Assignment9_CS_202151160.ipynb

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      "source": [
        "#Data Analytics and Visualization (CS/IT312)\n",
        "#Assignment 10\n",
        "#Name: Snehal Nalawade\n",
        "#ID: 202151160"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
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        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RGMCeJVZZqgz",
        "outputId": "5b670749-c124-4484-80c3-73609225126e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import random\n",
        "import seaborn as sns\n",
        "import numpy as np"
      ],
      "metadata": {
        "id": "EDj2glGjZrGl"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.read_csv('/content/drive/MyDrive/DAV sem 6/cookie_cats.csv')\n",
        "df.head()"
      ],
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          "height": 206
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      "execution_count": null,
      "outputs": [
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              "   userid  version  sum_gamerounds  retention_1  retention_7\n",
              "0     116  gate_30               3        False        False\n",
              "1     337  gate_30              38         True        False\n",
              "2     377  gate_40             165         True        False\n",
              "3     483  gate_40               1        False        False\n",
              "4     488  gate_40             179         True         True"
            ],
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            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df",
              "summary": "{\n  \"name\": \"df\",\n  \"rows\": 90189,\n  \"fields\": [\n    {\n      \"column\": \"userid\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 2883285,\n        \"min\": 116,\n        \"max\": 9999861,\n        \"num_unique_values\": 90189,\n        \"samples\": [\n          3266525,\n          3937667,\n          2861986\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"version\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          \"gate_40\",\n          \"gate_30\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"sum_gamerounds\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 195,\n        \"min\": 0,\n        \"max\": 49854,\n        \"num_unique_values\": 942,\n        \"samples\": [\n          346,\n          523\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"retention_1\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"retention_7\",\n      \"properties\": {\n        \"dtype\": \"boolean\",\n        \"num_unique_values\": 2,\n        \"samples\": [\n          true,\n          false\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
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          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "1. Check which version of the game is better by computing average ”sum gamerounds”."
      ],
      "metadata": {
        "id": "TIP8uZFuaXbr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "version1, version2 = df.groupby('version')['sum_gamerounds'].mean()\n",
        "if version1 > version2:\n",
        "    print('Version 1 has the highest average sum_gamerounds')\n",
        "else:\n",
        "    print('Version 2 has the highest average sum_gamerounds')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f_ckRVUkaQMz",
        "outputId": "183a32e6-81ea-4491-dacf-4e2fc5030e85"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Version 1 has the highest average sum_gamerounds\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        " 2. To check that the difference in average of ”sum gamerounds” is by chance or it is a real difference, perform the permutation Resampling on the data and derive the probability. Make the decision based on derived probability.permutation resampling"
      ],
      "metadata": {
        "id": "rUL8exXGajFb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def permutation_resampling(x, nA, nB):\n",
        "    n = nA + nB\n",
        "    indeX_B = set(random.sample(range(n), nB))\n",
        "    indeX_A = set(range(n)) - indeX_B\n",
        "    return x.loc[list(indeX_B)].mean() - x.loc[list(indeX_A)].mean()\n",
        "\n",
        "nA = df[df['version'] == 'gate_30']['sum_gamerounds'].count()\n",
        "nB = df[df['version'] == 'gate_40']['sum_gamerounds'].count()\n",
        "# permutation resampling 10000 times\n",
        "diff = [permutation_resampling(df['sum_gamerounds'], nA, nB) for i in range(1000)]\n",
        "# plot the histogram\n",
        "plt.hist(diff, bins=11, rwidth=0.9)\n",
        "plt.axvline(x=version1-version2, color='red', linestyle='--')\n",
        "plt.xlabel('Difference in average sum_gamerounds')\n",
        "plt.ylabel('Frequency')\n",
        "plt.show()\n",
        "obs_diff = df[df['version'] == 'gate_30']['sum_gamerounds'].mean() - df[df['version'] == 'gate_40']['sum_gamerounds'].mean()\n",
        "p_value = sum([1 for d in diff if abs(d) >= abs(obs_diff)]) / len(diff)\n",
        "print(\"The observed difference is:\", obs_diff)\n",
        "print(\"The p-value is:\", p_value)"
      ],
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              "<Figure size 640x480 with 1 Axes>"
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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The observed difference is: 1.157488453953249\n",
            "The p-value is: 0.472\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We are unable to reject the null hypothesis, which states that there is no difference in the mean number of game rounds between the two groups, because the p-value is higher than the traditional significance level of 0.05. Put otherwise, the observed variation is not statistically significant, and there isn't much evidence to support the idea that the version change from gate_30 to gate_40 affected how many game rounds people played.\n",
        "\n",
        "It's crucial to remember that this conclusion is dependent on the particular test that was conducted, and that other aspects or considerations would need to be taken into account when interpreting the findings."
      ],
      "metadata": {
        "id": "96rH3aX4bKdi"
      }
    }
  ]
}