Stats_by_Python2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Stats_by_Python2.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPcCPF/hMbl9/2uu+v/jazG",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/kimdesok/Statistical-Thinking-in-Python-Part-1-/blob/main/Stats_by_Python2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XNs4GrG8rbOa"
      },
      "source": [
        "#Quantitative Exploratory Data Analysis\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ZSnt_rDrecB"
      },
      "source": [
        "> * Mean is good for estimating the average but heavily influenced by outliers.\n",
        "> * Median could be better in that case.\n",
        ">> - Median is 50% percentile."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "beLSgxQp62VE"
      },
      "source": [
        "# Import plotting modules\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "#Importing numpy\n",
        "import numpy as np\n",
        "\n",
        "\n",
        "# Set default Seaborn style\n",
        "sns.set()\n",
        "\n",
        "#Datasets\n",
        "#Iris dataset consists of 150 rows and four columns.\n",
        "#This data set consists of three different types of irise : Setosa, Versicolor, and Virginica.\n",
        "#The first 50 rows represent data of Setoda and so on.\n",
        "#source: https://scikit-learn.org/stable/auto_examples/datasets/plot_iris_dataset.html#sphx-glr-auto-examples-datasets-plot-iris-dataset-py\n",
        "#Each column represents Sepal Length, Sepal Width, Petal Length and Petal Width.\n",
        "\n",
        "#To extract Versicolor's petal length & width data\n",
        "from sklearn.datasets import load_iris\n",
        "versicolor_petal_length = load_iris().data[50:100,2]\n",
        "versicolor_petal_width = load_iris().data[50:100,3]"
      ],
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xIYJ40MUfEVT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dcb323e7-6b17-4f6e-e771-3610cbc5f22c"
      },
      "source": [
        "# Compute the mean: mean_length_vers\n",
        "mean_length_vers = np.mean(versicolor_petal_length)\n",
        "\n",
        "# Print the result with some nice formatting\n",
        "print('I. versicolor:', mean_length_vers, 'cm')"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "I. versicolor: 4.26 cm\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DxtIvOqDtEdK",
        "outputId": "fa40745b-2f10-40ac-85c1-969cd697d12c"
      },
      "source": [
        "#percentiles\n",
        "# Specify array of percentiles: percentiles\n",
        "percentiles = np.array([2.5, 25, 50, 75, 97.5])\n",
        "\n",
        "# Compute percentiles: ptiles_vers\n",
        "ptiles_vers = np.percentile(versicolor_petal_length, percentiles)\n",
        "\n",
        "# Print the result\n",
        "print(ptiles_vers)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3.3    4.     4.35   4.6    4.9775]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1qTL6ENHg3By"
      },
      "source": [
        "#Percentile calculation and marking on the ecdf graph\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "upgAbkZ0fHFa"
      },
      "source": [
        "def ecdf(data):\n",
        "    \"\"\"Compute ECDF for a one-dimensional array of measurements.\"\"\"\n",
        "    # Number of data points: n\n",
        "    n = len(data)\n",
        "\n",
        "    # x-data for the ECDF: x\n",
        "    x = np.sort(data)\n",
        "\n",
        "    # y-data for the ECDF: y\n",
        "    y = np.arange(1, n+1) / n\n",
        "\n",
        "    return x, y"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "7R140wRkhTmC",
        "outputId": "9b8e7f80-1541-4d0d-f54e-06a8ceb78c43"
      },
      "source": [
        "# Compute ECDF for versicolor data: x_vers, y_vers\n",
        "x_vers, y_vers = ecdf(versicolor_petal_length)\n",
        "\n",
        "# Generate plot\n",
        "_ = plt.plot(x_vers, y_vers,marker = '.', linestyle = 'none')\n",
        "\n",
        "# Label the axes\n",
        "\n",
        "plt.xlabel('petal length (cm)')\n",
        "plt.ylabel('ECDF')\n",
        "\n",
        "# Overlay percentiles as red diamonds.\n",
        "_ = plt.plot(ptiles_vers, percentiles/100, marker='D', color='red',\n",
        "         linestyle='none')\n",
        "\n",
        "# Display the plot\n",
        "plt.show()\n",
        "\n"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mmY2Pi-euHNj"
      },
      "source": [
        "#Box plot \n",
        ">* invented by Tukey and provided by Seaborn\n",
        ">* good to represent non-Gaussian distribution with percentiles and outliers\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "NPqP6QpGQcVR",
        "outputId": "440a3016-e657-4501-a7da-f3f85d9a699e"
      },
      "source": [
        "import pandas as pd \n",
        "df = pd.DataFrame(load_iris().data)\n",
        "df.columns = ['sepal length (cm)',  'sepal width (cm)',  'petal length (cm)',  'petal width (cm)']\n",
        "df_ = 50*['setosa']\n",
        "df_[50:100] = 50*['versicolor']\n",
        "df_[100:150] = 50*['virginica']\n",
        "#print(len(df_))\n",
        "df['species'] = df_\n",
        "\n",
        "# Create box plot with Seaborn's default settings\n",
        "_ = sns.boxplot(x='species', y='petal length (cm)', data = df )\n",
        "\n",
        "\n",
        "\n",
        "# Label the axes\n",
        "plt.xlabel('species')\n",
        "plt.ylabel('petal length (cm)')\n",
        "\n",
        "# Show the plot\n",
        "plt.show()\n",
        "\n"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "ZnkgD5EnBXIE",
        "outputId": "975fbdd0-42e1-42f0-bb0c-6282035c4050"
      },
      "source": [
        "# Create bee swarm plot with Seaborn's default settings\n",
        "_ = sns.swarmplot(x='species', y='petal length (cm)', data=df)\n",
        "\n",
        "# Label the axes\n",
        "_ = plt.xlabel('species')\n",
        "_ = plt.ylabel('petal length (cm)')\n",
        "\n",
        "# Show the plot\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/categorical.py:1296: UserWarning: 14.0% of the points cannot be placed; you may want to decrease the size of the markers or use stripplot.\n",
            "  warnings.warn(msg, UserWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_nO4v-TSB3_U",
        "outputId": "b2ea3a33-25b5-4d88-c2c5-9e5cb4b3d7b7"
      },
      "source": [
        "# Array of differences to mean: differences\n",
        "differences = versicolor_petal_length - np.mean(versicolor_petal_length)\n",
        "\n",
        "# Square the differences: diff_sq\n",
        "diff_sq = differences**2\n",
        "\n",
        "# Compute the mean square difference: variance_explicit\n",
        "variance_explicit = np.mean(diff_sq)\n",
        "\n",
        "# Compute the variance using NumPy: variance_np\n",
        "variance_np = np.var(versicolor_petal_length)\n",
        "\n",
        "# Print the results\n",
        "\n",
        "print(variance_explicit, variance_np)"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.21640000000000004 0.21640000000000004\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xMoovFwvI4sW"
      },
      "source": [
        "# Compute the variance: variance\n",
        "variance = np.var(versicolor_petal_length)\n",
        "\n",
        "# Print the square root of the variance\n",
        "print(np.sqrt(variance))\n",
        "\n",
        "# Print the standard deviation\n",
        "print(np.std(versicolor_petal_length))\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ia_lvM0ZPFzl"
      },
      "source": [
        "#Covariance and correlation(Pearson's)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "ZztI67PQPCmH",
        "outputId": "12b73f19-5a20-458a-fa5b-eb728835f132"
      },
      "source": [
        "# Make a scatter plot\n",
        "_ = plt.plot(versicolor_petal_length, versicolor_petal_width, marker='.' , linestyle='none' )\n",
        "\n",
        "# Label the axes\n",
        "_ = plt.xlabel('petal length (cm)')\n",
        "_ = plt.ylabel('petal width (cm)')\n",
        "\n",
        "# Show the result\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "deK2sCe9R2fh",
        "outputId": "5d305b8c-f483-4b03-e540-fa79ad240816"
      },
      "source": [
        "# Compute the covariance matrix: covariance_matrix \n",
        "covariance_matrix = np.cov(versicolor_petal_length, versicolor_petal_width)\n",
        "\n",
        "# Print covariance matrix\n",
        "print(covariance_matrix)\n",
        "\n",
        "# Extract covariance of length and width of petals: petal_cov\n",
        "petal_cov = covariance_matrix [0,1]\n",
        "\n",
        "# Print the length/width covariance\n",
        "print(petal_cov)"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.22081633 0.07310204]\n",
            " [0.07310204 0.03910612]]\n",
            "0.07310204081632653\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2IbJOkJ1TAhm"
      },
      "source": [
        "#Pearson's correlation coefficient"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JAt-DpHuS-yO",
        "outputId": "d5c01c41-7ce5-4f67-d620-b370470eb166"
      },
      "source": [
        "def pearson_r(x, y):\n",
        "    \"\"\"Compute Pearson correlation coefficient between two arrays.\"\"\"\n",
        "    # Compute correlation matrix: corr_mat\n",
        "    corr_mat = np.corrcoef(x, y)\n",
        "    # Return entry [0,1]\n",
        "    return corr_mat[0,1]\n",
        "\n",
        "# Compute Pearson correlation coefficient for I. versicolor: r\n",
        "r = pearson_r(versicolor_petal_length, versicolor_petal_width)\n",
        "\n",
        "# Print the result\n",
        "print(r)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.7866680885228169\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}