Paired_t_test.ipynb

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        "<a href=\"https://colab.research.google.com/github/RichardMathewsII/G915-Hypothesis-Test/blob/master/Paired_t_test.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "id": "LZfA-vy9PnkK",
        "colab_type": "code",
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      },
      "source": [
        "import plotly.graph_objects as go\n",
        "import pandas as pd\n",
        "from scipy.stats import ttest_rel as paired_ttest\n",
        "from scipy.stats import shapiro"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1qUP4ebVnLHh",
        "colab_type": "text"
      },
      "source": [
        "#Load trial data into DataFrame"
      ]
    },
    {
      "cell_type": "code",
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      "source": [
        "WPM = pd.DataFrame(\n",
        "    data={\n",
        "        'G915': [70, 71, 70, 73, 72, 74, 72, 72, 72, 73, 71, 67, 73, 75, 69, 72, 74, 73, 74, 71], \n",
        "        'laptop': [68, 67, 70, 67, 68, 68, 72, 69, 70, 70, 69, 69, 69, 69, 70, 71, 66, 71, 67, 72]\n",
        "        }\n",
        "        )"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_IPBGrWPnVft",
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      },
      "source": [
        "# Plot distribution of WPM for each keyboard"
      ]
    },
    {
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        "outputId": "69cf2ee8-b423-4431-ffa1-d5ef32a3ee4f"
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      "source": [
        "fig = go.Figure()\n",
        "fig.add_trace(go.Histogram(x=WPM['G915'], name='Logitech G915', xbins=dict(size=1)))\n",
        "fig.add_trace(go.Histogram(x=WPM['laptop'], name='MSI Laptop', xbins=dict(size=1)))\n",
        "fig.update_layout(title_text='Words Per Minute Distribution', \n",
        "                  xaxis_title_text='Words Per Minute',\n",
        "                  yaxis_title_text='Count',\n",
        "                  bargap=0.2,\n",
        "                  bargroupgap=0.1)\n",
        "fig.show()"
      ],
      "execution_count": 3,
      "outputs": [
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_UoX_KV9neBc",
        "colab_type": "text"
      },
      "source": [
        "#Test for normality"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ptDVsN9Cdn0U",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
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        "outputId": "dac1def2-a2c1-47f7-a129-5c6b27e9e3a9"
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      "source": [
        "shapiro_test = shapiro(WPM['G915'])\n",
        "print('Shapiro-Wilk Test Statistic for G915:', shapiro_test[0])\n",
        "print('Shapiro-Wilk Test P-Value for G915:', shapiro_test[1])\n",
        "shapiro_test = shapiro(WPM['laptop'])\n",
        "print('Shapiro-Wilk Test Statistic for laptop:', shapiro_test[0])\n",
        "print('Shapiro-Wilk Test P-Value for laptop:', shapiro_test[1])"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shapiro-Wilk Test Statistic for G915: 0.9469935297966003\n",
            "Shapiro-Wilk Test P-Value for G915: 0.32374611496925354\n",
            "Shapiro-Wilk Test Statistic for laptop: 0.9591456651687622\n",
            "Shapiro-Wilk Test P-Value for laptop: 0.5269261002540588\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jv-ja4gRnhIu",
        "colab_type": "text"
      },
      "source": [
        "We can accept the null hypothesis that the data is sampled from a normal distribution. Since the sample sizes are small (N = 20) and the samples are normally distributed, the paired samples t-test applies."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XtdT74oFoQM2",
        "colab_type": "text"
      },
      "source": [
        "#Perform a Paired Samples t-Test\n",
        "Let's use a significance level of 0.05."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r9YbThzvQiKG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "37704bf5-eb97-4340-b6a4-0927c1c7cc9c"
      },
      "source": [
        "t_stat, p_val = paired_ttest(WPM['G915'], WPM['laptop'])\n",
        "print('t-statistic:', t_stat)\n",
        "print('P-Value:', p_val)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "t-statistic: 4.409815777991463\n",
            "P-Value: 0.0003009267702446885\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "The P-Value is less than the significance level of 0.05, so we can reject the null hypothesis that the means of both samples are the same.\n",
        "\n",
        "#Conclusion"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "siXPVnZ5ZvpW",
        "colab_type": "code",
        "colab": {
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          "height": 34
        },
        "outputId": "d9b0575c-d0f9-4e98-b0fd-881312266790"
      },
      "source": [
        "print('Difference in mean:', round(WPM['G915'].mean() - WPM['laptop'].mean()))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Difference in mean: 3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ixvCRyf1oiGd",
        "colab_type": "text"
      },
      "source": [
        "There is an average difference of 3 words per minute between both samples. Based on the results from the paired t-test, we can conclude the increase in typing speed from using Logitech's G915 keyboard is statistically significant."
      ]
    }
  ]
}