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Hypothesis_Testing.ipynb
{
"cells": [
{
"metadata": {
"id": "htVdIkB7x_JG",
"trusted": false
},
"cell_type": "code",
"source": "import pandas as pd\nimport scipy\nfrom scipy import stats\nfrom plotly import figure_factory as FF\n",
"execution_count": null,
"outputs": []
},
{
"metadata": {
"id": "Fzu7VOJt3Pub"
},
"cell_type": "markdown",
"source": "# Question 1"
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "GyTeTo2qytIz",
"outputId": "dd5db153-c9fc-4cdb-f555-5da468bb3fa9",
"trusted": false
},
"cell_type": "code",
"source": "df=pd.read_csv(\"Cutlets.csv\")\ndf",
"execution_count": null,
"outputs": [
{
"data": {
"text/html": "\n <div id=\"df-65dc8c9e-8654-4fbf-944e-d922de34ea70\">\n <div class=\"colab-df-container\">\n <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>Unit A</th>\n <th>Unit B</th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <th>0</th>\n <td>6.8090</td>\n <td>6.7703</td>\n </tr>\n <tr>\n <th>1</th>\n <td>6.4376</td>\n <td>7.5093</td>\n </tr>\n <tr>\n <th>2</th>\n <td>6.9157</td>\n <td>6.7300</td>\n </tr>\n <tr>\n <th>3</th>\n <td>7.3012</td>\n <td>6.7878</td>\n </tr>\n <tr>\n <th>4</th>\n <td>7.4488</td>\n <td>7.1522</td>\n </tr>\n <tr>\n <th>5</th>\n <td>7.3871</td>\n <td>6.8110</td>\n </tr>\n <tr>\n <th>6</th>\n <td>6.8755</td>\n <td>7.2212</td>\n </tr>\n <tr>\n <th>7</th>\n <td>7.0621</td>\n <td>6.6606</td>\n </tr>\n <tr>\n <th>8</th>\n <td>6.6840</td>\n <td>7.2402</td>\n </tr>\n <tr>\n <th>9</th>\n <td>6.8236</td>\n <td>7.0503</td>\n </tr>\n <tr>\n <th>10</th>\n <td>7.3930</td>\n <td>6.8810</td>\n </tr>\n <tr>\n <th>11</th>\n <td>7.5169</td>\n <td>7.4059</td>\n </tr>\n <tr>\n <th>12</th>\n <td>6.9246</td>\n <td>6.7652</td>\n </tr>\n <tr>\n <th>13</th>\n <td>6.9256</td>\n <td>6.0380</td>\n </tr>\n <tr>\n <th>14</th>\n <td>6.5797</td>\n <td>7.1581</td>\n </tr>\n <tr>\n <th>15</th>\n <td>6.8394</td>\n <td>7.0240</td>\n </tr>\n <tr>\n <th>16</th>\n <td>6.5970</td>\n <td>6.6672</td>\n </tr>\n <tr>\n <th>17</th>\n <td>7.2705</td>\n <td>7.4314</td>\n </tr>\n <tr>\n <th>18</th>\n <td>7.2828</td>\n <td>7.3070</td>\n </tr>\n <tr>\n <th>19</th>\n <td>7.3495</td>\n <td>6.7478</td>\n </tr>\n <tr>\n <th>20</th>\n <td>6.9438</td>\n <td>6.8889</td>\n </tr>\n <tr>\n <th>21</th>\n <td>7.1560</td>\n <td>7.4220</td>\n </tr>\n <tr>\n <th>22</th>\n <td>6.5341</td>\n <td>6.5217</td>\n </tr>\n <tr>\n <th>23</th>\n <td>7.2854</td>\n <td>7.1688</td>\n </tr>\n <tr>\n <th>24</th>\n <td>6.9952</td>\n <td>6.7594</td>\n </tr>\n <tr>\n <th>25</th>\n <td>6.8568</td>\n <td>6.9399</td>\n </tr>\n <tr>\n <th>26</th>\n <td>7.2163</td>\n <td>7.0133</td>\n </tr>\n <tr>\n <th>27</th>\n <td>6.6801</td>\n <td>6.9182</td>\n </tr>\n <tr>\n <th>28</th>\n <td>6.9431</td>\n <td>6.3346</td>\n </tr>\n <tr>\n <th>29</th>\n <td>7.0852</td>\n <td>7.5459</td>\n </tr>\n <tr>\n <th>30</th>\n <td>6.7794</td>\n <td>7.0992</td>\n </tr>\n <tr>\n <th>31</th>\n <td>7.2783</td>\n <td>7.1180</td>\n </tr>\n <tr>\n <th>32</th>\n <td>7.1561</td>\n <td>6.6965</td>\n </tr>\n <tr>\n <th>33</th>\n <td>7.3943</td>\n <td>6.5780</td>\n </tr>\n <tr>\n <th>34</th>\n <td>6.9405</td>\n <td>7.3875</td>\n </tr>\n </tbody>\n</table>\n</div>\n <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-65dc8c9e-8654-4fbf-944e-d922de34ea70')\"\n title=\"Convert this dataframe to an interactive table.\"\n style=\"display:none;\">\n \n <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n width=\"24px\">\n <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n </svg>\n </button>\n \n <style>\n .colab-df-container {\n display:flex;\n flex-wrap:wrap;\n gap: 12px;\n }\n\n .colab-df-convert {\n background-color: #E8F0FE;\n border: none;\n border-radius: 50%;\n cursor: pointer;\n display: none;\n fill: #1967D2;\n height: 32px;\n padding: 0 0 0 0;\n width: 32px;\n }\n\n .colab-df-convert:hover {\n background-color: #E2EBFA;\n box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n fill: #174EA6;\n }\n\n [theme=dark] .colab-df-convert {\n background-color: #3B4455;\n fill: #D2E3FC;\n }\n\n [theme=dark] .colab-df-convert:hover {\n background-color: #434B5C;\n box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n fill: #FFFFFF;\n }\n </style>\n\n <script>\n const buttonEl =\n document.querySelector('#df-65dc8c9e-8654-4fbf-944e-d922de34ea70 button.colab-df-convert');\n buttonEl.style.display =\n google.colab.kernel.accessAllowed ? 'block' : 'none';\n\n async function convertToInteractive(key) {\n const element = document.querySelector('#df-65dc8c9e-8654-4fbf-944e-d922de34ea70');\n const dataTable =\n await google.colab.kernel.invokeFunction('convertToInteractive',\n [key], {});\n if (!dataTable) return;\n\n const docLinkHtml = 'Like what you see? Visit the ' +\n '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n + ' to learn more about interactive tables.';\n element.innerHTML = '';\n dataTable['output_type'] = 'display_data';\n await google.colab.output.renderOutput(dataTable, element);\n const docLink = document.createElement('div');\n docLink.innerHTML = docLinkHtml;\n element.appendChild(docLink);\n }\n </script>\n </div>\n </div>\n ",
"text/plain": " Unit A Unit B\n0 6.8090 6.7703\n1 6.4376 7.5093\n2 6.9157 6.7300\n3 7.3012 6.7878\n4 7.4488 7.1522\n5 7.3871 6.8110\n6 6.8755 7.2212\n7 7.0621 6.6606\n8 6.6840 7.2402\n9 6.8236 7.0503\n10 7.3930 6.8810\n11 7.5169 7.4059\n12 6.9246 6.7652\n13 6.9256 6.0380\n14 6.5797 7.1581\n15 6.8394 7.0240\n16 6.5970 6.6672\n17 7.2705 7.4314\n18 7.2828 7.3070\n19 7.3495 6.7478\n20 6.9438 6.8889\n21 7.1560 7.4220\n22 6.5341 6.5217\n23 7.2854 7.1688\n24 6.9952 6.7594\n25 6.8568 6.9399\n26 7.2163 7.0133\n27 6.6801 6.9182\n28 6.9431 6.3346\n29 7.0852 7.5459\n30 6.7794 7.0992\n31 7.2783 7.1180\n32 7.1561 6.6965\n33 7.3943 6.5780\n34 6.9405 7.3875"
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "GHaPenray7BM",
"outputId": "4883f414-1864-4373-a486-bc4ef007acb8",
"trusted": false
},
"cell_type": "code",
"source": "stats.ttest_ind(df['Unit A'],df['Unit B'])",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "Ttest_indResult(statistic=0.7228688704678063, pvalue=0.4722394724599501)"
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"id": "Hn8vbIDM1S7G"
},
"cell_type": "markdown",
"source": "significance level is 5%\n\n* H0 : There is no difference in diameter of cutlets\n* H1 : There is difference in diameter of cutlets\n\n\npvalue is 0.47 which is greater than 0.05. \n"
},
{
"metadata": {
"id": "XS865Jel2mae"
},
"cell_type": "markdown",
"source": "Therefore, Accept H0\nThere is no difference in diameter of cutlets"
},
{
"metadata": {
"id": "zkHR9PDp3Vps"
},
"cell_type": "markdown",
"source": "# Question 2"
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "VjT1jeUV3Zyp",
"outputId": "edd34b8d-45e6-49ba-e702-3f2a0dc3dba7",
"trusted": false
},
"cell_type": "code",
"source": "df2=pd.read_csv(\"LabTAT.csv\")\ndf2.head",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "<bound method NDFrame.head of Laboratory 1 Laboratory 2 Laboratory 3 Laboratory 4\n0 185.35 165.53 176.70 166.13\n1 170.49 185.91 198.45 160.79\n2 192.77 194.92 201.23 185.18\n3 177.33 183.00 199.61 176.42\n4 193.41 169.57 204.63 152.60\n.. ... ... ... ...\n115 178.49 170.66 193.80 172.68\n116 176.08 183.98 215.25 177.64\n117 202.48 174.54 203.99 170.27\n118 182.40 197.18 194.52 150.87\n119 182.09 215.17 221.49 162.21\n\n[120 rows x 4 columns]>"
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"id": "0wYMHpA04kCI"
},
"cell_type": "markdown",
"source": "Significance level is 5%\n\n\n* H0 : All the means are same (all Lab's TAT averages are same)\n* H1 : Atleast one mean is different (Atleast 1 Lab's Average TAT is different)\n\n"
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "VT5EmKyh5m5E",
"outputId": "9d5611cb-e5ac-41ff-e289-cae396f27b78",
"trusted": false
},
"cell_type": "code",
"source": "#Calculating pvalue with the help of F-ratio\nstats.f_oneway(df2.iloc[:,0],df2.iloc[:,1],df2.iloc[:,2],df2.iloc[:,3])",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "F_onewayResult(statistic=118.70421654401437, pvalue=2.1156708949992414e-57)"
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"id": "RcKoLF2w7W88"
},
"cell_type": "markdown",
"source": "2.11 * 10 power -57 which almost 0 and less than alpha value (0.05)"
},
{
"metadata": {
"id": "HEsKpAR47sua"
},
"cell_type": "markdown",
"source": "There we accept alternate hypothesis (H1) and reject null hypothesis (H0). Atleast one mean is different (Atleast 1 Lab's Average TAT is different)."
},
{
"metadata": {
"id": "J4dHl9848g_-"
},
"cell_type": "markdown",
"source": "# Question 3"
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "uWVzmBPM9PLj",
"outputId": "3410a9cd-590f-426c-92f4-ccd6a855770d",
"trusted": false
},
"cell_type": "code",
"source": "df3=pd.read_csv(\"BuyerRatio.csv\")\ndf3.head",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "<bound method NDFrame.head of Observed Values East West North South\n0 Males 50 142 131 70\n1 Females 435 1523 1356 750>"
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"id": "T3deixX3DEZh"
},
"cell_type": "markdown",
"source": "\n\n* H0 : All proportions are equal\n* H1 : All proportions are not equal\n\n"
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "eth9PpIK9va4",
"outputId": "86904232-7a26-4fbd-b25b-ab76f4abed52",
"trusted": false
},
"cell_type": "code",
"source": "# using chi-square Test\nchi_results=stats.chi2_contingency([df3[\"East\"], df3[\"West\"], df3[\"North\"], df3[\"South\"]])\nchi_results",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "(1.5959455386610577,\n 0.6603094907091882,\n 3,\n array([[ 42.76531299, 442.23468701],\n [ 146.81287862, 1518.18712138],\n [ 131.11756787, 1355.88243213],\n [ 72.30424052, 747.69575948]]))"
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "XX8A8RPaCV5t",
"outputId": "8c04149c-5261-426a-ae3b-906216046104",
"trusted": false
},
"cell_type": "code",
"source": "chi_square=[['','Test Statistic','p-value'],['Sample Data',chi_results[0],chi_results[1]]]\nchi_square",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "[['', 'Test Statistic', 'p-value'],\n ['Sample Data', 1.5959455386610577, 0.6603094907091882]]"
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 127
},
"id": "NfiYYOnGB6Oj",
"outputId": "64a44472-69c3-41ea-f281-08da675609bf",
"trusted": false
},
"cell_type": "code",
"source": "FF.create_table(chi_square,index=True)",
"execution_count": null,
"outputs": [
{
"data": {
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{\"annotations\":[{\"align\":\"left\",\"font\":{\"color\":\"#ffffff\"},\"showarrow\":false,\"text\":\"<b></b>\",\"x\":-0.45,\"xanchor\":\"left\",\"xref\":\"x\",\"y\":0,\"yref\":\"y\"},{\"align\":\"left\",\"font\":{\"color\":\"#ffffff\"},\"showarrow\":false,\"text\":\"<b>Test Statistic</b>\",\"x\":0.55,\"xanchor\":\"left\",\"xref\":\"x\",\"y\":0,\"yref\":\"y\"},{\"align\":\"left\",\"font\":{\"color\":\"#ffffff\"},\"showarrow\":false,\"text\":\"<b>p-value</b>\",\"x\":1.55,\"xanchor\":\"left\",\"xref\":\"x\",\"y\":0,\"yref\":\"y\"},{\"align\":\"left\",\"font\":{\"color\":\"#ffffff\"},\"showarrow\":false,\"text\":\"<b>Sample 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},
"metadata": {},
"output_type": "display_data"
}
]
},
{
"metadata": {
"id": "qL0oIqFaB1jK"
},
"cell_type": "markdown",
"source": "p-value is 0.66 which is greater than 0.05.\n"
},
{
"metadata": {
"id": "urUYvn1YDo0S"
},
"cell_type": "markdown",
"source": "Accept null hypothesis. All proportions are equal"
},
{
"metadata": {
"id": "i_LBEgOLEh8s"
},
"cell_type": "markdown",
"source": "#Question 4\n"
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "FzkepnkTElsv",
"outputId": "2885e439-13e6-4c1a-eb15-ed201a9fbe61",
"trusted": false
},
"cell_type": "code",
"source": "df4=pd.read_csv(\"Costomer+OrderForm.csv\")\ndf4.head",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "<bound method NDFrame.head of Phillippines Indonesia Malta India\n0 Error Free Error Free Defective Error Free\n1 Error Free Error Free Error Free Defective\n2 Error Free Defective Defective Error Free\n3 Error Free Error Free Error Free Error Free\n4 Error Free Error Free Defective Error Free\n.. ... ... ... ...\n295 Error Free Error Free Error Free Error Free\n296 Error Free Error Free Error Free Error Free\n297 Error Free Error Free Defective Error Free\n298 Error Free Error Free Error Free Error Free\n299 Error Free Defective Defective Error Free\n\n[300 rows x 4 columns]>"
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"id": "V4tdfWEWG7X0"
},
"cell_type": "markdown",
"source": "\n\n* H0 : Defective % does not vary by centre \n* H1 : Defective % varies by centre\n\n"
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "F0oD9pP9ExIN",
"outputId": "63c9ba1d-37a7-4a10-cdce-8ea4850ad4ba",
"trusted": false
},
"cell_type": "code",
"source": "# using chi-square Test\nchi_results=stats.chi2_contingency([df4[\"Phillippines\"].value_counts(),df4[\"Indonesia\"].value_counts(),df4[\"Malta\"].value_counts(),df4[\"India\"].value_counts()])\nchi_results",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "(3.8589606858203545, 0.2771020991233144, 3, array([[271.75, 28.25],\n [271.75, 28.25],\n [271.75, 28.25],\n [271.75, 28.25]]))"
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "HdPxUgGPFyRl",
"outputId": "5d2db4a5-d3c8-4421-eb43-05f8120b3561",
"trusted": false
},
"cell_type": "code",
"source": "chi_square=[[\"\",\"Test statistic\",\"p-value\"],[\"Sample Data\",chi_results[0],chi_results[1]]]\nchi_square",
"execution_count": null,
"outputs": [
{
"data": {
"text/plain": "[['', 'Test statistic', 'p-value'],\n ['Sample Data', 3.8589606858203545, 0.2771020991233144]]"
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 127
},
"id": "ye5SR_7oGVQ4",
"outputId": "d722dace-0dc3-463a-a79c-c91c40f68370",
"trusted": false
},
"cell_type": "code",
"source": "FF.create_table(chi_square,index=True)",
"execution_count": null,
"outputs": [
{
"data": {
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