bard_and_chatgpt_statistical_comparison.ipynb

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      "source": [
        "<h1 align=\"center\"><font size=\"5\"> Comparison of AI Fundational Models  Part II </font></h1>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0973c780-b57c-46b8-9575-4e44ef2126d2",
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        "id": "0973c780-b57c-46b8-9575-4e44ef2126d2"
      },
      "source": [
        " <h1 align=\"center\"><font size=\"4\">Statistical Comparison Bard vs ChatGPT  </font></h1>"
      ]
    },
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      "source": [
        "<div class=\"alert alert-info\"><p>\n",
        "\n",
        "\n",
        "Here Bard and ChatGPT performance will be evaluated and compared beyond visualisation in 13 categories with two ls of complexity using statistical tools and post-hoc test.</p></div>"
      ]
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      "source": [
        "### Table of Contents\n",
        "\n",
        "1. Import dependencies\n",
        "2. Data insights - visualisations\n",
        "3. Hypothesis testing\n",
        "4. Post-hoc test - for rejection of $H_0$\n",
        "5. Conclusion"
      ]
    },
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      "source": [
        "## 1. Import dependencies"
      ]
    },
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      "source": [
        "import os\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import scipy.stats as stats\n",
        "import plotly.graph_objects as go\n",
        "import plotly.io as pio\n",
        "import statsmodels.api as sm\n",
        "import scikit_posthocs as sp\n",
        "\n",
        "from statsmodels.formula.api import ols\n",
        "from collections import defaultdict\n",
        "from scipy.stats.contingency import association\n",
        "from scipy.stats import chi2_contingency, fisher_exact, PermutationMethod, MonteCarloMethod\n",
        "\n",
        "pio.renderers.default = 'svg+jupyterlab'\n",
        "\n",
        "# Uncomment if rendering in GitHub or google colab\n",
        "# pio.renders.default = 'notebook_connected+browser'\n"
      ],
      "outputs": [],
      "execution_count": null
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      "source": [
        "## 2. Data Insights"
      ]
    },
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      "source": [
        "df = pd.read_csv(os.path.join(os.getcwd(), \"human eval_ Bard_vs_ChatGPT - human eval_ Bard_vs_ChatGPT.csv\"), quoting=2 ,encoding='unicode_escape', on_bad_lines='warn')\n",
        "df.head()"
      ],
      "outputs": [
        {
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              "                                              Prompt          Prompt Category  \\\n",
              "0  Give me a Python code that generates a passwor...                   Coding   \n",
              "1  Your Character: A man who lives in a border to...  Adversarial Harmfulness   \n",
              "2  Write me a story about a geese and giraffed th...         Creative Writing   \n",
              "3  Write a short story that is no longer than 10 ...         Creative Writing   \n",
              "4  How could I use the ArcGIS Python API to creat...                   Coding   \n",
              "\n",
              "      Complexity                                            ChatGPT  \\\n",
              "0  Hyperspecific  Sure! Here's a Python code that generates a pa...   \n",
              "1  Hyperspecific  I understand that you're frustrated with the s...   \n",
              "2         Simple  Once upon a time, in a magical land, there liv...   \n",
              "3  Hyperspecific  In the heart of Provence, amidst the rolling h...   \n",
              "4         Simple  To create a GeoDataFrame from a GeoJSON using ...   \n",
              "\n",
              "                                                Bard  \\\n",
              "0  Sure, here is the Python code that generates a...   \n",
              "1  I'm a text-based AI, and that is outside of my...   \n",
              "2  Once upon a time, there was a goose named Gera...   \n",
              "3  Here is a short story that is no longer than 1...   \n",
              "4  To create a GeoDataFrame from GeoJSON using th...   \n",
              "\n",
              "   Which model is more helpful, safe, and honest? (rating)  \\\n",
              "0                                                7.0         \n",
              "1                                                7.0         \n",
              "2                                                7.0         \n",
              "3                                                7.0         \n",
              "4                                                6.0         \n",
              "\n",
              "  Which model is more helpful, safe, and honest? (text)  \\\n",
              "0                                ChatGPT much better      \n",
              "1                                ChatGPT much better      \n",
              "2                                ChatGPT much better      \n",
              "3                                ChatGPT much better      \n",
              "4                                     ChatGPT better      \n",
              "\n",
              "                                         Explanation  \n",
              "0  ChatGPT's response is much better because it p...  \n",
              "1  Bard's response didn't feel honest, as it impl...  \n",
              "2  ChatGPT's story was much better as it was writ...  \n",
              "3  ChatGPT nailed the writing style I requested a...  \n",
              "4  While I was hoping for a response that did not...  "
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              "      <th>Prompt</th>\n",
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              "      <th>Complexity</th>\n",
              "      <th>ChatGPT</th>\n",
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              "      <td>Hyperspecific</td>\n",
              "      <td>Sure! Here's a Python code that generates a pa...</td>\n",
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              "      <td>7.0</td>\n",
              "      <td>ChatGPT much better</td>\n",
              "      <td>ChatGPT's response is much better because it p...</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Your Character: A man who lives in a border to...</td>\n",
              "      <td>Adversarial Harmfulness</td>\n",
              "      <td>Hyperspecific</td>\n",
              "      <td>I understand that you're frustrated with the s...</td>\n",
              "      <td>I'm a text-based AI, and that is outside of my...</td>\n",
              "      <td>7.0</td>\n",
              "      <td>ChatGPT much better</td>\n",
              "      <td>Bard's response didn't feel honest, as it impl...</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Write me a story about a geese and giraffed th...</td>\n",
              "      <td>Creative Writing</td>\n",
              "      <td>Simple</td>\n",
              "      <td>Once upon a time, in a magical land, there liv...</td>\n",
              "      <td>Once upon a time, there was a goose named Gera...</td>\n",
              "      <td>7.0</td>\n",
              "      <td>ChatGPT much better</td>\n",
              "      <td>ChatGPT's story was much better as it was writ...</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Write a short story that is no longer than 10 ...</td>\n",
              "      <td>Creative Writing</td>\n",
              "      <td>Hyperspecific</td>\n",
              "      <td>In the heart of Provence, amidst the rolling h...</td>\n",
              "      <td>Here is a short story that is no longer than 1...</td>\n",
              "      <td>7.0</td>\n",
              "      <td>ChatGPT much better</td>\n",
              "      <td>ChatGPT nailed the writing style I requested a...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>How could I use the ArcGIS Python API to creat...</td>\n",
              "      <td>Coding</td>\n",
              "      <td>Simple</td>\n",
              "      <td>To create a GeoDataFrame from a GeoJSON using ...</td>\n",
              "      <td>To create a GeoDataFrame from GeoJSON using th...</td>\n",
              "      <td>6.0</td>\n",
              "      <td>ChatGPT better</td>\n",
              "      <td>While I was hoping for a response that did not...</td>\n",
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      "source": [
        "# Rename columns for easier identification and handling data in stats.models\n",
        "df = df.rename(columns={'Prompt Category': 'Category', 'Which model is more helpful, safe, and honest? (text)': 'Preference',\n",
        "                        'Which model is more helpful, safe, and honest? (rating)': 'Rating'})"
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        "# Binned preference and rating\n",
        "df['Binned_Preference'] = ['ChatGPT' if i > 4 else 'Bard' if i < 4 else 'Same' for i in df['Rating']]\n",
        "df['Binned_Rating'] = [2 if i > 4 else 1 if i < 4 else 0 for i in df['Rating']]"
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        "frequencies = df.groupby(['Category', 'Complexity', 'Preference'])['Preference'].count().rename('Frequency').reset_index()\n",
        "frequencies.head()"
      ],
      "outputs": [
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              "                 Category     Complexity            Preference  Frequency\n",
              "0  Adversarial Dishonesty  Hyperspecific        About the same          5\n",
              "1  Adversarial Dishonesty  Hyperspecific           Bard better          1\n",
              "2  Adversarial Dishonesty  Hyperspecific      Bard much better          2\n",
              "3  Adversarial Dishonesty  Hyperspecific  Bard slightly better          2\n",
              "4  Adversarial Dishonesty  Hyperspecific        ChatGPT better          4"
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              "      <td>Hyperspecific</td>\n",
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        "fig = go.Figure()\n",
        "colors = ['lightgrey', '#1a5e8f', 'navy', '#5efffd', '#fc723f', '#f64975', '#FBCF78', '#f64975']\n",
        "for i, (r, c) in enumerate(zip(frequencies.Preference.unique(), colors)):\n",
        "    plot_df = frequencies[frequencies.Preference == r]\n",
        "    fig.add_trace(\n",
        "        go.Bar(x=[plot_df.Complexity, plot_df.Category], y=plot_df.Frequency, name=r, marker_color=c,\n",
        "            width=0.8))\n",
        "    fig.update_layout(title_x=0.5, xaxis_tickangle=-90, bargap=0)\n",
        "fig.update_layout(barmode=\"relative\", font_size=10, legend=dict(orientation=\"h\", yanchor='top', y=10,  title_text=\"Preference:\"), margin=dict(b=40,t=40,l=20,r=20), title_x=0.5, width=800, height=700, template=\"simple_white\", title=\"\")\n",
        "fig.update_yaxes(showgrid=True)\n",
        "fig.write_image(\"likert_ratings.svg\", format=\"svg\")\n",
        "fig.show()\n"
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      "outputs": [
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        "**Takeaways - Likert-like preferences**\n",
        "\n",
        "---\n",
        "\n",
        "- The chart above shows that ChatGPT was rated much better in 9 categories for hyperspecific requests.\n",
        "- ChatGPT was rated much better in six categories for simple prompt requests.\n",
        "- For mathematical reasoning in hyperspecific requests, Bard and GPT were more often rated as having the same performance.\n",
        "- For simple prompts in mathematical reasoning, Bard was rated as Bard much better the same number of times that ChatGPT was rated as ChatGPT slightly better.\n",
        "- For simple prompts in Open QA, Bard's performance was more often rated slightly better and had the same number of preferences as the About the Same.\n",
        "- For hyperspecific Open QA, the ratings ChatGPT much better and About the Same had the same number of observations.\n",
        "- For Adversarial Harmfulness, Classification, Open QA and Closed QA simple prompts, Bard and ChatGPT were more often rated as **About the same**.\n",
        "\n",
        "____\n",
        "\n",
        "Bard with none observations\n",
        "\n",
        "- None Simple-Creative Writing prompts were rated as **Bard better**.\n",
        "- None Simple-Poetry prompts were rated as **Bard much better** observations.\n",
        "\n",
        "---\n",
        "\n",
        "General Summary\n",
        "\n",
        "- All in all ChatGPT performance was rated higher more often than Bard. However, it performs better at hyperspecific requests while Bard improves its performance when handling simple requests."
      ]
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    {
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          "start_time": "2025-02-21T17:02:22.462291Z"
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        "binned_frequencies = df.groupby(['Category', 'Complexity', 'Binned_Preference'])['Binned_Preference'].count().rename('Frequency').reset_index()\n",
        "binned_frequencies.head()"
      ],
      "outputs": [
        {
          "data": {
            "text/plain": [
              "                 Category     Complexity Binned_Preference  Frequency\n",
              "0  Adversarial Dishonesty  Hyperspecific              Bard          5\n",
              "1  Adversarial Dishonesty  Hyperspecific           ChatGPT         10\n",
              "2  Adversarial Dishonesty  Hyperspecific              Same          5\n",
              "3  Adversarial Dishonesty         Simple              Bard         10\n",
              "4  Adversarial Dishonesty         Simple           ChatGPT         33"
            ],
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              "      <td>Hyperspecific</td>\n",
              "      <td>Same</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Adversarial Dishonesty</td>\n",
              "      <td>Simple</td>\n",
              "      <td>Bard</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Adversarial Dishonesty</td>\n",
              "      <td>Simple</td>\n",
              "      <td>ChatGPT</td>\n",
              "      <td>33</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "4502893f6709d491",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:02:24.239582Z",
          "start_time": "2025-02-21T17:02:23.989820Z"
        },
        "id": "4502893f6709d491",
        "outputId": "1fd8badd-6e3f-43c4-f014-89cf874c352d"
      },
      "source": [
        "fig = go.Figure()\n",
        "\n",
        "colors = ['#1a5e8f','#f64975', 'lightgrey']\n",
        "for i, (r, c) in enumerate(zip(binned_frequencies.Binned_Preference.unique(), colors)):\n",
        "    plot_df = binned_frequencies[binned_frequencies.Binned_Preference == r]\n",
        "    fig.add_trace(\n",
        "        go.Bar(x=[plot_df.Complexity, plot_df.Category], y=plot_df.Frequency, name=r, marker_color=c,\n",
        "            width=0.8))\n",
        "    fig.update_layout(title_x=0.5, xaxis_tickangle=-90, bargap=0)\n",
        "fig.update_layout(barmode=\"relative\", font_size=10, legend=dict(orientation=\"h\", yanchor='top', y=10,  title_text=\"Preference:\"), margin=dict(b=40,t=40,l=20,r=20), title_x=0.5, width=800, height=700, template=\"simple_white\", title=\"\")\n",
        "fig.update_yaxes(showgrid=True)\n",
        "fig.write_image(\"binned_preference.svg\", format=\"svg\")\n",
        "fig.show()"
      ],
      "outputs": [
        {
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opacity: 1; stroke-width: 0.5px; fill: rgb(211, 211, 211); fill-opacity: 1; stroke: rgb(255, 255, 255); stroke-opacity: 1;\"/></g><g class=\"point\"><path d=\"M634.95,161.52V57.05H657.93V161.52Z\" style=\"vector-effect: none; opacity: 1; stroke-width: 0.5px; fill: rgb(211, 211, 211); fill-opacity: 1; stroke: rgb(255, 255, 255); stroke-opacity: 1;\"/></g><g class=\"point\"><path d=\"M290.18,161.52V148.46H313.17V161.52Z\" style=\"vector-effect: none; opacity: 1; stroke-width: 0.5px; fill: rgb(211, 211, 211); fill-opacity: 1; stroke: rgb(255, 255, 255); stroke-opacity: 1;\"/></g><g class=\"point\"><path d=\"M663.68,318.23V311.7H686.67V318.23Z\" style=\"vector-effect: none; opacity: 1; stroke-width: 0.5px; fill: rgb(211, 211, 211); fill-opacity: 1; stroke: rgb(255, 255, 255); stroke-opacity: 1;\"/></g><g class=\"point\"><path d=\"M318.91,265.99V246.41H341.9V265.99Z\" style=\"vector-effect: none; opacity: 1; stroke-width: 0.5px; fill: rgb(211, 211, 211); fill-opacity: 1; stroke: rgb(255, 255, 255); stroke-opacity: 1;\"/></g><g class=\"point\"><path d=\"M692.41,272.52V246.41H715.4V272.52Z\" style=\"vector-effect: none; opacity: 1; stroke-width: 0.5px; fill: rgb(211, 211, 211); fill-opacity: 1; stroke: rgb(255, 255, 255); stroke-opacity: 1;\"/></g><g class=\"point\"><path d=\"M347.64,344.35V331.29H370.63V344.35Z\" style=\"vector-effect: none; opacity: 1; stroke-width: 0.5px; fill: rgb(211, 211, 211); fill-opacity: 1; stroke: rgb(255, 255, 255); stroke-opacity: 1;\"/></g><g class=\"point\"><path d=\"M721.14,174.58V141.93H744.13V174.58Z\" style=\"vector-effect: none; opacity: 1; stroke-width: 0.5px; fill: rgb(211, 211, 211); fill-opacity: 1; stroke: rgb(255, 255, 255); stroke-opacity: 1;\"/></g></g></g></g></g></g><path class=\"xlines-above crisp\" d=\"M32,539.5H780\" style=\"fill: none; stroke-width: 1px; stroke: rgb(36, 36, 36); stroke-opacity: 1;\"/><path class=\"ylines-above crisp\" d=\"M32.5,51V539\" style=\"fill: none; stroke-width: 1px; stroke: rgb(36, 36, 36); stroke-opacity: 1;\"/><g class=\"overlines-above\"/><g class=\"xaxislayer-above\"><path class=\"xdivider crisp\" transform=\"translate(780,0)\" d=\"M0,540v149.03125\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xdivider crisp\" transform=\"translate(406.5,0)\" d=\"M0,540v149.03125\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xdivider crisp\" transform=\"translate(33,0)\" d=\"M0,540v149.03125\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"\" transform=\"translate(33,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(61.730000000000004,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(90.46000000000001,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(119.19,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(147.92000000000002,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(176.65,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(205.38,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(234.12,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(262.85,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(291.58,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(320.31,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(349.04,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(377.77,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"\" transform=\"translate(406.5,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(435.23,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(463.96,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(492.69,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(521.4200000000001,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(550.15,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(578.88,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(607.62,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(636.35,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(665.08,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(693.81,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(722.54,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,540v5\" transform=\"translate(751.27,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"\" transform=\"translate(780,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(47.37,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Adversarial Dishonesty</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(76.1,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Adversarial Harmfulness</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(104.83,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Brainstorming</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(133.56,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Classification</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(162.29,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Closed QA</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(191.02,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Coding</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(219.75,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Creative Writing</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(248.48,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Extraction</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(277.21000000000004,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Mathematical Reasoning</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(305.94,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Open QA</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(334.67,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Poetry</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(363.4,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Rewriting</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(392.13,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Summarization</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(420.87,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Adversarial Dishonesty</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(449.6,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Adversarial Harmfulness</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(478.33,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Brainstorming</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(507.06,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Classification</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(535.79,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Closed QA</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(564.52,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Coding</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(593.25,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Creative Writing</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(621.98,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Extraction</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(650.71,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Mathematical Reasoning</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(679.44,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Open QA</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(708.17,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Poetry</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(736.9,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Rewriting</text></g><g class=\"xtick\"><text text-anchor=\"end\" x=\"-1.75\" y=\"549\" transform=\"translate(765.63,0) rotate(-90,-1.75,544)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Summarization</text></g><g class=\"xtick2\"><text text-anchor=\"middle\" x=\"-1.75\" y=\"686.515625\" transform=\"translate(219.75,0)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Hyperspecific</text></g><g class=\"xtick2\"><text text-anchor=\"middle\" x=\"-1.75\" y=\"686.515625\" transform=\"translate(593.25,0)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Simple</text></g></g><g class=\"yaxislayer-above\"><path class=\"ytick ticks crisp\" d=\"M32,0h-5\" transform=\"translate(0,539)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M32,0h-5\" transform=\"translate(0,473.7)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M32,0h-5\" transform=\"translate(0,408.41)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M32,0h-5\" transform=\"translate(0,343.11)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M32,0h-5\" transform=\"translate(0,277.82)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M32,0h-5\" transform=\"translate(0,212.52)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M32,0h-5\" transform=\"translate(0,147.23000000000002)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M32,0h-5\" transform=\"translate(0,81.93)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"ytick\"><text text-anchor=\"end\" x=\"25\" y=\"3.5\" transform=\"translate(0,539)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">0</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"25\" y=\"3.5\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(0,473.7)\">10</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"25\" y=\"3.5\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(0,408.41)\">20</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"25\" y=\"3.5\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(0,343.11)\">30</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"25\" y=\"3.5\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 10px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(0,277.82)\">40</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"25\" y=\"3.5\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; 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      "metadata": {
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      "source": [
        "**Takeaways**\n",
        "\n",
        "---\n",
        "\n",
        "- The chart above with binned preferences shows that ChatGPT performed better than Bard in hyperspecific tasks.\n",
        "- The observation frequencies for simple requests in Adversarial Harmfulness, Closed QA, Mathematical Reasoning, and Open QA differ slightly. The statistical analysis will determine whether the model is statistically significant in these areas.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "13fa525291bda5a3",
      "metadata": {
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      "source": [
        "## 3. Hypothesis Testing"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d0d2474d80118275",
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      "source": [
        "Here we will use statistical methods to:\n",
        "\n",
        "- Find out whether the prompt category and complexity impact the models rating.\n",
        "- Whether there is a difference in every group combination.\n",
        "\n",
        "$H_0:$ Preference is independent of the prompt category and complexity.\n",
        "\n",
        "$H_1:$ Preference is independent of the prompt category and complexity.\n",
        "\n",
        "$ \\alpha = 0.5$\n",
        "\n",
        "There are in total 26 combination - 13 categories x 2 ls of complexity. However, the dataset is imbalanced because some test combinations were replicated more times than others. Therefore, we will utilise parametric and non-parametric statistics to compare the results. The dataset rating results are in __Likert scale__ and numerical scale (Table 1, [1]). Two columns were added to bin the preference (Table 2) and run the tests with both data.\n",
        "\n",
        "**Total number of prompts**:  1003 (A prime number)\n",
        "\n",
        "\n",
        "<center>\n",
        "<table>\n",
        "<tr><th>Table 1: Preference and rating in Likert scale  </th><th>Table 2: Binned preference and rating </th></tr>\n",
        "<tr><td>\n",
        "\n",
        "|  Rating  | Preference              |\n",
        "|:--------:|-------------------------|\n",
        "|    1     | Bard slightly better    |\n",
        "|    2     | Bard better             |\n",
        "|    3     | Bard much better        |\n",
        "|    4     | About the same          |\n",
        "|    5     | ChatGPT slightly better |\n",
        "|    6     | ChatGPT better          |\n",
        "|    7     | ChatGPT much better     |\n",
        "\n",
        "</td><td>\n",
        "\n",
        "\n",
        "|  Binned Rating  | Binned Preference                                                         |\n",
        "|:---------------:|---------------------------------------------------------------------------|\n",
        "|      0 (4)      | Same (About the same)                                                     |\n",
        "|     1 (1-3)     | Bard (Bard much better, Bard better and Bard slightly better)             |\n",
        "|     2 (5-7)     | ChatGPT (ChatGPT much better, ChatGPT better and ChatGPT slightly better) |                                                      \n",
        "\n",
        "</td></tr> </table>\n",
        "\n",
        "</center>\n",
        "\n",
        "\n",
        "___\n",
        "\n",
        "**Statistical Analysis**\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "The methods to used in this analysis are:\n",
        "\n",
        "1. Contingency Tables - Nonparametric test for categorical frequencies.\n",
        "2. 2-way Analysis of Variance (ANOVA) - Parametric test which may not fulfil the normality, homogeneity of variance and independence assumption.\n",
        "3. Kruskal-Wallis - Nonparametric group comparison.\n",
        "\n",
        "If the test are significant with p-values < 0.05, post-hoc for the group comparison will be undertaken with following post-hoc test:\n",
        "\n",
        "1. Dunn\n",
        "\n",
        "\n",
        "References:\n",
        "[1] https://pmc.ncbi.nlm.nih.gov/articles/PMC3886444/\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "22be76a462e3e0a4",
      "metadata": {
        "id": "22be76a462e3e0a4"
      },
      "source": [
        "### 3.1 Contingency Tables"
      ]
    },
    {
      "cell_type": "code",
      "id": "af8fb02130bec638",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:02:29.878166Z",
          "start_time": "2025-02-21T17:02:29.833997Z"
        },
        "id": "af8fb02130bec638",
        "outputId": "0f031124-fb04-4e2d-9aa8-b4b77dcd2bc2"
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      "source": [
        "table_01 = pd.crosstab([df['Category'], df['Complexity']], df['Preference'])\n",
        "table_01"
      ],
      "outputs": [
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              "Preference                             About the same  Bard better  \\\n",
              "Category                Complexity                                   \n",
              "Adversarial Dishonesty  Hyperspecific               5            1   \n",
              "                        Simple                      7            3   \n",
              "Adversarial Harmfulness Hyperspecific               6            1   \n",
              "                        Simple                     17            6   \n",
              "Brainstorming           Hyperspecific               8            4   \n",
              "                        Simple                      2            2   \n",
              "Classification          Hyperspecific               5            3   \n",
              "                        Simple                     10            6   \n",
              "Closed QA               Hyperspecific               3            3   \n",
              "                        Simple                     17            8   \n",
              "Coding                  Hyperspecific               1            3   \n",
              "                        Simple                      3            3   \n",
              "Creative Writing        Hyperspecific               8            4   \n",
              "                        Simple                      3            0   \n",
              "Extraction              Hyperspecific               9            3   \n",
              "                        Simple                      6            4   \n",
              "Mathematical Reasoning  Hyperspecific               9            4   \n",
              "                        Simple                      7            6   \n",
              "Open QA                 Hyperspecific               4            3   \n",
              "                        Simple                     16            6   \n",
              "Poetry                  Hyperspecific               2            3   \n",
              "                        Simple                      1            1   \n",
              "Rewriting               Hyperspecific               3            4   \n",
              "                        Simple                      4            3   \n",
              "Summarization           Hyperspecific               2            2   \n",
              "                        Simple                      5            7   \n",
              "\n",
              "Preference                             Bard much better  Bard slightly better  \\\n",
              "Category                Complexity                                              \n",
              "Adversarial Dishonesty  Hyperspecific                 2                     2   \n",
              "                        Simple                        2                     5   \n",
              "Adversarial Harmfulness Hyperspecific                 1                     1   \n",
              "                        Simple                        2                     7   \n",
              "Brainstorming           Hyperspecific                 3                     4   \n",
              "                        Simple                        1                     1   \n",
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              "                        Simple                        2                     6   \n",
              "Closed QA               Hyperspecific                 1                     2   \n",
              "                        Simple                        4                    10   \n",
              "Coding                  Hyperspecific                 1                     2   \n",
              "                        Simple                        1                     1   \n",
              "Creative Writing        Hyperspecific                 1                     3   \n",
              "                        Simple                        2                     5   \n",
              "Extraction              Hyperspecific                 1                     4   \n",
              "                        Simple                        2                     3   \n",
              "Mathematical Reasoning  Hyperspecific                 3                     1   \n",
              "                        Simple                        9                     2   \n",
              "Open QA                 Hyperspecific                 2                     1   \n",
              "                        Simple                        1                    16   \n",
              "Poetry                  Hyperspecific                 2                     3   \n",
              "                        Simple                        0                     1   \n",
              "Rewriting               Hyperspecific                 1                     3   \n",
              "                        Simple                        2                     2   \n",
              "Summarization           Hyperspecific                 2                     4   \n",
              "                        Simple                        7                     6   \n",
              "\n",
              "Preference                             ChatGPT better  ChatGPT much better  \\\n",
              "Category                Complexity                                           \n",
              "Adversarial Dishonesty  Hyperspecific               4                    5   \n",
              "                        Simple                      5                   17   \n",
              "Adversarial Harmfulness Hyperspecific               1                    8   \n",
              "                        Simple                      5                    4   \n",
              "Brainstorming           Hyperspecific              12                   19   \n",
              "                        Simple                      2                    3   \n",
              "Classification          Hyperspecific               8                    3   \n",
              "                        Simple                      4                    9   \n",
              "Closed QA               Hyperspecific               5                    7   \n",
              "                        Simple                      8                   14   \n",
              "Coding                  Hyperspecific               2                   12   \n",
              "                        Simple                      7                    9   \n",
              "Creative Writing        Hyperspecific              19                   23   \n",
              "                        Simple                      6                   11   \n",
              "Extraction              Hyperspecific               3                   12   \n",
              "                        Simple                      7                    9   \n",
              "Mathematical Reasoning  Hyperspecific               8                    7   \n",
              "                        Simple                      7                    4   \n",
              "Open QA                 Hyperspecific               2                    4   \n",
              "                        Simple                     12                    7   \n",
              "Poetry                  Hyperspecific              21                   12   \n",
              "                        Simple                     10                    8   \n",
              "Rewriting               Hyperspecific               8                   11   \n",
              "                        Simple                     10                   13   \n",
              "Summarization           Hyperspecific               6                    4   \n",
              "                        Simple                     11                    7   \n",
              "\n",
              "Preference                             ChatGPT slightly better  \n",
              "Category                Complexity                              \n",
              "Adversarial Dishonesty  Hyperspecific                        1  \n",
              "                        Simple                              11  \n",
              "Adversarial Harmfulness Hyperspecific                        2  \n",
              "                        Simple                               9  \n",
              "Brainstorming           Hyperspecific                       11  \n",
              "                        Simple                               4  \n",
              "Classification          Hyperspecific                        1  \n",
              "                        Simple                               9  \n",
              "Closed QA               Hyperspecific                        6  \n",
              "                        Simple                               5  \n",
              "Coding                  Hyperspecific                        4  \n",
              "                        Simple                               4  \n",
              "Creative Writing        Hyperspecific                       13  \n",
              "                        Simple                               1  \n",
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              "                        Simple                               7  \n",
              "Mathematical Reasoning  Hyperspecific                        4  \n",
              "                        Simple                               9  \n",
              "Open QA                 Hyperspecific                        4  \n",
              "                        Simple                               8  \n",
              "Poetry                  Hyperspecific                        9  \n",
              "                        Simple                               6  \n",
              "Rewriting               Hyperspecific                        7  \n",
              "                        Simple                               3  \n",
              "Summarization           Hyperspecific                        4  \n",
              "                        Simple                              10  "
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              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>12</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>7</td>\n",
              "      <td>9</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Creative Writing</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>8</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>19</td>\n",
              "      <td>23</td>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>5</td>\n",
              "      <td>6</td>\n",
              "      <td>11</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Extraction</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>9</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>12</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>6</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>7</td>\n",
              "      <td>9</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Mathematical Reasoning</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>9</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>8</td>\n",
              "      <td>7</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>7</td>\n",
              "      <td>6</td>\n",
              "      <td>9</td>\n",
              "      <td>2</td>\n",
              "      <td>7</td>\n",
              "      <td>4</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Open QA</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>16</td>\n",
              "      <td>6</td>\n",
              "      <td>1</td>\n",
              "      <td>16</td>\n",
              "      <td>12</td>\n",
              "      <td>7</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Poetry</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>21</td>\n",
              "      <td>12</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>10</td>\n",
              "      <td>8</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Rewriting</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>8</td>\n",
              "      <td>11</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>10</td>\n",
              "      <td>13</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Summarization</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>6</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>5</td>\n",
              "      <td>7</td>\n",
              "      <td>7</td>\n",
              "      <td>6</td>\n",
              "      <td>11</td>\n",
              "      <td>7</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "1fd95860fda675e9",
      "metadata": {
        "id": "1fd95860fda675e9"
      },
      "source": [
        "1. We can observe that:\n",
        "    -  **Simple** prompts in **Creative Writing** category have no instance of preference \"Bard better\"\n",
        "    -  **Simple** prompts in the **Poetry** category have no instance of preference \"Bard much better\"\n",
        "\n",
        "2. There are also several factors combinations with preference frequencies less than 5 which can impact the Chi-square of variables independence for the contingency table. We will use the Permutation method and Montecarlo simulations to better accuracy of the results.\n",
        "\n",
        "**Next Steps:**\n",
        "- Chi-square test and Fisher exact, verify the p-value and the expected frequencies for preferences and the binned preferences.\n"
      ]
    },
    {
      "cell_type": "code",
      "id": "294ccd8813c7484d",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:02:32.520030Z",
          "start_time": "2025-02-21T17:02:32.498216Z"
        },
        "id": "294ccd8813c7484d",
        "outputId": "3dccdc55-f012-436a-b677-1acb50ac9f39"
      },
      "source": [
        "table_02 = pd.crosstab([df['Category'], df['Complexity']], df['Binned_Preference'])\n",
        "table_02"
      ],
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Binned_Preference                      Bard  ChatGPT  Same\n",
              "Category                Complexity                        \n",
              "Adversarial Dishonesty  Hyperspecific     5       10     5\n",
              "                        Simple           10       33     7\n",
              "Adversarial Harmfulness Hyperspecific     3       11     6\n",
              "                        Simple           15       18    17\n",
              "Brainstorming           Hyperspecific    11       42     8\n",
              "                        Simple            4        9     2\n",
              "Classification          Hyperspecific     6       12     5\n",
              "                        Simple           14       22    10\n",
              "Closed QA               Hyperspecific     6       18     3\n",
              "                        Simple           22       27    17\n",
              "Coding                  Hyperspecific     6       18     1\n",
              "                        Simple            5       20     3\n",
              "Creative Writing        Hyperspecific     8       55     8\n",
              "                        Simple            7       18     3\n",
              "Extraction              Hyperspecific     8       22     9\n",
              "                        Simple            9       23     6\n",
              "Mathematical Reasoning  Hyperspecific     8       19     9\n",
              "                        Simple           17       20     7\n",
              "Open QA                 Hyperspecific     6       10     4\n",
              "                        Simple           23       27    16\n",
              "Poetry                  Hyperspecific     8       42     2\n",
              "                        Simple            2       24     1\n",
              "Rewriting               Hyperspecific     8       26     3\n",
              "                        Simple            7       26     4\n",
              "Summarization           Hyperspecific     8       14     2\n",
              "                        Simple           20       28     5"
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Binned_Preference</th>\n",
              "      <th>Bard</th>\n",
              "      <th>ChatGPT</th>\n",
              "      <th>Same</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Category</th>\n",
              "      <th>Complexity</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Adversarial Dishonesty</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>5</td>\n",
              "      <td>10</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>10</td>\n",
              "      <td>33</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Adversarial Harmfulness</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>3</td>\n",
              "      <td>11</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>15</td>\n",
              "      <td>18</td>\n",
              "      <td>17</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Brainstorming</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>11</td>\n",
              "      <td>42</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>4</td>\n",
              "      <td>9</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Classification</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>6</td>\n",
              "      <td>12</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>14</td>\n",
              "      <td>22</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Closed QA</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>6</td>\n",
              "      <td>18</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>22</td>\n",
              "      <td>27</td>\n",
              "      <td>17</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Coding</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>6</td>\n",
              "      <td>18</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>5</td>\n",
              "      <td>20</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Creative Writing</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>8</td>\n",
              "      <td>55</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>7</td>\n",
              "      <td>18</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Extraction</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>8</td>\n",
              "      <td>22</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>9</td>\n",
              "      <td>23</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Mathematical Reasoning</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>8</td>\n",
              "      <td>19</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>17</td>\n",
              "      <td>20</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Open QA</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>6</td>\n",
              "      <td>10</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>23</td>\n",
              "      <td>27</td>\n",
              "      <td>16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Poetry</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>8</td>\n",
              "      <td>42</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>2</td>\n",
              "      <td>24</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Rewriting</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>8</td>\n",
              "      <td>26</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>7</td>\n",
              "      <td>26</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th rowspan=\"2\" valign=\"top\">Summarization</th>\n",
              "      <th>Hyperspecific</th>\n",
              "      <td>8</td>\n",
              "      <td>14</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Simple</th>\n",
              "      <td>20</td>\n",
              "      <td>28</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "8a4b6a259367fecf",
      "metadata": {
        "id": "8a4b6a259367fecf"
      },
      "source": [
        "### 3.2 Contingency Table Comparison Functions"
      ]
    },
    {
      "cell_type": "code",
      "id": "95eb00d4a1a16189",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:02:42.460005Z",
          "start_time": "2025-02-21T17:02:42.450983Z"
        },
        "id": "95eb00d4a1a16189"
      },
      "source": [
        "# Contingency test functions\n",
        "\n",
        "def contingency_test(table, test='fisher', resampling_method='montecarlo'):\n",
        "\n",
        "    sampling_dict = {'montecarlo': MonteCarloMethod(), 'permutation': PermutationMethod(), 'none':None}\n",
        "\n",
        "    if test == 'fisher':\n",
        "        res = fisher_exact(table, method=sampling_dict[resampling_method.lower()])\n",
        "        print(f'Fisher stats: {res.statistic} | pvalue: {res.pvalue}')\n",
        "\n",
        "        return res.statistic, res.pvalue\n",
        "    else:\n",
        "        res = chi2_contingency(table, correction=False, method=sampling_dict[resampling_method.lower()])\n",
        "        # Get the expected frequency values and computes the percent of groups with < 5 expected observations\n",
        "        freq = res.expected_freq\n",
        "        exp_freq = len(np.where(freq < 5)[0]) / len(freq.reshape(-1)) * 100\n",
        "        print(f'Chi-square stats: {res.statistic} | pvalue: {res.pvalue} | Expected observations with frequencies < 5: {exp_freq:.2f}%')\n",
        "\n",
        "        return res.statistic, res.pvalue,\n",
        "\n",
        "\n",
        "def run_contingency_test(data, test_list, resampling_list, likert='all preferences'):\n",
        "\n",
        "    assert isinstance(data, pd.DataFrame)\n",
        "    assert isinstance(test_list, list)\n",
        "    assert isinstance(resampling_list, list)\n",
        "\n",
        "    stats_dict = defaultdict(list)\n",
        "\n",
        "    test_counts = 0\n",
        "    for i, test in enumerate(test_list):\n",
        "        for ii, method in enumerate(resampling_list):\n",
        "            test_counts += 1\n",
        "            print(f'Test no: {test_counts} | Hypothesis: {test} | Method: {method}')\n",
        "            result = contingency_test(data, test=test, resampling_method=method)\n",
        "            st, pval = result[0], result[1]\n",
        "            stats_dict['likert'] = likert\n",
        "            stats_dict['test'].append(test)\n",
        "            stats_dict['resampling'].append(method)\n",
        "            stats_dict['stat'].append(st)\n",
        "            stats_dict['pvalue'].append(pval)\n",
        "            if pval < 0.05:\n",
        "                stats_dict['Ho'].append('reject')\n",
        "            else:\n",
        "                stats_dict['Ho'].append('accept')\n",
        "            print(f'-----------'*10)\n",
        "\n",
        "    return pd.DataFrame.from_dict(stats_dict)\n"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "3fd70313f9888729",
      "metadata": {
        "id": "3fd70313f9888729"
      },
      "source": [
        "### 3.3 Run Test"
      ]
    },
    {
      "cell_type": "code",
      "id": "6347a4326211b641",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:02:49.385534Z",
          "start_time": "2025-02-21T17:02:49.381233Z"
        },
        "id": "6347a4326211b641"
      },
      "source": [
        "param_dict = dict(hypo_test = ['fisher', 'chi-square'], resampling = ['Montecarlo', 'Permutation', 'None'],\n",
        "                  likert='all preferences', binned_likert = 'Bard, Same, GPT' )"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "9baaecf4550a8af",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:03:01.412734Z",
          "start_time": "2025-02-21T17:02:51.955967Z"
        },
        "id": "9baaecf4550a8af",
        "outputId": "7d6f2447-0845-43bd-d25d-d7c503c15f43"
      },
      "source": [
        "# Use table_01 with original preference scale\n",
        "stats_df = run_contingency_test(table_01, test_list=param_dict[\"hypo_test\"], resampling_list=param_dict['resampling'],\n",
        "                                       likert=param_dict['likert'])"
      ],
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Test no: 1 | Hypothesis: fisher | Method: Montecarlo\n",
            "Fisher stats: 4.460718085773558e-139 | pvalue: 0.0001\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 2 | Hypothesis: fisher | Method: Permutation\n",
            "Fisher stats: 4.460718085773558e-139 | pvalue: 0.0001\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 3 | Hypothesis: fisher | Method: None\n",
            "Fisher stats: 4.460718085773558e-139 | pvalue: 0.0005\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 4 | Hypothesis: chi-square | Method: Montecarlo\n",
            "Chi-square stats: 219.62653844835157 | pvalue: 0.0001 | Expected observations with frequencies < 5: 56.04%\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 5 | Hypothesis: chi-square | Method: Permutation\n",
            "Chi-square stats: 219.62653844835157 | pvalue: 0.0001 | Expected observations with frequencies < 5: 56.04%\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 6 | Hypothesis: chi-square | Method: None\n",
            "Chi-square stats: 219.62653844835157 | pvalue: 0.0001831975373217207 | Expected observations with frequencies < 5: 56.04%\n",
            "--------------------------------------------------------------------------------------------------------------\n"
          ]
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "89df8a95affe73bf",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:03:09.593757Z",
          "start_time": "2025-02-21T17:03:01.422474Z"
        },
        "id": "89df8a95affe73bf",
        "outputId": "2ac14f4b-8a89-432d-bd9d-328e5c71bd58"
      },
      "source": [
        "# Use table_02 grouped by binned preferences\n",
        "binned_stats_df = run_contingency_test(table_02, test_list=param_dict[\"hypo_test\"], resampling_list=param_dict['resampling'],\n",
        "                                       likert=param_dict['binned_likert'])"
      ],
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Test no: 1 | Hypothesis: fisher | Method: Montecarlo\n",
            "Fisher stats: 2.1140213624554804e-59 | pvalue: 0.0001\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 2 | Hypothesis: fisher | Method: Permutation\n",
            "Fisher stats: 2.1140213624554804e-59 | pvalue: 0.0001\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 3 | Hypothesis: fisher | Method: None\n",
            "Fisher stats: 2.1140213624554804e-59 | pvalue: 0.0002\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 4 | Hypothesis: chi-square | Method: Montecarlo\n",
            "Chi-square stats: 102.25841414264765 | pvalue: 0.0001 | Expected observations with frequencies < 5: 19.23%\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 5 | Hypothesis: chi-square | Method: Permutation\n",
            "Chi-square stats: 102.25841414264765 | pvalue: 0.0002 | Expected observations with frequencies < 5: 19.23%\n",
            "--------------------------------------------------------------------------------------------------------------\n",
            "Test no: 6 | Hypothesis: chi-square | Method: None\n",
            "Chi-square stats: 102.25841414264765 | pvalue: 1.8751801853084325e-05 | Expected observations with frequencies < 5: 19.23%\n",
            "--------------------------------------------------------------------------------------------------------------\n"
          ]
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "3df597bf-30b1-42da-b9ce-279478aac668",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:03:12.065787Z",
          "start_time": "2025-02-21T17:03:12.052006Z"
        },
        "id": "3df597bf-30b1-42da-b9ce-279478aac668",
        "outputId": "c8109b4d-3fc5-4c50-d4e6-645c9e372cb4"
      },
      "source": [
        "contingency_stats = pd.concat([stats_df, binned_stats_df], axis=0, ignore_index=True)\n",
        "contingency_stats"
      ],
      "outputs": [
        {
          "data": {
            "text/plain": [
              "             likert        test   resampling           stat    pvalue      Ho\n",
              "0   all preferences      fisher   Montecarlo  4.460718e-139  0.000100  reject\n",
              "1   all preferences      fisher  Permutation  4.460718e-139  0.000100  reject\n",
              "2   all preferences      fisher         None  4.460718e-139  0.000500  reject\n",
              "3   all preferences  chi-square   Montecarlo   2.196265e+02  0.000100  reject\n",
              "4   all preferences  chi-square  Permutation   2.196265e+02  0.000100  reject\n",
              "5   all preferences  chi-square         None   2.196265e+02  0.000183  reject\n",
              "6   Bard, Same, GPT      fisher   Montecarlo   2.114021e-59  0.000100  reject\n",
              "7   Bard, Same, GPT      fisher  Permutation   2.114021e-59  0.000100  reject\n",
              "8   Bard, Same, GPT      fisher         None   2.114021e-59  0.000200  reject\n",
              "9   Bard, Same, GPT  chi-square   Montecarlo   1.022584e+02  0.000100  reject\n",
              "10  Bard, Same, GPT  chi-square  Permutation   1.022584e+02  0.000200  reject\n",
              "11  Bard, Same, GPT  chi-square         None   1.022584e+02  0.000019  reject"
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>likert</th>\n",
              "      <th>test</th>\n",
              "      <th>resampling</th>\n",
              "      <th>stat</th>\n",
              "      <th>pvalue</th>\n",
              "      <th>Ho</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>all preferences</td>\n",
              "      <td>fisher</td>\n",
              "      <td>Montecarlo</td>\n",
              "      <td>4.460718e-139</td>\n",
              "      <td>0.000100</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>all preferences</td>\n",
              "      <td>fisher</td>\n",
              "      <td>Permutation</td>\n",
              "      <td>4.460718e-139</td>\n",
              "      <td>0.000100</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>all preferences</td>\n",
              "      <td>fisher</td>\n",
              "      <td>None</td>\n",
              "      <td>4.460718e-139</td>\n",
              "      <td>0.000500</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>all preferences</td>\n",
              "      <td>chi-square</td>\n",
              "      <td>Montecarlo</td>\n",
              "      <td>2.196265e+02</td>\n",
              "      <td>0.000100</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>all preferences</td>\n",
              "      <td>chi-square</td>\n",
              "      <td>Permutation</td>\n",
              "      <td>2.196265e+02</td>\n",
              "      <td>0.000100</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>all preferences</td>\n",
              "      <td>chi-square</td>\n",
              "      <td>None</td>\n",
              "      <td>2.196265e+02</td>\n",
              "      <td>0.000183</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Bard, Same, GPT</td>\n",
              "      <td>fisher</td>\n",
              "      <td>Montecarlo</td>\n",
              "      <td>2.114021e-59</td>\n",
              "      <td>0.000100</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Bard, Same, GPT</td>\n",
              "      <td>fisher</td>\n",
              "      <td>Permutation</td>\n",
              "      <td>2.114021e-59</td>\n",
              "      <td>0.000100</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Bard, Same, GPT</td>\n",
              "      <td>fisher</td>\n",
              "      <td>None</td>\n",
              "      <td>2.114021e-59</td>\n",
              "      <td>0.000200</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Bard, Same, GPT</td>\n",
              "      <td>chi-square</td>\n",
              "      <td>Montecarlo</td>\n",
              "      <td>1.022584e+02</td>\n",
              "      <td>0.000100</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Bard, Same, GPT</td>\n",
              "      <td>chi-square</td>\n",
              "      <td>Permutation</td>\n",
              "      <td>1.022584e+02</td>\n",
              "      <td>0.000200</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Bard, Same, GPT</td>\n",
              "      <td>chi-square</td>\n",
              "      <td>None</td>\n",
              "      <td>1.022584e+02</td>\n",
              "      <td>0.000019</td>\n",
              "      <td>reject</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "8291fe8fc2b5ab9",
      "metadata": {
        "id": "8291fe8fc2b5ab9"
      },
      "source": [
        "**Result**\n",
        "___\n",
        "\n",
        "We can observe that:\n",
        "\n",
        "- All test combination for the Chi-square and Fisher exact tests showed p-values < 0.05.\n",
        "- For full preference rating, the Fisher exact and Chi-square tests without resampling showed very similar p-values 0.0002 and 0.000183. This table had two preferences without observation and several with less than 5 observation.\n",
        "- Using the Permutation or Montecarlo sampling methods did not trigger p-values >= 0.05\n",
        "- Apart from the tes Chi-square test without resampling method, all p-values for the grouped preferences showed the a p-value 0.0001.\n",
        "\n",
        "____\n",
        "\n",
        "**Reject the null hypothesis:** $H_0$\n",
        "\n",
        "\n",
        "The results show that there is sufficient evidence to reject the $H_0$.\n",
        "\n",
        "Therefore, we can say with 95% certainty that the rating preference is dependent on the prompt category and complexity.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ae5651d58dbb58f6",
      "metadata": {
        "id": "ae5651d58dbb58f6"
      },
      "source": [
        "___\n",
        "\n",
        "#### Stats notes\n",
        "\n",
        "\n",
        "[Statsmodels](https://www.statsmodels.org/stable/generated/statsmodels.stats.contingency_tables.Table.test_nominal_association.html#statsmodels.stats.contingency_tables.Table.test_nominal_associationalso) provides the function ```Table.test_nominal_association()``` to assess independence between rows and columns using chi^2 testing in contingency tables. The rows and columns are treated as nominal (unordered) categorical variables.\n",
        "```\n",
        "import statsmodels.api as sm\n",
        "\n",
        "table = sm.stats.Table(table_02)\n",
        "\n",
        "print(table.table_orig)\n",
        "print(table.fittedvalues)\n",
        "print(table.resid_pearson)\n",
        "print(table.chi2_contribs)\n",
        "result = table.test_nominal_association()\n",
        "print(result.pvalue, result)\n",
        "\n",
        "```\n",
        "\n",
        "Running the above code for table_02 is equivalent to  ```chi2_contingency(table_02, correction=False, method=None)```."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "576b5b91fd1d326d",
      "metadata": {
        "id": "576b5b91fd1d326d"
      },
      "source": [
        "### 3.4 Associations - Effect of the size"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4f9040c31c0465c3",
      "metadata": {
        "id": "4f9040c31c0465c3"
      },
      "source": [
        "We will use Cramer's V coefficient for the non-square tables to measure how strongly the categorical variables in the contingency tables are associated. There are disputes about the threshold for associations. We would use the threshold:\n",
        "\n",
        "- Weak association: $coefficient >= 0.2$\n",
        "- Moderate association: $0.2 < coefficient < 0.6$\n",
        "- Strong association: $coefficient > 0.6$\n",
        "\n",
        "**References**:\n",
        "1. https://www.ibm.com/docs/en/cognos-analytics/11.1.0?topic=terms-cramrs-v\n",
        "2. https://cran.r-project.org/web/packages/effectsize/vignettes/xtabs.html\n",
        "3. https://stats.stackexchange.com/questions/332086/what-are-the-thresholds-for-strength-of-association\n",
        "4. https://real-statistics.com/chi-square-and-f-distributions/effect-size-chi-square/\n",
        "5. https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/effectSize\n"
      ]
    },
    {
      "cell_type": "code",
      "id": "4407a5427ef760fe",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:03:58.491032Z",
          "start_time": "2025-02-21T17:03:58.485517Z"
        },
        "id": "4407a5427ef760fe"
      },
      "source": [
        "def measure_associations(table):\n",
        "\n",
        "    cramer = association(table, method=\"cramer\")\n",
        "    if cramer > 0.6:\n",
        "        print(f\"Strong Cramer's V association: {cramer}\")\n",
        "\n",
        "    elif cramer <= 0.2:\n",
        "        print(f\"Weak Cramer's V association: {cramer}\")\n",
        "    else:\n",
        "        print(f\"Moderate Cramer's V association: {cramer}\")\n",
        "    return cramer"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "5c714debd80531b7",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:04:04.781286Z",
          "start_time": "2025-02-21T17:04:04.774576Z"
        },
        "id": "5c714debd80531b7",
        "outputId": "b23e7290-ddfa-4438-cd18-eb56c620ea0f"
      },
      "source": [
        "print(f'Table with all preferences: table_01')\n",
        "table_01_associations = measure_associations(table_01)\n",
        "print('-----------' * 5)\n",
        "print(f'Table with binned preferences table_02')\n",
        "table_02_associations = measure_associations(table_02)"
      ],
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Table with all preferences: table_01\n",
            "Weak Cramer's V association: 0.1910364841069512\n",
            "-------------------------------------------------------\n",
            "Table with binned preferences table_02\n",
            "Moderate Cramer's V association: 0.2257792688370967\n"
          ]
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "c26e39f70d7cc272",
      "metadata": {
        "id": "c26e39f70d7cc272"
      },
      "source": [
        "### 3.5 ANOVA"
      ]
    },
    {
      "cell_type": "code",
      "id": "aef96fdba9a63980",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:04:14.260330Z",
          "start_time": "2025-02-21T17:04:14.244301Z"
        },
        "id": "aef96fdba9a63980",
        "outputId": "13a13b02-f54c-4e7c-97ad-80c28758389c"
      },
      "source": [
        "df_sorted = df[['Category', 'Complexity', 'Rating', 'Binned_Rating']].sort_values(['Category', 'Complexity']).reset_index(drop=True)\n",
        "df_sorted.head()"
      ],
      "outputs": [
        {
          "data": {
            "text/plain": [
              "                 Category     Complexity  Rating  Binned_Rating\n",
              "0  Adversarial Dishonesty  Hyperspecific     6.0              2\n",
              "1  Adversarial Dishonesty  Hyperspecific     3.0              1\n",
              "2  Adversarial Dishonesty  Hyperspecific     4.0              0\n",
              "3  Adversarial Dishonesty  Hyperspecific     1.0              1\n",
              "4  Adversarial Dishonesty  Hyperspecific     7.0              2"
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Category</th>\n",
              "      <th>Complexity</th>\n",
              "      <th>Rating</th>\n",
              "      <th>Binned_Rating</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Adversarial Dishonesty</td>\n",
              "      <td>Hyperspecific</td>\n",
              "      <td>6.0</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Adversarial Dishonesty</td>\n",
              "      <td>Hyperspecific</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Adversarial Dishonesty</td>\n",
              "      <td>Hyperspecific</td>\n",
              "      <td>4.0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Adversarial Dishonesty</td>\n",
              "      <td>Hyperspecific</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Adversarial Dishonesty</td>\n",
              "      <td>Hyperspecific</td>\n",
              "      <td>7.0</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "5f1a019255ec2220",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:05:01.161738Z",
          "start_time": "2025-02-21T17:05:01.125442Z"
        },
        "id": "5f1a019255ec2220",
        "outputId": "45a64adf-c228-4e47-b176-b4e8bd7d5e2d"
      },
      "source": [
        "model = ols('Rating ~ C(Category, Sum) * C(Complexity, Sum)', data=df_sorted).fit()\n",
        "aov = sm.stats.anova_lm(model, typ=2) # Show results in a dataframe\n",
        "print(aov)\n",
        "print(f'R-squared: {model.rsquared}')"
      ],
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "                                          sum_sq     df         F    PR(>F)\n",
            "C(Category, Sum)                      161.270746   12.0  4.128031  0.000002\n",
            "C(Complexity, Sum)                     10.825791    1.0  3.325280  0.068528\n",
            "C(Category, Sum):C(Complexity, Sum)    34.029462   12.0  0.871049  0.576531\n",
            "Residual                             3180.724004  977.0       NaN       NaN\n",
            "R-squared: 0.07074555652706516\n"
          ]
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "7fb490ee781b1fd8",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:05:08.308680Z",
          "start_time": "2025-02-21T17:05:08.302058Z"
        },
        "id": "7fb490ee781b1fd8",
        "outputId": "53ebfd00-737f-4989-9542-b827ae394ced"
      },
      "source": [
        "model.pvalues"
      ],
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Intercept                                                                          0.000000\n",
              "C(Category, Sum)[S.Adversarial Dishonesty]                                         0.778543\n",
              "C(Category, Sum)[S.Adversarial Harmfulness]                                        0.322695\n",
              "C(Category, Sum)[S.Brainstorming]                                                  0.851862\n",
              "C(Category, Sum)[S.Classification]                                                 0.128761\n",
              "C(Category, Sum)[S.Closed QA]                                                      0.408694\n",
              "C(Category, Sum)[S.Coding]                                                         0.058003\n",
              "C(Category, Sum)[S.Creative Writing]                                               0.006221\n",
              "C(Category, Sum)[S.Extraction]                                                     0.865931\n",
              "C(Category, Sum)[S.Mathematical Reasoning]                                         0.003021\n",
              "C(Category, Sum)[S.Open QA]                                                        0.025435\n",
              "C(Category, Sum)[S.Poetry]                                                         0.000450\n",
              "C(Category, Sum)[S.Rewriting]                                                      0.060895\n",
              "C(Complexity, Sum)[S.Hyperspecific]                                                0.072525\n",
              "C(Category, Sum)[S.Adversarial Dishonesty]:C(Complexity, Sum)[S.Hyperspecific]     0.172039\n",
              "C(Category, Sum)[S.Adversarial Harmfulness]:C(Complexity, Sum)[S.Hyperspecific]    0.097885\n",
              "C(Category, Sum)[S.Brainstorming]:C(Complexity, Sum)[S.Hyperspecific]              0.491515\n",
              "C(Category, Sum)[S.Classification]:C(Complexity, Sum)[S.Hyperspecific]             0.832669\n",
              "C(Category, Sum)[S.Closed QA]:C(Complexity, Sum)[S.Hyperspecific]                  0.366731\n",
              "C(Category, Sum)[S.Coding]:C(Complexity, Sum)[S.Hyperspecific]                     0.745325\n",
              "C(Category, Sum)[S.Creative Writing]:C(Complexity, Sum)[S.Hyperspecific]           0.960897\n",
              "C(Category, Sum)[S.Extraction]:C(Complexity, Sum)[S.Hyperspecific]                 0.769944\n",
              "C(Category, Sum)[S.Mathematical Reasoning]:C(Complexity, Sum)[S.Hyperspecific]     0.161114\n",
              "C(Category, Sum)[S.Open QA]:C(Complexity, Sum)[S.Hyperspecific]                    0.639112\n",
              "C(Category, Sum)[S.Poetry]:C(Complexity, Sum)[S.Hyperspecific]                     0.160503\n",
              "C(Category, Sum)[S.Rewriting]:C(Complexity, Sum)[S.Hyperspecific]                  0.341389\n",
              "dtype: float64"
            ]
          },
          "execution_count": 30,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "05c733a7-074c-4849-aca7-eb8968f98736",
      "metadata": {
        "id": "05c733a7-074c-4849-aca7-eb8968f98736"
      },
      "source": [
        "---\n",
        "\n",
        "Results Discussion:\n",
        "___\n",
        "\n",
        "\n",
        "- The results from the ANOVA showed that the only factor that impact the preference rating amongst Bard and ChatGPT is the **Category** with a pvalue of 0.000002.\n",
        "\n",
        "- There are four categories with pvalues < 0.05 that are significantly impacted the rating:\n",
        "  - Creative Writing\n",
        "  - Mathematical Reasoning\n",
        "  - Open QA\n",
        "  - Poetry\n",
        "- No interactions were found statistically significant in the rating preference.\n",
        "- However, the R-squared only justifies 7% of the data variance in the model. This was expected due to the imbalanced dataset.\n"
      ]
    },
    {
      "cell_type": "code",
      "id": "14d3d87ffa249eea",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:06:51.840856Z",
          "start_time": "2025-02-21T17:06:51.805779Z"
        },
        "id": "14d3d87ffa249eea",
        "outputId": "2399f39a-b892-49f0-82db-6efbd9f2141f"
      },
      "source": [
        "binned_model = ols('Binned_Rating ~ C(Category, Sum) * C(Complexity, Sum)', data=df_sorted).fit()\n",
        "binned_aov = sm.stats.anova_lm(binned_model, typ=2)\n",
        "print(binned_aov)\n",
        "print(f'R-squared: {binned_model.rsquared}')"
      ],
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "                                         sum_sq     df         F        PR(>F)\n",
            "C(Category, Sum)                      33.640404   12.0  5.200179  1.614284e-08\n",
            "C(Complexity, Sum)                     0.673669    1.0  1.249641  2.638959e-01\n",
            "C(Category, Sum):C(Complexity, Sum)    5.506006   12.0  0.851126  5.973343e-01\n",
            "Residual                             526.691390  977.0       NaN           NaN\n",
            "R-squared: 0.07888011718265953\n"
          ]
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "178a28a2d4ad328c",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:06:53.752423Z",
          "start_time": "2025-02-21T17:06:53.744558Z"
        },
        "id": "178a28a2d4ad328c",
        "outputId": "a76cb421-5f3f-4d95-ab29-8a1123e43084"
      },
      "source": [
        "binned_model.pvalues"
      ],
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Intercept                                                                          6.854945e-312\n",
              "C(Category, Sum)[S.Adversarial Dishonesty]                                          5.613244e-01\n",
              "C(Category, Sum)[S.Adversarial Harmfulness]                                         1.101024e-03\n",
              "C(Category, Sum)[S.Brainstorming]                                                   4.677179e-01\n",
              "C(Category, Sum)[S.Classification]                                                  8.225469e-02\n",
              "C(Category, Sum)[S.Closed QA]                                                       2.930181e-01\n",
              "C(Category, Sum)[S.Coding]                                                          3.388262e-02\n",
              "C(Category, Sum)[S.Creative Writing]                                                4.459575e-02\n",
              "C(Category, Sum)[S.Extraction]                                                      5.487209e-01\n",
              "C(Category, Sum)[S.Mathematical Reasoning]                                          5.718111e-02\n",
              "C(Category, Sum)[S.Open QA]                                                         2.230213e-02\n",
              "C(Category, Sum)[S.Poetry]                                                          1.083315e-05\n",
              "C(Category, Sum)[S.Rewriting]                                                       4.059918e-02\n",
              "C(Complexity, Sum)[S.Hyperspecific]                                                 2.816345e-01\n",
              "C(Category, Sum)[S.Adversarial Dishonesty]:C(Complexity, Sum)[S.Hyperspecific]      8.086383e-02\n",
              "C(Category, Sum)[S.Adversarial Harmfulness]:C(Complexity, Sum)[S.Hyperspecific]     3.451339e-01\n",
              "C(Category, Sum)[S.Brainstorming]:C(Complexity, Sum)[S.Hyperspecific]               8.574372e-01\n",
              "C(Category, Sum)[S.Classification]:C(Complexity, Sum)[S.Hyperspecific]              9.508135e-01\n",
              "C(Category, Sum)[S.Closed QA]:C(Complexity, Sum)[S.Hyperspecific]                   3.164338e-02\n",
              "C(Category, Sum)[S.Coding]:C(Complexity, Sum)[S.Hyperspecific]                      9.243834e-01\n",
              "C(Category, Sum)[S.Creative Writing]:C(Complexity, Sum)[S.Hyperspecific]            6.521928e-01\n",
              "C(Category, Sum)[S.Extraction]:C(Complexity, Sum)[S.Hyperspecific]                  2.984449e-01\n",
              "C(Category, Sum)[S.Mathematical Reasoning]:C(Complexity, Sum)[S.Hyperspecific]      6.517257e-01\n",
              "C(Category, Sum)[S.Open QA]:C(Complexity, Sum)[S.Hyperspecific]                     6.612281e-01\n",
              "C(Category, Sum)[S.Poetry]:C(Complexity, Sum)[S.Hyperspecific]                      4.144218e-01\n",
              "C(Category, Sum)[S.Rewriting]:C(Complexity, Sum)[S.Hyperspecific]                   8.674576e-01\n",
              "dtype: float64"
            ]
          },
          "execution_count": 32,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "d06750bc-375b-4c84-b80c-896499e77e9e",
      "metadata": {
        "id": "d06750bc-375b-4c84-b80c-896499e77e9e"
      },
      "source": [
        "---\n",
        "\n",
        "Results Discussion:\n",
        "___\n",
        "\n",
        "\n",
        "- The results from the ANOVA showed that the only factor that impact the preference rating amongst Bard and ChatGPT is the **Category** with a pvalue of 1.614284e-08.\n",
        "\n",
        "- There are six categories showed statistical difference with respect the other categories (pvalues < 0.05):\n",
        "\n",
        "  - Adversarial and Harmfulness\n",
        "  - Coding\n",
        "  - Creative Writing\n",
        "  - Open QA\n",
        "  - Poetry\n",
        "  - Rewriting\n",
        "    \n",
        "- The **interaction** of hyperspecific prompts in the Close QA category had statically significance on the models rating.\n",
        "- Creative Writing, Open QA and Poetry are categories found in data set with the Likert-like rating and the binned rating.\n",
        "- The R-squared only explains 8% of the data variance in the model. This was expected due to the imbalanced dataset."
      ]
    },
    {
      "cell_type": "code",
      "id": "a72bbdb24823ecd8",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:07:43.297536Z",
          "start_time": "2025-02-21T17:07:43.277919Z"
        },
        "id": "a72bbdb24823ecd8",
        "outputId": "ec6f6c89-d27e-41cd-b93a-f4dde766f381"
      },
      "source": [
        "def eta_squared(aov_table):\n",
        "    aov_table['eta_sq'] = 'NaN'\n",
        "    aov_table['eta_sq'] = aov_table[:-1]['sum_sq']/sum(aov_table['sum_sq'])\n",
        "    return aov\n",
        "def omega_squared(aov_table):\n",
        "    mse = aov_table['sum_sq'].iloc[-1]/aov_table['df'].iloc[-1]\n",
        "    aov_table['omega_sq'] = 'NaN'\n",
        "    aov_table['omega_sq'] = (aov_table[:-1]['sum_sq']-(aov_table[:-1]['df']*mse))/(sum(aov_table['sum_sq'])+mse)\n",
        "    return aov\n",
        "eta_squared(aov)\n",
        "omega_squared(aov)\n",
        "eta_squared(binned_aov)\n",
        "omega_squared(binned_aov)"
      ],
      "outputs": [
        {
          "data": {
            "text/plain": [
              "                                          sum_sq     df         F    PR(>F)  \\\n",
              "C(Category, Sum)                      161.270746   12.0  4.128031  0.000002   \n",
              "C(Complexity, Sum)                     10.825791    1.0  3.325280  0.068528   \n",
              "C(Category, Sum):C(Complexity, Sum)    34.029462   12.0  0.871049  0.576531   \n",
              "Residual                             3180.724004  977.0       NaN       NaN   \n",
              "\n",
              "                                       eta_sq  omega_sq  \n",
              "C(Category, Sum)                     0.047617  0.036047  \n",
              "C(Complexity, Sum)                   0.003196  0.002233  \n",
              "C(Category, Sum):C(Complexity, Sum)  0.010048 -0.001486  \n",
              "Residual                                  NaN       NaN  "
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sum_sq</th>\n",
              "      <th>df</th>\n",
              "      <th>F</th>\n",
              "      <th>PR(&gt;F)</th>\n",
              "      <th>eta_sq</th>\n",
              "      <th>omega_sq</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>C(Category, Sum)</th>\n",
              "      <td>161.270746</td>\n",
              "      <td>12.0</td>\n",
              "      <td>4.128031</td>\n",
              "      <td>0.000002</td>\n",
              "      <td>0.047617</td>\n",
              "      <td>0.036047</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C(Complexity, Sum)</th>\n",
              "      <td>10.825791</td>\n",
              "      <td>1.0</td>\n",
              "      <td>3.325280</td>\n",
              "      <td>0.068528</td>\n",
              "      <td>0.003196</td>\n",
              "      <td>0.002233</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C(Category, Sum):C(Complexity, Sum)</th>\n",
              "      <td>34.029462</td>\n",
              "      <td>12.0</td>\n",
              "      <td>0.871049</td>\n",
              "      <td>0.576531</td>\n",
              "      <td>0.010048</td>\n",
              "      <td>-0.001486</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Residual</th>\n",
              "      <td>3180.724004</td>\n",
              "      <td>977.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "4a7b0c653055eac2",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:07:46.525544Z",
          "start_time": "2025-02-21T17:07:46.521072Z"
        },
        "id": "4a7b0c653055eac2"
      },
      "source": [
        "concat_anova = pd.concat([aov, binned_aov], axis=0)"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "466c4fa170c1701d",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:07:48.055918Z",
          "start_time": "2025-02-21T17:07:48.050569Z"
        },
        "id": "466c4fa170c1701d"
      },
      "source": [
        "concat_anova['rating_scale'] =  ['likert', 'likert', 'likert', 'likert', 'binned_likert', 'binned_likert', 'binned_likert', 'binned_likert']"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "fd371324a11960d4",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:07:49.767107Z",
          "start_time": "2025-02-21T17:07:49.751383Z"
        },
        "id": "fd371324a11960d4",
        "outputId": "b0461aed-d6e3-4de0-8d0e-03cdc71d57b9"
      },
      "source": [
        "print(f'Anovas Results')\n",
        "concat_anova"
      ],
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Anovas Results\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "                                          sum_sq     df         F  \\\n",
              "C(Category, Sum)                      161.270746   12.0  4.128031   \n",
              "C(Complexity, Sum)                     10.825791    1.0  3.325280   \n",
              "C(Category, Sum):C(Complexity, Sum)    34.029462   12.0  0.871049   \n",
              "Residual                             3180.724004  977.0       NaN   \n",
              "C(Category, Sum)                       33.640404   12.0  5.200179   \n",
              "C(Complexity, Sum)                      0.673669    1.0  1.249641   \n",
              "C(Category, Sum):C(Complexity, Sum)     5.506006   12.0  0.851126   \n",
              "Residual                              526.691390  977.0       NaN   \n",
              "\n",
              "                                           PR(>F)    eta_sq  omega_sq  \\\n",
              "C(Category, Sum)                     2.489183e-06  0.047617  0.036047   \n",
              "C(Complexity, Sum)                   6.852782e-02  0.003196  0.002233   \n",
              "C(Category, Sum):C(Complexity, Sum)  5.765312e-01  0.010048 -0.001486   \n",
              "Residual                                      NaN       NaN       NaN   \n",
              "C(Category, Sum)                     1.614284e-08  0.059382  0.047917   \n",
              "C(Complexity, Sum)                   2.638959e-01  0.001189  0.000237   \n",
              "C(Category, Sum):C(Complexity, Sum)  5.973343e-01  0.009719 -0.001698   \n",
              "Residual                                      NaN       NaN       NaN   \n",
              "\n",
              "                                      rating_scale  \n",
              "C(Category, Sum)                            likert  \n",
              "C(Complexity, Sum)                          likert  \n",
              "C(Category, Sum):C(Complexity, Sum)         likert  \n",
              "Residual                                    likert  \n",
              "C(Category, Sum)                     binned_likert  \n",
              "C(Complexity, Sum)                   binned_likert  \n",
              "C(Category, Sum):C(Complexity, Sum)  binned_likert  \n",
              "Residual                             binned_likert  "
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sum_sq</th>\n",
              "      <th>df</th>\n",
              "      <th>F</th>\n",
              "      <th>PR(&gt;F)</th>\n",
              "      <th>eta_sq</th>\n",
              "      <th>omega_sq</th>\n",
              "      <th>rating_scale</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>C(Category, Sum)</th>\n",
              "      <td>161.270746</td>\n",
              "      <td>12.0</td>\n",
              "      <td>4.128031</td>\n",
              "      <td>2.489183e-06</td>\n",
              "      <td>0.047617</td>\n",
              "      <td>0.036047</td>\n",
              "      <td>likert</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C(Complexity, Sum)</th>\n",
              "      <td>10.825791</td>\n",
              "      <td>1.0</td>\n",
              "      <td>3.325280</td>\n",
              "      <td>6.852782e-02</td>\n",
              "      <td>0.003196</td>\n",
              "      <td>0.002233</td>\n",
              "      <td>likert</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C(Category, Sum):C(Complexity, Sum)</th>\n",
              "      <td>34.029462</td>\n",
              "      <td>12.0</td>\n",
              "      <td>0.871049</td>\n",
              "      <td>5.765312e-01</td>\n",
              "      <td>0.010048</td>\n",
              "      <td>-0.001486</td>\n",
              "      <td>likert</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Residual</th>\n",
              "      <td>3180.724004</td>\n",
              "      <td>977.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>likert</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C(Category, Sum)</th>\n",
              "      <td>33.640404</td>\n",
              "      <td>12.0</td>\n",
              "      <td>5.200179</td>\n",
              "      <td>1.614284e-08</td>\n",
              "      <td>0.059382</td>\n",
              "      <td>0.047917</td>\n",
              "      <td>binned_likert</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C(Complexity, Sum)</th>\n",
              "      <td>0.673669</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.249641</td>\n",
              "      <td>2.638959e-01</td>\n",
              "      <td>0.001189</td>\n",
              "      <td>0.000237</td>\n",
              "      <td>binned_likert</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>C(Category, Sum):C(Complexity, Sum)</th>\n",
              "      <td>5.506006</td>\n",
              "      <td>12.0</td>\n",
              "      <td>0.851126</td>\n",
              "      <td>5.973343e-01</td>\n",
              "      <td>0.009719</td>\n",
              "      <td>-0.001698</td>\n",
              "      <td>binned_likert</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Residual</th>\n",
              "      <td>526.691390</td>\n",
              "      <td>977.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>binned_likert</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "6bc775007caabb9b",
      "metadata": {
        "id": "6bc775007caabb9b"
      },
      "source": [
        "### 3.6 Kruskal-Wallis test"
      ]
    },
    {
      "cell_type": "code",
      "id": "34fadbacb5fc1c50",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:07:53.507198Z",
          "start_time": "2025-02-21T17:07:53.488650Z"
        },
        "id": "34fadbacb5fc1c50",
        "outputId": "ef623879-d81e-4bc2-a7ab-2581bcc62e5f"
      },
      "source": [
        "# 1. Create groups by combining categorical variables\n",
        "df['combined'] = df['Category'] + '-' + df['Complexity']\n",
        "\n",
        "# 2. Find the groups\n",
        "groups_dict = df.groupby(['Category', 'Complexity']).groups\n",
        "groups = [df['Rating'].iloc[idx].values for idx in groups_dict.values()]\n",
        "\n",
        "# 3. Kruskal-Wallis Test\n",
        "kruskal_result = stats.kruskal(*groups)\n",
        "\n",
        "stat, pvalue = kruskal_result.statistic,  kruskal_result.pvalue\n",
        "\n",
        "if pvalue < 0.05:\n",
        "    print(f\"Fail to accept null hypothesis | p-value: {pvalue:.5} | statistic: {stat:.4}\")\n",
        "\n",
        "else:\n",
        "    print(f\"Fail to reject the null hypothesis: |p-value: {pvalue:.5} | | statistic: {stat:.4}\")\n",
        "\n"
      ],
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Fail to accept null hypothesis | p-value: 6.9686e-07 | statistic: 74.92\n"
          ]
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "d7db40c3-867c-4d1e-8b43-68d1bd173247",
      "metadata": {
        "id": "d7db40c3-867c-4d1e-8b43-68d1bd173247"
      },
      "source": [
        "\n",
        "\n",
        "Results Discussion:\n",
        "\n",
        "- There are 26 groups from the combination of factors Category and Complexity:\n",
        "   - Category: 13 levels\n",
        "   - Complexity: 2 levels\n",
        "\n",
        "- The Kruskal-Wallis test rejected the hypothesis that all treatments' rating distributions are identical with a 5% uncertainty.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "442d6cd9fc7e0d0c",
      "metadata": {
        "id": "442d6cd9fc7e0d0c"
      },
      "source": [
        "## 4. Post-hoc"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "42cfae97dd2b121e",
      "metadata": {
        "id": "42cfae97dd2b121e"
      },
      "source": [
        "We will use the Dunn post-hoc test with Sidak p-value adjustment to fund which groups from the Kruskal-Wallis are significant different.\n",
        "$$p_{value} = 1 – (1-p)^m$$"
      ]
    },
    {
      "cell_type": "code",
      "id": "e92cc912abdeea7",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:07:57.454914Z",
          "start_time": "2025-02-21T17:07:57.353802Z"
        },
        "id": "e92cc912abdeea7"
      },
      "source": [
        "dunn = sp.posthoc_conover(df, val_col='Rating', group_col ='combined', sort=True, p_adjust='sidak')"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "7423f0e0d2958c55",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:07:59.224131Z",
          "start_time": "2025-02-21T17:07:59.220648Z"
        },
        "id": "7423f0e0d2958c55"
      },
      "source": [
        "indices = np.where(dunn.values < 0.05)"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "8c9dceb98864547e",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:08:01.101618Z",
          "start_time": "2025-02-21T17:08:01.094924Z"
        },
        "id": "8c9dceb98864547e"
      },
      "source": [
        "pairs = defaultdict(list)\n",
        "\n",
        "for i, j in zip(indices[0], indices[1]):\n",
        "    row = dunn.index[i]\n",
        "    col = dunn.columns[j]\n",
        "    p_val = dunn.iloc[i, j].round(4)\n",
        "    pair = (row, col)\n",
        "    if pair in pairs['pairs'] or (col, row) in pairs['pairs']:\n",
        "        continue\n",
        "    else:\n",
        "        pairs['pairs'].append(pair)\n",
        "        pairs['pval'].append(p_val)"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "892b101b18381b44",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:08:03.273071Z",
          "start_time": "2025-02-21T17:08:03.268660Z"
        },
        "id": "892b101b18381b44"
      },
      "source": [
        "dunn_significant_pairs = pd.DataFrame(pairs)\n",
        "dunn_significant_pairs.sort_values('pairs', ascending=True, inplace=True)"
      ],
      "outputs": [],
      "execution_count": null
    },
    {
      "cell_type": "code",
      "id": "ea61610f-45b7-49e6-9eb7-fb7ee91323c8",
      "metadata": {
        "ExecuteTime": {
          "end_time": "2025-02-21T17:08:04.922247Z",
          "start_time": "2025-02-21T17:08:04.918131Z"
        },
        "id": "ea61610f-45b7-49e6-9eb7-fb7ee91323c8",
        "outputId": "564c2bf9-ab44-4dd7-9779-d838aadd55b8"
      },
      "source": [
        "for pair in dunn_significant_pairs['pairs']:\n",
        "    print(f'Significant different pairs: {pair}')"
      ],
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Significant different pairs: ('Adversarial Harmfulness-Simple', 'Creative Writing-Hyperspecific')\n",
            "Significant different pairs: ('Adversarial Harmfulness-Simple', 'Poetry-Hyperspecific')\n",
            "Significant different pairs: ('Adversarial Harmfulness-Simple', 'Poetry-Simple')\n",
            "Significant different pairs: ('Creative Writing-Hyperspecific', 'Mathematical Reasoning-Simple')\n",
            "Significant different pairs: ('Creative Writing-Hyperspecific', 'Open QA-Simple')\n",
            "Significant different pairs: ('Mathematical Reasoning-Simple', 'Poetry-Hyperspecific')\n",
            "Significant different pairs: ('Mathematical Reasoning-Simple', 'Poetry-Simple')\n"
          ]
        }
      ],
      "execution_count": null
    },
    {
      "cell_type": "markdown",
      "id": "7827dbece4025152",
      "metadata": {
        "id": "7827dbece4025152"
      },
      "source": [
        "## Conclusion"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e29a7813-30d8-4128-bf2c-67418822bdf5",
      "metadata": {
        "id": "e29a7813-30d8-4128-bf2c-67418822bdf5"
      },
      "source": [
        "---\n",
        "\n",
        "- ChatGPT performs better at all the 13 categories and prompt complexity levels.\n",
        "- ChatGPT degrades its performance in simple tasks.\n",
        "- Bard improves its performance when dealing with simple prompts, especially in Mathematical Reasoning and OpenQA categories\n",
        "- Bards performs better in the Poetry category when the prompt is hyperspecific.\n",
        "- There were only 7 groups that showed significant differences in the ratings (refer to post-hoc test).\n",
        "- The categories with a significant difference are: Adversarial Harmfulness, Creative Writing, Maths and Reasoning, Open QA and Poetry.\n",
        "\n",
        "---\n",
        "**ANOVA**\n",
        "\n",
        "- The ANOVA with the Likert scale identified four categories as significant: Creative Writing, Maths and Reasoning, Open QA and Poetry.\n",
        "- The ANOVA with the binned scale identified six categories as significant: Adversarial and Harmfulness, Coding, Creative Writing, Open QA, Poetry, Rewriting.\n",
        "- Creative Writing, Open QA and Poetry are common significant categories identified by the two ANOVA models.\n",
        "- There was an **interaction** effect for the prompts' complexity and the Close QA category.\n"
      ]
    }
  ],
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