20, p = 0.8, loc = 0)\n",
        "print(data_binom)\n",
        "ax = sb.distplot(data_binom, kde=True, color='blue', hist_kws = {\"linewidth\":25, 'alpha':1} )\n",
        "ax.set(xlabel=\"Binomial\", ylabel=\"Frequency\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 438
        },
        "id": "9YhAwJ-GQ9b1",
        "outputId": "73c13c00-e90b-406c-af37-c50baa9059c5"
      },
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[14 18 18 14 17 20 15 16 17 17 18 14 14 17 15 16 14 15 18 15 15 16 16 13\n",
            " 15 16 15 15 16 18 16 16 14 10 14 16 16 18 12 17 16 16 15 16 18 18 18 16\n",
            " 18 15 14 11 12 17 16 18 18 13 14 14 18 14 15 18 17 19 14 15 13 18 15 16\n",
            " 13 15 20 15 16 15 16 15 15 18 19 15 17 17 18 15 18 13 17 14 16 19 18 16\n",
            " 12 18 16 17]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
            "  warnings.warn(msg, FutureWarning)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Text(0, 0.5, 'Frequency'), Text(0.5, 0, 'Binomial')]"
            ]
          },
          "metadata": {},
          "execution_count": 64
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Binomial distribution functions\n",
        "from scipy import stats\n",
        "X = stats.binom(10, 0.2) # Declare X to be a binomial random variable\n",
        "print(X.pmf(3))           # P(X = 3)\n",
        "print(X.cdf(4))           # P(X <= 4)\n",
        "print(X.mean())           # E[X]\n",
        "print(X.var())            # Var(X)\n",
        "print(X.std())            # Std(X)\n",
        "print(X.rvs())            # Get a random sample from X\n",
        "print(X.rvs(10))          # Get 10 random samples form X"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QhhKBCFvXKFj",
        "outputId": "e73012d7-fdaa-4168-8194-111ca1b81996"
      },
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.20132659200000022\n",
            "0.9672065024000001\n",
            "2.0\n",
            "1.6\n",
            "1.2649110640673518\n",
            "5\n",
            "[3 2 2 3 5 2 2 2 4 1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Binomial distribution functions\n",
        "from scipy import stats\n",
        "X = stats.binom(10, 0.2) # Declare X to be a binomial random variable\n",
        "help(X)                  # List all methods defined for X"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pwzXfBlUXWfH",
        "outputId": "65466164-b9e2-44fc-ebe6-4c0df06fd44e"
      },
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Help on rv_frozen in module scipy.stats._distn_infrastructure object:\n",
            "\n",
            "class rv_frozen(builtins.object)\n",
            " |  rv_frozen(dist, *args, **kwds)\n",
            " |  \n",
            " |  # Frozen RV class\n",
            " |  \n",
            " |  Methods defined here:\n",
            " |  \n",
            " |  __init__(self, dist, *args, **kwds)\n",
            " |      Initialize self.  See help(type(self)) for accurate signature.\n",
            " |  \n",
            " |  cdf(self, x)\n",
            " |  \n",
            " |  entropy(self)\n",
            " |  \n",
            " |  expect(self, func=None, lb=None, ub=None, conditional=False, **kwds)\n",
            " |  \n",
            " |  interval(self, alpha)\n",
            " |  \n",
            " |  isf(self, q)\n",
            " |  \n",
            " |  logcdf(self, x)\n",
            " |  \n",
            " |  logpdf(self, x)\n",
            " |  \n",
            " |  logpmf(self, k)\n",
            " |  \n",
            " |  logsf(self, x)\n",
            " |  \n",
            " |  mean(self)\n",
            " |  \n",
            " |  median(self)\n",
            " |  \n",
            " |  moment(self, n)\n",
            " |  \n",
            " |  pdf(self, x)\n",
            " |  \n",
            " |  pmf(self, k)\n",
            " |  \n",
            " |  ppf(self, q)\n",
            " |  \n",
            " |  rvs(self, size=None, random_state=None)\n",
            " |  \n",
            " |  sf(self, x)\n",
            " |  \n",
            " |  stats(self, moments='mv')\n",
            " |  \n",
            " |  std(self)\n",
            " |  \n",
            " |  support(self)\n",
            " |  \n",
            " |  var(self)\n",
            " |  \n",
            " |  ----------------------------------------------------------------------\n",
            " |  Data descriptors defined here:\n",
            " |  \n",
            " |  __dict__\n",
            " |      dictionary for instance variables (if defined)\n",
            " |  \n",
            " |  __weakref__\n",
            " |      list of weak references to the object (if defined)\n",
            " |  \n",
            " |  random_state\n",
            "\n"
          ]
        }
      ]
    }
  ]
}