|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "metadata": {}, |
| 6 | + "source": [ |
| 7 | + "# Module 3 Hypothesis Testing" |
| 8 | + ] |
| 9 | + }, |
| 10 | + { |
| 11 | + "cell_type": "code", |
| 12 | + "execution_count": 21, |
| 13 | + "metadata": {}, |
| 14 | + "outputs": [], |
| 15 | + "source": [ |
| 16 | + "import statsmodels.api as sm\n", |
| 17 | + "sleep = sm.datasets.get_rdataset(\"sleep\").data" |
| 18 | + ] |
| 19 | + }, |
| 20 | + { |
| 21 | + "cell_type": "code", |
| 22 | + "execution_count": 22, |
| 23 | + "metadata": {}, |
| 24 | + "outputs": [ |
| 25 | + { |
| 26 | + "data": { |
| 27 | + "text/html": [ |
| 28 | + "<div>\n", |
| 29 | + "<style scoped>\n", |
| 30 | + " .dataframe tbody tr th:only-of-type {\n", |
| 31 | + " vertical-align: middle;\n", |
| 32 | + " }\n", |
| 33 | + "\n", |
| 34 | + " .dataframe tbody tr th {\n", |
| 35 | + " vertical-align: top;\n", |
| 36 | + " }\n", |
| 37 | + "\n", |
| 38 | + " .dataframe thead th {\n", |
| 39 | + " text-align: right;\n", |
| 40 | + " }\n", |
| 41 | + "</style>\n", |
| 42 | + "<table border=\"1\" class=\"dataframe\">\n", |
| 43 | + " <thead>\n", |
| 44 | + " <tr style=\"text-align: right;\">\n", |
| 45 | + " <th></th>\n", |
| 46 | + " <th>extra</th>\n", |
| 47 | + " <th>group</th>\n", |
| 48 | + " <th>ID</th>\n", |
| 49 | + " </tr>\n", |
| 50 | + " </thead>\n", |
| 51 | + " <tbody>\n", |
| 52 | + " <tr>\n", |
| 53 | + " <th>0</th>\n", |
| 54 | + " <td>0.7</td>\n", |
| 55 | + " <td>1</td>\n", |
| 56 | + " <td>1</td>\n", |
| 57 | + " </tr>\n", |
| 58 | + " <tr>\n", |
| 59 | + " <th>1</th>\n", |
| 60 | + " <td>-1.6</td>\n", |
| 61 | + " <td>1</td>\n", |
| 62 | + " <td>2</td>\n", |
| 63 | + " </tr>\n", |
| 64 | + " <tr>\n", |
| 65 | + " <th>2</th>\n", |
| 66 | + " <td>-0.2</td>\n", |
| 67 | + " <td>1</td>\n", |
| 68 | + " <td>3</td>\n", |
| 69 | + " </tr>\n", |
| 70 | + " <tr>\n", |
| 71 | + " <th>3</th>\n", |
| 72 | + " <td>-1.2</td>\n", |
| 73 | + " <td>1</td>\n", |
| 74 | + " <td>4</td>\n", |
| 75 | + " </tr>\n", |
| 76 | + " <tr>\n", |
| 77 | + " <th>4</th>\n", |
| 78 | + " <td>-0.1</td>\n", |
| 79 | + " <td>1</td>\n", |
| 80 | + " <td>5</td>\n", |
| 81 | + " </tr>\n", |
| 82 | + " <tr>\n", |
| 83 | + " <th>5</th>\n", |
| 84 | + " <td>3.4</td>\n", |
| 85 | + " <td>1</td>\n", |
| 86 | + " <td>6</td>\n", |
| 87 | + " </tr>\n", |
| 88 | + " <tr>\n", |
| 89 | + " <th>6</th>\n", |
| 90 | + " <td>3.7</td>\n", |
| 91 | + " <td>1</td>\n", |
| 92 | + " <td>7</td>\n", |
| 93 | + " </tr>\n", |
| 94 | + " <tr>\n", |
| 95 | + " <th>7</th>\n", |
| 96 | + " <td>0.8</td>\n", |
| 97 | + " <td>1</td>\n", |
| 98 | + " <td>8</td>\n", |
| 99 | + " </tr>\n", |
| 100 | + " <tr>\n", |
| 101 | + " <th>8</th>\n", |
| 102 | + " <td>0.0</td>\n", |
| 103 | + " <td>1</td>\n", |
| 104 | + " <td>9</td>\n", |
| 105 | + " </tr>\n", |
| 106 | + " <tr>\n", |
| 107 | + " <th>9</th>\n", |
| 108 | + " <td>2.0</td>\n", |
| 109 | + " <td>1</td>\n", |
| 110 | + " <td>10</td>\n", |
| 111 | + " </tr>\n", |
| 112 | + " <tr>\n", |
| 113 | + " <th>10</th>\n", |
| 114 | + " <td>1.9</td>\n", |
| 115 | + " <td>2</td>\n", |
| 116 | + " <td>1</td>\n", |
| 117 | + " </tr>\n", |
| 118 | + " <tr>\n", |
| 119 | + " <th>11</th>\n", |
| 120 | + " <td>0.8</td>\n", |
| 121 | + " <td>2</td>\n", |
| 122 | + " <td>2</td>\n", |
| 123 | + " </tr>\n", |
| 124 | + " <tr>\n", |
| 125 | + " <th>12</th>\n", |
| 126 | + " <td>1.1</td>\n", |
| 127 | + " <td>2</td>\n", |
| 128 | + " <td>3</td>\n", |
| 129 | + " </tr>\n", |
| 130 | + " <tr>\n", |
| 131 | + " <th>13</th>\n", |
| 132 | + " <td>0.1</td>\n", |
| 133 | + " <td>2</td>\n", |
| 134 | + " <td>4</td>\n", |
| 135 | + " </tr>\n", |
| 136 | + " <tr>\n", |
| 137 | + " <th>14</th>\n", |
| 138 | + " <td>-0.1</td>\n", |
| 139 | + " <td>2</td>\n", |
| 140 | + " <td>5</td>\n", |
| 141 | + " </tr>\n", |
| 142 | + " <tr>\n", |
| 143 | + " <th>15</th>\n", |
| 144 | + " <td>4.4</td>\n", |
| 145 | + " <td>2</td>\n", |
| 146 | + " <td>6</td>\n", |
| 147 | + " </tr>\n", |
| 148 | + " <tr>\n", |
| 149 | + " <th>16</th>\n", |
| 150 | + " <td>5.5</td>\n", |
| 151 | + " <td>2</td>\n", |
| 152 | + " <td>7</td>\n", |
| 153 | + " </tr>\n", |
| 154 | + " <tr>\n", |
| 155 | + " <th>17</th>\n", |
| 156 | + " <td>1.6</td>\n", |
| 157 | + " <td>2</td>\n", |
| 158 | + " <td>8</td>\n", |
| 159 | + " </tr>\n", |
| 160 | + " <tr>\n", |
| 161 | + " <th>18</th>\n", |
| 162 | + " <td>4.6</td>\n", |
| 163 | + " <td>2</td>\n", |
| 164 | + " <td>9</td>\n", |
| 165 | + " </tr>\n", |
| 166 | + " <tr>\n", |
| 167 | + " <th>19</th>\n", |
| 168 | + " <td>3.4</td>\n", |
| 169 | + " <td>2</td>\n", |
| 170 | + " <td>10</td>\n", |
| 171 | + " </tr>\n", |
| 172 | + " </tbody>\n", |
| 173 | + "</table>\n", |
| 174 | + "</div>" |
| 175 | + ], |
| 176 | + "text/plain": [ |
| 177 | + " extra group ID\n", |
| 178 | + "0 0.7 1 1\n", |
| 179 | + "1 -1.6 1 2\n", |
| 180 | + "2 -0.2 1 3\n", |
| 181 | + "3 -1.2 1 4\n", |
| 182 | + "4 -0.1 1 5\n", |
| 183 | + "5 3.4 1 6\n", |
| 184 | + "6 3.7 1 7\n", |
| 185 | + "7 0.8 1 8\n", |
| 186 | + "8 0.0 1 9\n", |
| 187 | + "9 2.0 1 10\n", |
| 188 | + "10 1.9 2 1\n", |
| 189 | + "11 0.8 2 2\n", |
| 190 | + "12 1.1 2 3\n", |
| 191 | + "13 0.1 2 4\n", |
| 192 | + "14 -0.1 2 5\n", |
| 193 | + "15 4.4 2 6\n", |
| 194 | + "16 5.5 2 7\n", |
| 195 | + "17 1.6 2 8\n", |
| 196 | + "18 4.6 2 9\n", |
| 197 | + "19 3.4 2 10" |
| 198 | + ] |
| 199 | + }, |
| 200 | + "execution_count": 22, |
| 201 | + "metadata": {}, |
| 202 | + "output_type": "execute_result" |
| 203 | + } |
| 204 | + ], |
| 205 | + "source": [ |
| 206 | + "sleep" |
| 207 | + ] |
| 208 | + }, |
| 209 | + { |
| 210 | + "cell_type": "code", |
| 211 | + "execution_count": 99, |
| 212 | + "metadata": {}, |
| 213 | + "outputs": [ |
| 214 | + { |
| 215 | + "data": { |
| 216 | + "text/plain": [ |
| 217 | + "<matplotlib.axes._subplots.AxesSubplot at 0x131209710>" |
| 218 | + ] |
| 219 | + }, |
| 220 | + "execution_count": 99, |
| 221 | + "metadata": {}, |
| 222 | + "output_type": "execute_result" |
| 223 | + }, |
| 224 | + { |
| 225 | + "data": { |
| 226 | + "image/png": "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\n", |
| 227 | + "text/plain": [ |
| 228 | + "<Figure size 432x288 with 1 Axes>" |
| 229 | + ] |
| 230 | + }, |
| 231 | + "metadata": {}, |
| 232 | + "output_type": "display_data" |
| 233 | + } |
| 234 | + ], |
| 235 | + "source": [ |
| 236 | + "gp1 = sleep[sleep.group==1].extra\n", |
| 237 | + "gp2 = sleep[sleep.group==2].extra\n", |
| 238 | + "\n", |
| 239 | + "c = pd.DataFrame({'gp 1':gp1.values,'gp 2':gp2.values})\n", |
| 240 | + "c.plot(kind='box')" |
| 241 | + ] |
| 242 | + }, |
| 243 | + { |
| 244 | + "cell_type": "code", |
| 245 | + "execution_count": 100, |
| 246 | + "metadata": {}, |
| 247 | + "outputs": [ |
| 248 | + { |
| 249 | + "data": { |
| 250 | + "text/plain": [ |
| 251 | + "0.07918671421593818" |
| 252 | + ] |
| 253 | + }, |
| 254 | + "execution_count": 100, |
| 255 | + "metadata": {}, |
| 256 | + "output_type": "execute_result" |
| 257 | + } |
| 258 | + ], |
| 259 | + "source": [ |
| 260 | + "import scipy\n", |
| 261 | + "\n", |
| 262 | + "result = scipy.stats.ttest_ind(gp1,gp2)\n", |
| 263 | + "result.pvalue" |
| 264 | + ] |
| 265 | + }, |
| 266 | + { |
| 267 | + "cell_type": "code", |
| 268 | + "execution_count": 101, |
| 269 | + "metadata": {}, |
| 270 | + "outputs": [ |
| 271 | + { |
| 272 | + "data": { |
| 273 | + "text/plain": [ |
| 274 | + "0.00283289019738427" |
| 275 | + ] |
| 276 | + }, |
| 277 | + "execution_count": 101, |
| 278 | + "metadata": {}, |
| 279 | + "output_type": "execute_result" |
| 280 | + } |
| 281 | + ], |
| 282 | + "source": [ |
| 283 | + "a1 = gp1.reset_index().extra\n", |
| 284 | + "b1 = gp2.reset_index().extra\n", |
| 285 | + "result = stats.ttest_1samp(a1-b1, 0)\n", |
| 286 | + "result.pvalue" |
| 287 | + ] |
| 288 | + }, |
| 289 | + { |
| 290 | + "cell_type": "code", |
| 291 | + "execution_count": 72, |
| 292 | + "metadata": {}, |
| 293 | + "outputs": [], |
| 294 | + "source": [ |
| 295 | + "chickwts = sm.datasets.get_rdataset(\"chickwts\").data" |
| 296 | + ] |
| 297 | + }, |
| 298 | + { |
| 299 | + "cell_type": "code", |
| 300 | + "execution_count": 98, |
| 301 | + "metadata": {}, |
| 302 | + "outputs": [ |
| 303 | + { |
| 304 | + "data": { |
| 305 | + "text/plain": [ |
| 306 | + "8.254541016953191e-07" |
| 307 | + ] |
| 308 | + }, |
| 309 | + "execution_count": 98, |
| 310 | + "metadata": {}, |
| 311 | + "output_type": "execute_result" |
| 312 | + } |
| 313 | + ], |
| 314 | + "source": [ |
| 315 | + "horsebean = chickwts[chickwts.feed=='horsebean'].weight\n", |
| 316 | + "casein = chickwts[chickwts.feed=='casein'].weight\n", |
| 317 | + "\n", |
| 318 | + "result = scipy.stats.ttest_ind(horsebean,casein)\n", |
| 319 | + "result.pvalue" |
| 320 | + ] |
| 321 | + }, |
| 322 | + { |
| 323 | + "cell_type": "code", |
| 324 | + "execution_count": null, |
| 325 | + "metadata": {}, |
| 326 | + "outputs": [], |
| 327 | + "source": [] |
| 328 | + } |
| 329 | + ], |
| 330 | + "metadata": { |
| 331 | + "kernelspec": { |
| 332 | + "display_name": "Python 3", |
| 333 | + "language": "python", |
| 334 | + "name": "python3" |
| 335 | + }, |
| 336 | + "language_info": { |
| 337 | + "codemirror_mode": { |
| 338 | + "name": "ipython", |
| 339 | + "version": 3 |
| 340 | + }, |
| 341 | + "file_extension": ".py", |
| 342 | + "mimetype": "text/x-python", |
| 343 | + "name": "python", |
| 344 | + "nbconvert_exporter": "python", |
| 345 | + "pygments_lexer": "ipython3", |
| 346 | + "version": "3.6.5" |
| 347 | + } |
| 348 | + }, |
| 349 | + "nbformat": 4, |
| 350 | + "nbformat_minor": 2 |
| 351 | +} |
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