/* This example shows the analysis for the RBD with sampling */ /* using the rubber data example we looked at in class */ /* Entering the data and defining the variables: */ data rubber; input OBS LAB MATERIAL $ STRETCHING; cards; 1 1 A 72 2 1 A 79 3 1 A 61 4 1 A 71 5 1 B 133 6 1 B 129 7 1 B 123 8 1 B 156 9 1 C 37 10 1 C 36 11 1 C 26 12 1 C 24 13 1 D 63 14 1 D 49 15 1 D 63 16 1 D 43 17 1 E 35 18 1 E 26 19 1 E 24 20 1 E 61 21 1 F 31 22 1 F 32 23 1 F 28 24 1 F 26 25 1 G 43 26 1 G 40 27 1 G 35 28 1 G 38 29 2 A 61 30 2 A 49 31 2 A 57 32 2 A 61 33 2 B 129 34 2 B 125 35 2 B 136 36 2 B 127 37 2 C 20 38 2 C 14 39 2 C 30 40 2 C 27 41 2 D 51 42 2 D 52 43 2 D 62 44 2 D 52 45 2 E 27 46 2 E 27 47 2 E 26 48 2 E 26 49 2 F 22 50 2 F 20 51 2 F 29 52 2 F 28.0 53 2 G 32.0 54 2 G 29.0 55 2 G 45.0 56 2 G 40.0 57 3 A 70.0 58 3 A 62.0 59 3 A 62.0 60 3 A 76.0 61 3 B 121.0 62 3 B 125.0 63 3 B 109.0 64 3 B 128.0 65 3 C 33.0 66 3 C 33.0 67 3 C 27.0 68 3 C 29.5 69 3 D 58.0 70 3 D 64.0 71 3 D 56.0 72 3 D 55.0 73 3 E 28.0 74 3 E 28.0 75 3 E 27.0 76 3 E 29.0 77 3 F 27.0 78 3 F 30.5 79 3 F 27.0 80 3 F 27.0 81 3 G 44.0 82 3 G 44.0 83 3 G 45.0 84 3 G 49.0 85 4 A 36.0 86 4 A 39.0 87 4 A 41.0 88 4 A 45.0 89 4 B 57.0 90 4 B 58.0 91 4 B 59.0 92 4 B 67.0 93 4 C 27.0 94 4 C 24.0 95 4 C 22.0 96 4 C 25.0 97 4 D 38.0 98 4 D 38.0 99 4 D 37.0 100 4 D 38.0 101 4 E 22.0 102 4 E 23.0 103 4 E 20 104 4 E 20 105 4 F 22 106 4 F 23 107 4 F 22 108 4 F 22 109 4 G 31 110 4 G 31 111 4 G 28 112 4 G 30 113 5 A 58 114 5 A 57 115 5 A 58 116 5 A 53 117 5 B 122 118 5 B 98 119 5 B 107 120 5 B 110 121 5 C 34 122 5 C 27 123 5 C 26 124 5 C 26 125 5 D 53 126 5 D 47 127 5 D 48 128 5 D 47 129 5 E 25 130 5 E 25 131 5 E 21 132 5 E 19 133 5 F 26 134 5 F 25 135 5 F 22 136 5 F 18 137 5 G 43 138 5 G 35 139 5 G 43 140 5 G 36 141 6 A 52 142 6 A 56 143 6 A 52 144 6 A 50 145 6 B 109 146 6 B 120 147 6 B 112 148 6 B 107 149 6 C 30 150 6 C 31 151 6 C 31 152 6 C 28 153 6 D 50 154 6 D 50.0 155 6 D 50.0 156 6 D 51.0 157 6 E 25.0 158 6 E 25.0 159 6 E 26.0 160 6 E 26.0 161 6 F 24.0 162 6 F 26.0 163 6 F 25.0 164 6 F 26.0 165 6 G 38.0 166 6 G 41.0 167 6 G 40.0 168 6 G 43.0 169 7 A 40.7 170 7 A 45.9 171 7 A 43.1 172 7 A 37.3 173 7 B 80.0 174 7 B 71.9 175 7 B 75.8 176 7 B 63.7 177 7 C 26.5 178 7 C 27.1 179 7 C 26.6 180 7 C 25.6 181 7 D 38.8 182 7 D 39.4 183 7 D 40.7 184 7 D 38.0 185 7 E 23.0 186 7 E 22.9 187 7 E 22.5 188 7 E 35.7 189 7 F 22.2 190 7 F 23.9 191 7 F 22.6 192 7 F 25.5 193 7 G 29.4 194 7 G 31.6 195 7 G 29.6 196 7 G 29.3 197 8 A 68.1 198 8 A 69.8 199 8 A 65.9 200 8 A 62.1 201 8 B 135.0 202 8 B 151.0 203 8 B 143.0 204 8 B 142.0 205 8 C 38.1 206 8 C 37.4 207 8 C 37.9 208 8 C 37.1 209 8 D 64.5 210 8 D 65.7 211 8 D 64.0 212 8 D 62.5 213 8 E 32.1 214 8 E 35.2 215 8 E 33.0 216 8 E 34.9 217 8 F 32.7 218 8 F 32.4 219 8 F 30.3 220 8 F 35.6 221 8 G 50.2 222 8 G 50.4 223 8 G 42.5 224 8 G 45.0 225 9 A 46.0 226 9 A 47.0 227 9 A 46.0 228 9 A 45.0 229 9 B 69.0 230 9 B 69.0 231 9 B 73.0 232 9 B 70.0 233 9 C 26.0 234 9 C 26.0 235 9 C 25.0 236 9 C 25.0 237 9 D 40.0 238 9 D 38.0 239 9 D 39.0 240 9 D 39.0 241 9 E 24.0 242 9 E 24.0 243 9 E 24.0 244 9 E 25.0 245 9 F 23.0 246 9 F 24.0 247 9 F 24.0 248 9 F 23.0 249 9 G 32.0 250 9 G 31.0 251 9 G 32.0 252 9 G 30.0 253 10 A 77.0 254 10 A 74.0 255 10 A 77.0 256 10 A 72 257 10 B 132 258 10 B 129 259 10 B 141 260 10 B 137 261 10 C 45 262 10 C 41 263 10 C 39 264 10 C 38 265 10 D 71 266 10 D 69 267 10 D 66 268 10 D 68 269 10 E 36 270 10 E 33 271 10 E 35 272 10 E 25 273 10 F 38 274 10 F 36 275 10 F 38 276 10 F 38 277 10 G 56 278 10 G 48 279 10 G 48 280 10 G 50 281 11 A 76 282 11 A 55 283 11 A 60 284 11 A 58 285 11 B 118 286 11 B 109 287 11 B 115 288 11 B 106 289 11 C 27 290 11 C 32 291 11 C 26 292 11 C 26 293 11 D 52 294 11 D 45 295 11 D 48 296 11 D 54 297 11 E 22 298 11 E 19 299 11 E 18 300 11 E 23 301 11 F 23 302 11 F 23 303 11 F 23 304 11 F 24 305 11 G 32 306 11 G 37 307 11 G 37.0 308 11 G 39.0 309 12 A 72.5 310 12 A 76.0 311 12 A 69.5 312 12 A 70.5 313 12 B 133.0 314 12 B 133.0 315 12 B 128.5 316 12 B 128.5 317 12 C 32.5 318 12 C 32.8 319 12 C 32.9 320 12 C 34.6 321 12 D 63.0 322 12 D 64.5 323 12 D 61.5 324 12 D 62.7 325 12 E 31.2 326 12 E 30.2 327 12 E 29.0 328 12 E 29.7 329 12 F 30.7 330 12 F 30.8 331 12 F 30.0 332 12 F 29.5 333 12 G 45.8 334 12 G 45.2 335 12 G 43.5 336 12 G 46.5 337 13 A 51.0 338 13 A 50.0 339 13 A 49.0 340 13 A 49.0 341 13 B 86.0 342 13 B 84.0 343 13 B 96.0 344 13 B 81.0 345 13 C 24.0 346 13 C 24.0 347 13 C 24.0 348 13 C 26.0 349 13 D 45.0 350 13 D 43.0 351 13 D 42.0 352 13 D 45.0 353 13 E 21.8 354 13 E 21.8 355 13 E 24.0 356 13 E 22.0 357 13 F 24.0 358 13 F 24 359 13 F 22 360 13 F 24 361 13 G 33 362 13 G 33 363 13 G 31 364 13 G 31 ; run; /**************************************************************************/ /* The PROC GLM syntax is familiar here. LAB and MATERIAL are factors. */ /* STRETCHING is the response variable, MATERIAL is the treatment factor, */ /* and LAB represents the blocks. Also, the block LAB has random effects. */ /* We MUST specify the LAB*MATERIAL interaction in the MODEL statement!!! */ /* This will serve as our "experimental error" term. */ /* The regular "Error" line in SAS will serve as our "sampling error" term. */ PROC GLM data=rubber; CLASS LAB MATERIAL; MODEL STRETCHING = MATERIAL LAB LAB*MATERIAL; RANDOM LAB; TEST H = MATERIAL E = LAB*MATERIAL; MEANS MATERIAL / ALPHA=0.05 TUKEY E = LAB*MATERIAL; MEANS MATERIAL / ALPHA=0.05 TUKEY CLDIFF E = LAB*MATERIAL; /*Same thing, different format of output*/ RUN; /* The TEST statement tells SAS that when we test for a MATERIAL (treatment) effect, */ /* The correct denominator involves the LAB*MATERIAL (experimental error) term. */ /* Clearly there is a significant MATERIAL effect (F = 135.48, P-value < .0001). */ /* To determine which materials are significantly different, we use a Tukey multiple */ /* comparisons procedure. Again we specify that the correct denominator involves */ /* the LAB*MATERIAL (experimental error) term. */