CTolbert_DS_Unit_1_Sprint_Challenge_4.ipynb

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      "name": "CTolbert DS Unit 1 Sprint Challenge 4.ipynb",
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      "cell_type": "markdown",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/hughjafro/DS-Unit-1-Sprint-4-Statistical-Tests-and-Experiments/blob/master/CTolbert_DS_Unit_1_Sprint_Challenge_4.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "metadata": {
        "id": "NooAiTdnafkz",
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      "cell_type": "markdown",
      "source": [
        "# Data Science Unit 1 Sprint Challenge 4\n",
        "\n",
        "## Exploring Data, Testing Hypotheses\n",
        "\n",
        "In this sprint challenge you will look at a dataset of people being approved or rejected for credit.\n",
        "\n",
        "https://archive.ics.uci.edu/ml/datasets/Credit+Approval\n",
        "\n",
        "Data Set Information: This file concerns credit card applications. All attribute names and values have been changed to meaningless symbols to protect confidentiality of the data. This dataset is interesting because there is a good mix of attributes -- continuous, nominal with small numbers of values, and nominal with larger numbers of values. There are also a few missing values.\n",
        "\n",
        "Attribute Information:\n",
        "- A1: b, a.\n",
        "- A2: continuous.\n",
        "- A3: continuous.\n",
        "- A4: u, y, l, t.\n",
        "- A5: g, p, gg.\n",
        "- A6: c, d, cc, i, j, k, m, r, q, w, x, e, aa, ff.\n",
        "- A7: v, h, bb, j, n, z, dd, ff, o.\n",
        "- A8: continuous.\n",
        "- A9: t, f.\n",
        "- A10: t, f.\n",
        "- A11: continuous.\n",
        "- A12: t, f.\n",
        "- A13: g, p, s.\n",
        "- A14: continuous.\n",
        "- A15: continuous.\n",
        "- A16: +,- (class attribute)\n",
        "\n",
        "Yes, most of that doesn't mean anything. A16 (the class attribute) is the most interesting, as it separates the 307 approved cases from the 383 rejected cases. The remaining variables have been obfuscated for privacy - a challenge you may have to deal with in your data science career.\n",
        "\n",
        "Sprint challenges are evaluated based on satisfactory completion of each part. It is suggested you work through it in order, getting each aspect reasonably working, before trying to deeply explore, iterate, or refine any given step. Once you get to the end, if you want to go back and improve things, go for it!"
      ]
    },
    {
      "metadata": {
        "id": "5wch6ksCbJtZ",
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      "source": [
        "## Part 1 - Load and validate the data\n",
        "\n",
        "- Load the data as a `pandas` data frame.\n",
        "- Validate that it has the appropriate number of observations (you can check the raw file, and also read the dataset description from UCI).\n",
        "- UCI says there should be missing data - check, and if necessary change the data so pandas recognizes it as na\n",
        "- Make sure that the loaded features are of the types described above (continuous values should be treated as float), and correct as necessary\n",
        "\n",
        "This is review, but skills that you'll use at the start of any data exploration. Further, you may have to do some investigation to figure out which file to load from - that is part of the puzzle."
      ]
    },
    {
      "metadata": {
        "id": "Q79xDLckzibS",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy import stats"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "CsqY6Gcxgn9D",
        "colab_type": "code",
        "outputId": "f73e35f7-6cca-4199-dfd8-19c066c23fd5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 221
        }
      },
      "cell_type": "code",
      "source": [
        "# Set new column names\n",
        "col_names = ['A1', 'A2', 'A3', 'A4', 'A5', 'A6', 'A7', 'A8', 'A9', 'A10', 'A11', 'A12', 'A13', 'A14', 'A15', 'A16']\n",
        "#import dataset\n",
        "df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/credit-screening/crx.data', header=None)\n",
        "# change names of columns\n",
        "df.columns = col_names\n",
        "\n",
        "# replace ? with NaN, - to 0 and + to 1\n",
        "df = df.replace({'?': np.nan, '-': 0, '+': 1})\n",
        "\n",
        "print(df.shape) # Should be 690 rows and 16 columns\n",
        "df.head()"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(690, 16)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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              "      <th>A16</th>\n",
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              "      <th>0</th>\n",
              "      <td>b</td>\n",
              "      <td>30.83</td>\n",
              "      <td>0.000</td>\n",
              "      <td>u</td>\n",
              "      <td>g</td>\n",
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              "      <th>1</th>\n",
              "      <td>a</td>\n",
              "      <td>58.67</td>\n",
              "      <td>4.460</td>\n",
              "      <td>u</td>\n",
              "      <td>g</td>\n",
              "      <td>q</td>\n",
              "      <td>h</td>\n",
              "      <td>3.04</td>\n",
              "      <td>t</td>\n",
              "      <td>t</td>\n",
              "      <td>6</td>\n",
              "      <td>f</td>\n",
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              "      <td>00043</td>\n",
              "      <td>560</td>\n",
              "      <td>1</td>\n",
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              "      <th>2</th>\n",
              "      <td>a</td>\n",
              "      <td>24.50</td>\n",
              "      <td>0.500</td>\n",
              "      <td>u</td>\n",
              "      <td>g</td>\n",
              "      <td>q</td>\n",
              "      <td>h</td>\n",
              "      <td>1.50</td>\n",
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              "      <td>0</td>\n",
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              "      <td>00280</td>\n",
              "      <td>824</td>\n",
              "      <td>1</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>b</td>\n",
              "      <td>27.83</td>\n",
              "      <td>1.540</td>\n",
              "      <td>u</td>\n",
              "      <td>g</td>\n",
              "      <td>w</td>\n",
              "      <td>v</td>\n",
              "      <td>3.75</td>\n",
              "      <td>t</td>\n",
              "      <td>t</td>\n",
              "      <td>5</td>\n",
              "      <td>t</td>\n",
              "      <td>g</td>\n",
              "      <td>00100</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>b</td>\n",
              "      <td>20.17</td>\n",
              "      <td>5.625</td>\n",
              "      <td>u</td>\n",
              "      <td>g</td>\n",
              "      <td>w</td>\n",
              "      <td>v</td>\n",
              "      <td>1.71</td>\n",
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              "  A1     A2     A3 A4 A5 A6 A7    A8 A9 A10  A11 A12 A13    A14  A15  A16\n",
              "0  b  30.83  0.000  u  g  w  v  1.25  t   t    1   f   g  00202    0    1\n",
              "1  a  58.67  4.460  u  g  q  h  3.04  t   t    6   f   g  00043  560    1\n",
              "2  a  24.50  0.500  u  g  q  h  1.50  t   f    0   f   g  00280  824    1\n",
              "3  b  27.83  1.540  u  g  w  v  3.75  t   t    5   t   g  00100    3    1\n",
              "4  b  20.17  5.625  u  g  w  v  1.71  t   f    0   f   s  00120    0    1"
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          "execution_count": 56
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 323
        }
      },
      "cell_type": "code",
      "source": [
        "# Check NaN\n",
        "print('Number of total NAN: ', df.isna().sum().sum())\n",
        "df.isna().sum()"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of total NAN:  67\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "A1     12\n",
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              "A5      6\n",
              "A6      9\n",
              "A7      9\n",
              "A8      0\n",
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              "A10     0\n",
              "A11     0\n",
              "A12     0\n",
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              "A15     0\n",
              "A16     0\n",
              "dtype: int64"
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          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "metadata": {
        "id": "MAuaT4QzncmW",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Change columns to proper data types\n",
        "df[['A2', 'A3', 'A8', 'A11', 'A14', 'A15']] = df[['A2', 'A3', 'A8', 'A11', 'A14', 'A15']].apply(pd.to_numeric)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "cC9R-Yb3ltd2",
        "colab_type": "code",
        "outputId": "a6e4ab0a-b7f4-490f-a0b4-f16ac9fb9104",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        }
      },
      "cell_type": "code",
      "source": [
        "df.describe()"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>A2</th>\n",
              "      <th>A3</th>\n",
              "      <th>A8</th>\n",
              "      <th>A11</th>\n",
              "      <th>A14</th>\n",
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              "      <th>A16</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>678.000000</td>\n",
              "      <td>690.000000</td>\n",
              "      <td>690.000000</td>\n",
              "      <td>690.00000</td>\n",
              "      <td>677.000000</td>\n",
              "      <td>690.000000</td>\n",
              "      <td>690.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>31.568171</td>\n",
              "      <td>4.758725</td>\n",
              "      <td>2.223406</td>\n",
              "      <td>2.40000</td>\n",
              "      <td>184.014771</td>\n",
              "      <td>1017.385507</td>\n",
              "      <td>0.444928</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>11.957862</td>\n",
              "      <td>4.978163</td>\n",
              "      <td>3.346513</td>\n",
              "      <td>4.86294</td>\n",
              "      <td>173.806768</td>\n",
              "      <td>5210.102598</td>\n",
              "      <td>0.497318</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>13.750000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>22.602500</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.165000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>75.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>28.460000</td>\n",
              "      <td>2.750000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.00000</td>\n",
              "      <td>160.000000</td>\n",
              "      <td>5.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>38.230000</td>\n",
              "      <td>7.207500</td>\n",
              "      <td>2.625000</td>\n",
              "      <td>3.00000</td>\n",
              "      <td>276.000000</td>\n",
              "      <td>395.500000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>80.250000</td>\n",
              "      <td>28.000000</td>\n",
              "      <td>28.500000</td>\n",
              "      <td>67.00000</td>\n",
              "      <td>2000.000000</td>\n",
              "      <td>100000.000000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ],
            "text/plain": [
              "               A2          A3          A8        A11          A14  \\\n",
              "count  678.000000  690.000000  690.000000  690.00000   677.000000   \n",
              "mean    31.568171    4.758725    2.223406    2.40000   184.014771   \n",
              "std     11.957862    4.978163    3.346513    4.86294   173.806768   \n",
              "min     13.750000    0.000000    0.000000    0.00000     0.000000   \n",
              "25%     22.602500    1.000000    0.165000    0.00000    75.000000   \n",
              "50%     28.460000    2.750000    1.000000    0.00000   160.000000   \n",
              "75%     38.230000    7.207500    2.625000    3.00000   276.000000   \n",
              "max     80.250000   28.000000   28.500000   67.00000  2000.000000   \n",
              "\n",
              "                 A15         A16  \n",
              "count     690.000000  690.000000  \n",
              "mean     1017.385507    0.444928  \n",
              "std      5210.102598    0.497318  \n",
              "min         0.000000    0.000000  \n",
              "25%         0.000000    0.000000  \n",
              "50%         5.000000    0.000000  \n",
              "75%       395.500000    1.000000  \n",
              "max    100000.000000    1.000000  "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "metadata": {
        "id": "C0xktiN9wuCU",
        "colab_type": "code",
        "outputId": "fa935785-7fe5-4104-acbf-8b6ad4110b26",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        }
      },
      "cell_type": "code",
      "source": [
        "df.info()"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 690 entries, 0 to 689\n",
            "Data columns (total 16 columns):\n",
            "A1     678 non-null object\n",
            "A2     678 non-null float64\n",
            "A3     690 non-null float64\n",
            "A4     684 non-null object\n",
            "A5     684 non-null object\n",
            "A6     681 non-null object\n",
            "A7     681 non-null object\n",
            "A8     690 non-null float64\n",
            "A9     690 non-null object\n",
            "A10    690 non-null object\n",
            "A11    690 non-null int64\n",
            "A12    690 non-null object\n",
            "A13    690 non-null object\n",
            "A14    677 non-null float64\n",
            "A15    690 non-null int64\n",
            "A16    690 non-null int64\n",
            "dtypes: float64(4), int64(3), object(9)\n",
            "memory usage: 86.3+ KB\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "6VyFwL8PHvc0",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "df[\"A11\"] = df.A11.astype(float)\n",
        "df[\"A15\"] = df.A11.astype(float)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "rV_FsuYxy0q9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "outputId": "6e5b12b9-8650-48d5-e46a-667f5946ab00"
      },
      "cell_type": "code",
      "source": [
        "df.dtypes"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "A1      object\n",
              "A2     float64\n",
              "A3     float64\n",
              "A4      object\n",
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              "A7      object\n",
              "A8     float64\n",
              "A9      object\n",
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              "A11    float64\n",
              "A12     object\n",
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              "A14    float64\n",
              "A15    float64\n",
              "A16      int64\n",
              "dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 62
        }
      ]
    },
    {
      "metadata": {
        "id": "G7rLytbrO38L",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Part 2 - Exploring data, Testing hypotheses\n",
        "\n",
        "The only thing we really know about this data is that A16 is the class label. Besides that, we have 6 continuous (float) features and 9 categorical features.\n",
        "\n",
        "***Explore the data***: you can use whatever approach (tables, utility functions, visualizations) to get an impression of the distributions and relationships of the variables. In general, your goal is to understand how the features are different when grouped by the two class labels (`+` and `-`).\n",
        "\n",
        "For the **6 continuous features**, how are they different when split between the two class labels? **Choose two features to run t-tests** (again split by class label) - specifically, select one feature that is *extremely* different between the classes, and another feature that is notably less different (though perhaps still \"statistically significantly\" different). You may have to explore more than two features to do this.\n",
        "\n",
        "For the ***categorical features***, explore by ***creating \"cross tabs\"*** between them and the class label, and apply the ***Chi-squared test *** to them. There are 9 categorical features - as with the t-test, try to ***find one where the Chi-squared test returns an extreme result*** (rejecting the null that the data are independent), and one where it is less extreme.\n",
        "\n",
        "**NOTE** - \"less extreme\" just means smaller test statistic/larger p-value. Even the least extreme differences may be strongly statistically significant.\n",
        "\n",
        "Your *main* goal is the ***hypothesis tests***, so don't spend too much time on the exploration/visualization piece. That is just a means to an end. This is challenging, so manage your time and aim for a baseline of at least running two t-tests and two Chi-squared tests before polishing. And don't forget to answer the questions in part 3, even if your results in this part aren't what you want them to be."
      ]
    },
    {
      "metadata": {
        "id": "UqzepfEVGFLN",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#Seperate into approved and denied from A16\n",
        "df_approved = df[df.A16 == 1]\n",
        "df_denied = df[df.A16 == 0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "3tdZCAZTHADD",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#df_approved.sum().sum() / (df_approved.sum().sum() + df_denied.sum().sum())"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "26qbz9gsGY_c",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        },
        "outputId": "ae55cec0-4868-4540-897e-a15477daf38f"
      },
      "cell_type": "code",
      "source": [
        "df_denied.sum() / (df_approved.sum() + df_denied.sum())"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "A2     0.519477\n",
              "A3     0.447903\n",
              "A8     0.314040\n",
              "A11    0.146135\n",
              "A14    0.602731\n",
              "A15    0.146135\n",
              "A16    0.000000\n",
              "dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        }
      ]
    },
    {
      "metadata": {
        "id": "_nqcgc0yzm68",
        "colab_type": "code",
        "outputId": "8b32f49a-d407-4a2c-cf96-29fca7b16252",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "# check prob of acceptance - Only a 44% approval rate\n",
        "df.A16.sum() / len(df.A16)"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4449275362318841"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        }
      ]
    },
    {
      "metadata": {
        "id": "079m3ZiUyOTO",
        "colab_type": "code",
        "outputId": "f71b71b0-803f-416f-a949-13d7de04ee4b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "cell_type": "code",
      "source": [
        "# Look at value counts of each unique value in A16 to match data description\n",
        "df.A16.value_counts()"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    383\n",
              "1    307\n",
              "Name: A16, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        }
      ]
    },
    {
      "metadata": {
        "id": "bNSEcEtXzLdl",
        "colab_type": "code",
        "outputId": "1463af26-3497-4fe4-de6e-70122eeb2ebd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 345
        }
      },
      "cell_type": "code",
      "source": [
        "df.A16.value_counts().plot.bar();"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gyAAAGIAgAwBggCUF+fLly6qpqVFvb68kqb29XT/60Y+0c+dO7dy5U5cuXZIk9ff3a9u2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\nAAxAkAEAMABBBgDAAP8DQypdv956A6IAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f7b6e9b57b8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "AzxIEWgA7dBK",
        "colab_type": "code",
        "outputId": "8c48b918-8383-4836-cb16-0e6554b44e51",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1011
        }
      },
      "cell_type": "code",
      "source": [
        "# Group by the accept/reject column 16 and plot\n",
        "accept = df.groupby(df.A16)\n",
        "accept.plot.hist();"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AAAsjyAEAsDCCHAAACyPIAQCwMIIcAAALI8gBALAwghwAAAsjyAEAsDCCHAAA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\nuQ6bnj72QZAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f7b6e9b5198>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AAAsjyAEAsDCCHAAACyPIAQCwMIIcAAALI8gBALAwghwAAAsjyAEAsDCCHAAA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\nuQ6bnj72QZAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f7b6e8c4128>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f7b6e82bb00>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "ZqMLKNaD4FXi",
        "colab_type": "code",
        "outputId": "9a69c3f3-5188-47be-955f-b9686967008f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "cell_type": "code",
      "source": [
        "# Equal chance to be accepted or rejected\n",
        "# Years employed approved\n",
        "stats.ttest_1samp(df_approved.A8, 0.5)"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_1sampResult(statistic=12.449289487126055, pvalue=4.6132667541039515e-29)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 97
        }
      ]
    },
    {
      "metadata": {
        "id": "OuEPQTiUJIQB",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "e2e810d8-497f-4185-804a-d369e71e95af"
      },
      "cell_type": "code",
      "source": [
        "# Years employed denied\n",
        "stats.ttest_1samp(df_denied.A8, 0.5)"
      ],
      "execution_count": 99,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_1sampResult(statistic=6.995051170689755, pvalue=1.1936831195754194e-11)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 99
        }
      ]
    },
    {
      "metadata": {
        "id": "TjIkLsHvJlAn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "7637a488-616b-4a47-b365-2e6a13a24bbc"
      },
      "cell_type": "code",
      "source": [
        "# Credit score approved\n",
        "stats.ttest_1samp(df_approved.A11, 0.5)"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_1sampResult(statistic=11.382560629001722, pvalue=2.8798299332810433e-25)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 102
        }
      ]
    },
    {
      "metadata": {
        "id": "htZ7IzvoJk7z",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "a11594e5-d945-498e-c01b-416233bfa348"
      },
      "cell_type": "code",
      "source": [
        "# Credit score denied\n",
        "stats.ttest_1samp(df_denied.A11, 0.5)"
      ],
      "execution_count": 114,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_1sampResult(statistic=1.3580856177707235, pvalue=0.17523808826084886)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 114
        }
      ]
    },
    {
      "metadata": {
        "id": "Rlod9nl48qFn",
        "colab_type": "code",
        "outputId": "0e880171-1726-42d6-f98b-a7b00b1d9c14",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "cell_type": "code",
      "source": [
        "# quick look at all means for numbers\n",
        "print(df.A2.mean()) # age\n",
        "print(df.A3.mean()) # debt\n",
        "print(df.A8.mean()) # Yrs employed\n",
        "print(df.A11.mean()) # credit score\n",
        "print(df.A14.mean()) # zip code\n",
        "print(df.A15.mean()) # income"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "31.56817109144543\n",
            "4.758724637681159\n",
            "2.223405797101449\n",
            "2.4\n",
            "184.01477104874445\n",
            "2.4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "46z6VE9X8C82",
        "colab_type": "code",
        "outputId": "3e10e0ad-f89b-4de1-f622-2a3f857ca861",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "cell_type": "code",
      "source": [
        "# Accept and years employed\n",
        "stats.ttest_ind(df.A16, df.A8) "
      ],
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_indResult(statistic=-13.808203659393687, pvalue=1.022666202998416e-40)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 104
        }
      ]
    },
    {
      "metadata": {
        "id": "kg-JndHl-sS-",
        "colab_type": "code",
        "outputId": "7b7f8649-870a-4449-ba5c-4199d0af8543",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "cell_type": "code",
      "source": [
        "# Accept and credit score\n",
        "stats.ttest_ind(df.A16, df.A11)\n"
      ],
      "execution_count": 117,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_indResult(statistic=-10.50580271265132, pvalue=6.883898239954908e-25)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 117
        }
      ]
    },
    {
      "metadata": {
        "id": "c89OXJ0n_5_5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 582
        },
        "outputId": "0232417c-221f-4654-a024-b1284a949346"
      },
      "cell_type": "code",
      "source": [
        "# Crosstab A16 and A6\n",
        "approval_debt = pd.crosstab(df.A6, df.A16)\n",
        "print(approval_debt.sum())\n",
        "approval_debt"
      ],
      "execution_count": 118,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A16\n",
            "0    378\n",
            "1    303\n",
            "dtype: int64\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>A16</th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A6</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>aa</th>\n",
              "      <td>35</td>\n",
              "      <td>19</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>c</th>\n",
              "      <td>75</td>\n",
              "      <td>62</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>cc</th>\n",
              "      <td>12</td>\n",
              "      <td>29</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>d</th>\n",
              "      <td>23</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>e</th>\n",
              "      <td>11</td>\n",
              "      <td>14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>ff</th>\n",
              "      <td>46</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>i</th>\n",
              "      <td>45</td>\n",
              "      <td>14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>j</th>\n",
              "      <td>7</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>k</th>\n",
              "      <td>37</td>\n",
              "      <td>14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>m</th>\n",
              "      <td>22</td>\n",
              "      <td>16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>q</th>\n",
              "      <td>27</td>\n",
              "      <td>51</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>r</th>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>w</th>\n",
              "      <td>31</td>\n",
              "      <td>33</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>x</th>\n",
              "      <td>6</td>\n",
              "      <td>32</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "A16   0   1\n",
              "A6         \n",
              "aa   35  19\n",
              "c    75  62\n",
              "cc   12  29\n",
              "d    23   7\n",
              "e    11  14\n",
              "ff   46   7\n",
              "i    45  14\n",
              "j     7   3\n",
              "k    37  14\n",
              "m    22  16\n",
              "q    27  51\n",
              "r     1   2\n",
              "w    31  33\n",
              "x     6  32"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 118
        }
      ]
    },
    {
      "metadata": {
        "id": "Gfe9i2k6D8tZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 142
        },
        "outputId": "9060cfea-fed2-4f1b-d8dc-0ea91fedc78a"
      },
      "cell_type": "code",
      "source": [
        "# Crosstab A16 and A9\n",
        "approval_debt2 = pd.crosstab(df.A9, df.A16)\n",
        "approval_debt2"
      ],
      "execution_count": 119,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "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>A16</th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>A9</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>f</th>\n",
              "      <td>306</td>\n",
              "      <td>23</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>t</th>\n",
              "      <td>77</td>\n",
              "      <td>284</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "A16    0    1\n",
              "A9           \n",
              "f    306   23\n",
              "t     77  284"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 119
        }
      ]
    },
    {
      "metadata": {
        "id": "1sGtOOTeO1zf",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "##Chi Square"
      ]
    },
    {
      "metadata": {
        "id": "ZOh6ATwkC3-X",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "outputId": "de21897e-7e65-4abe-b93a-591196f6b63b"
      },
      "cell_type": "code",
      "source": [
        "# Chi square with A6/A16\n",
        "stats.chi2_contingency(approval_debt)"
      ],
      "execution_count": 120,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(98.32520342679135,\n",
              " 3.4999300402715717e-15,\n",
              " 13,\n",
              " array([[29.97356828, 24.02643172],\n",
              "        [76.04405286, 60.95594714],\n",
              "        [22.75770925, 18.24229075],\n",
              "        [16.65198238, 13.34801762],\n",
              "        [13.87665198, 11.12334802],\n",
              "        [29.4185022 , 23.5814978 ],\n",
              "        [32.74889868, 26.25110132],\n",
              "        [ 5.55066079,  4.44933921],\n",
              "        [28.30837004, 22.69162996],\n",
              "        [21.09251101, 16.90748899],\n",
              "        [43.29515419, 34.70484581],\n",
              "        [ 1.66519824,  1.33480176],\n",
              "        [35.52422907, 28.47577093],\n",
              "        [21.09251101, 16.90748899]]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 120
        }
      ]
    },
    {
      "metadata": {
        "id": "Xl-yyz0_EsB-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "c2921ca0-fda6-47de-adc9-ddd83cf9497c"
      },
      "cell_type": "code",
      "source": [
        "# Chi square with A9/A16\n",
        "stats.chi2_contingency(approval_debt2)"
      ],
      "execution_count": 116,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(355.2038167412799,\n",
              " 3.1185900878457007e-79,\n",
              " 1,\n",
              " array([[182.61884058, 146.38115942],\n",
              "        [200.38115942, 160.61884058]]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 116
        }
      ]
    },
    {
      "metadata": {
        "id": "m9W33crSTMSq",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#help(stats.chi2_contingency)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "sSSf1X87BJ4d",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# USe Chi Square to analyze\n",
        "# stats.chisquare(approval_debt)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "BLTanTGpOMgt",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# stats.chisquare(approval_debt2)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "GYcQ6kDZCzPf",
        "colab_type": "code",
        "outputId": "9b74c857-82b5-43c2-c30b-0256f10d623b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        }
      },
      "cell_type": "code",
      "source": [
        "approval_debt.plot.hist();"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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XezlV23z22Wf69NNPNWrUKG9HuSGFhYWKiYlRp06d5HA4tGzZMm9HarOIiAhV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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f7b6fc6a630>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "SP4qgTo3E6EV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        },
        "outputId": "b0b5093e-bc7c-463b-9017-b9385802f1f5"
      },
      "cell_type": "code",
      "source": [
        "approval_debt2.plot.hist();"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PhzeQJScnq7Gx0TddXl6ujIwMbkcDAOA7Cup93l3h3Oeif/755yovL9fatWt17NixoL6f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\nGIbwBgDAMP8f0seRcwJPaGsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f7b72b3f390>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "r9X9-WG1CV5q",
        "colab_type": "code",
        "outputId": "761f6adf-e137-45f5-eddf-f97152058173",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 221
        }
      },
      "cell_type": "code",
      "source": [
        "# I think A7 is ethnicity, compare A7 and A16\n",
        "approval_eth = pd.crosstab(df.A7, df.A16)\n",
        "stats.chi2_contingency(approval_eth)"
      ],
      "execution_count": 83,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(45.03420714024056,\n",
              " 3.62545287237226e-07,\n",
              " 8,\n",
              " array([[ 32.74889868,  26.25110132],\n",
              "        [  3.33039648,   2.66960352],\n",
              "        [ 31.63876652,  25.36123348],\n",
              "        [ 76.59911894,  61.40088106],\n",
              "        [  4.44052863,   3.55947137],\n",
              "        [  2.22026432,   1.77973568],\n",
              "        [  1.11013216,   0.88986784],\n",
              "        [221.47136564, 177.52863436],\n",
              "        [  4.44052863,   3.55947137]]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 83
        }
      ]
    },
    {
      "metadata": {
        "id": "zLD0J7C3C7xl",
        "colab_type": "code",
        "outputId": "37e22a8b-13f6-4d61-8ab6-b4bb302f767f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 347
        }
      },
      "cell_type": "code",
      "source": [
        "approval_eth.plot.hist();"
      ],
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f7b7028b828>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "sDPSb9kN4t6T",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#df_age = pd.crosstab(df.A16, df.A2)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "EjEdXb305I-o",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#df_debt = pd.crosstab(df.A16, df.A3)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ZM8JckA2bgnp",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Part 3 - Analysis and Interpretation\n",
        "\n",
        "Now that you've looked at the data, answer the following questions:\n",
        "\n",
        "- Interpret and explain the two t-tests you ran - what do they tell you about the relationships between the continuous features you selected and the class labels?\n",
        "- Interpret and explain the two Chi-squared tests you ran - what do they tell you about the relationships between the categorical features you selected and the class labels?\n",
        "- What was the most challenging part of this sprint challenge?\n",
        "\n",
        "Answer with text, but feel free to intersperse example code/results or refer to it from earlier."
      ]
    },
    {
      "metadata": {
        "id": "LIozLDNG2Uhu",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "I ran two t-tests using the continuous features of A8 and A11 (probably years employed and credit score, respectively). The tests for A8 (approval and denial) and A11 approval have p-values that suggests to reject the null hypothesis. The test for A11 denial has a high p-value that suggests we fail to reject the null hypothesis.\n",
        "\n",
        "\n",
        "The Chi squared tests were run for A6 and A9. The chi square statistics was over 3 times higher for A9 than A6 which shows a bigger relationship between A9 and A16 than A6 and A16. The p-values for all tests were significantly small and suggests that these two features are not uniformally distributed over the sample data.\n",
        "\n",
        "\n",
        "For me, the most challenging part of the this sprint was understanding what each feature represented. More detailed information, other than the data type, may have made it easier to select which features to compare. But, maybe that is better in order to avoid certain biases."
      ]
    },
    {
      "metadata": {
        "id": "Wj3d8Ig1WK2V",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}