Independent_2_sample_t_test.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "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/Manish-k723/100-days-of-ML/blob/main/Independent_2_sample_t_test.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "59WZZpC9HIsO",
        "outputId": "c6a45dae-721b-40b9-96b4-6978dbb41f07"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.256369746933224e-06\n"
          ]
        }
      ],
      "source": [
        "from scipy.stats import t\n",
        "\n",
        "# Set the t-value and degrees of freedom\n",
        "t_value = -5.25\n",
        "df = 58  # Replace this with your specific degrees of freedom\n",
        "\n",
        "# Calculate the CDF value\n",
        "cdf_value = t.cdf(t_value, df)\n",
        "print(cdf_value*2)\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# The Shapiro-Wilk test returns two values: the test statistic (W) and the p-value.\n",
        "# If the p-value is greater than your chosen significance level (α = 0.05),\n",
        "# you can assume the data comes from a normally distributed population.\n",
        "# If the p-value is less than or equal to the significance level, the normality assumption is not met,\n",
        "# and you should consider applying a data transformation or using a non-parametric test like the Mann-Whitney U test.\n",
        "\n",
        "\n",
        "from scipy.stats import shapiro\n",
        "\n",
        "# Input the data as lists\n",
        "desktop_users = [12, 15, 18, 16, 20, 17, 14, 22, 19, 21, 23, 18, 25, 17, 16, 24, 20, 19, 22, 18, 15, 14, 23, 16, 12, 21, 19, 17, 20, 14]\n",
        "mobile_users = [10, 12, 14, 13, 16, 15, 11, 17, 14, 16, 18, 14, 20, 15, 14, 19, 16, 15, 17, 14, 12, 11, 18, 15, 10, 16, 15, 13, 16, 11]\n",
        "\n",
        "# Perform the Shapiro-Wilk test for both desktop and mobile users\n",
        "shapiro_desktop = shapiro(desktop_users)\n",
        "shapiro_mobile = shapiro(mobile_users)\n",
        "\n",
        "print(\"Shapiro-Wilk test for desktop users:\", shapiro_desktop)\n",
        "print(\"Shapiro-Wilk test for mobile users:\", shapiro_mobile)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MG589MbeRZJQ",
        "outputId": "fbe6454f-daff-4283-8c79-39d6c410dee7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Shapiro-Wilk test for desktop users: ShapiroResult(statistic=0.9783114194869995, pvalue=0.7790969014167786)\n",
            "Shapiro-Wilk test for mobile users: ShapiroResult(statistic=0.9714356064796448, pvalue=0.5791608691215515)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# If the p-value from Levene's test is greater than your chosen significance level (α = 0.05), you can assume equal variances\n",
        "#  If the p-value is less than or equal to the significance level, the assumption of equal variances is not met,\n",
        "# and you should consider using Welch's t-test instead of the regular independent two-sample t-test.\n",
        "\n",
        "from scipy.stats import levene\n",
        "\n",
        "# Input the data as lists\n",
        "desktop_users = [12, 15, 18, 16, 20, 17, 14, 22, 19, 21, 23, 18, 25, 17, 16, 24, 20, 19, 22, 18, 15, 14, 23, 16, 12, 21, 19, 17, 20, 14]\n",
        "mobile_users = [10, 12, 14, 13, 16, 15, 11, 17, 14, 16, 18, 14, 20, 15, 14, 19, 16, 15, 17, 14, 12, 11, 18, 15, 10, 16, 15, 13, 16, 11]\n",
        "\n",
        "# Perform Levene's test\n",
        "levene_test = levene(desktop_users, mobile_users)\n",
        "print(levene_test)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uctKh0IsHON-",
        "outputId": "e38a30bb-cd05-4122-edd8-37ab5fbed536"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "LeveneResult(statistic=2.94395488191752, pvalue=0.09153720526741761)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import scipy.stats as stats\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "before = np.array([80, 92, 75, 68, 85, 78, 73, 90, 70, 88, 76, 84, 82, 77, 91])\n",
        "after = np.array([78, 93, 81, 67, 88, 76, 74, 91, 69, 88, 77, 81, 80, 79, 88])\n"
      ],
      "metadata": {
        "id": "iTFZKtBzPp3l"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "differences = after - before"
      ],
      "metadata": {
        "id": "vHCfxY50fSoY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.hist(differences)\n",
        "plt.title(\"Histogram of Weight Differences\")\n",
        "plt.xlabel(\"Weight Differences (kg)\")\n",
        "plt.ylabel(\"Frequency\")\n",
        "plt.show()\n",
        "\n",
        "shapiro_test = stats.shapiro(differences)\n",
        "print(\"Shapiro-Wilk test:\", shapiro_test)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "id": "Meoy64fQfWIy",
        "outputId": "1338d40f-9ee3-4b6b-eaab-3e1685a47470"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Shapiro-Wilk test: ShapiroResult(statistic=0.9220570921897888, pvalue=0.20704729855060577)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mean_diff = np.mean(differences)\n",
        "std_diff = np.std(differences, ddof=1)"
      ],
      "metadata": {
        "id": "13dPf7-Wf4EB"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "n = len(differences)\n",
        "t_statistic = mean_diff / (std_diff / np.sqrt(n))\n",
        "df = n - 1"
      ],
      "metadata": {
        "id": "DAxgFO5Wgbzz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "t_statistic"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P3A57rKdg312",
        "outputId": "91b44309-4365-4cb7-f5cf-398f6b3b98da"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.10482848367219182"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "alpha = 0.05\n",
        "p_value = stats.t.cdf(t_statistic, df)"
      ],
      "metadata": {
        "id": "P6vf3xK0ghKh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "p_value"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ciY8VkIPgxKW",
        "outputId": "b4882a20-a269-47ce-a3ca-42cd0ea0a3c1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5410005146857456"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "EjqvWBZugylZ"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}