1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 1 14:31 Tuesday, August 21, 2001 The GLM Procedure Class Level Information Class Levels Values PROGRAM 3 CONT RI WI Number of observations 57 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 2 14:31 Tuesday, August 21, 2001 The GLM Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable S1 S2 S3 S4 S5 Level of TIME 1 2 3 4 5 Repeated Measures Level Information Dependent Variable S6 S7 Level of TIME 6 7 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 54 S1 S2 S3 S4 S1 1.000000 0.960210 0.924649 0.871580 <.0001 <.0001 <.0001 S2 0.960210 1.000000 0.939585 0.876990 <.0001 <.0001 <.0001 S3 0.924649 0.939585 1.000000 0.955591 <.0001 <.0001 <.0001 S4 0.871580 0.876990 0.955591 1.000000 <.0001 <.0001 <.0001 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 54 S5 S6 S7 S1 0.842113 0.809118 0.796771 <.0001 <.0001 <.0001 S2 0.859610 0.827336 0.791740 <.0001 <.0001 <.0001 S3 0.937237 0.897542 0.875517 <.0001 <.0001 <.0001 S4 0.960087 0.909447 0.887424 <.0001 <.0001 <.0001 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 3 14:31 Tuesday, August 21, 2001 The GLM Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 54 S1 S2 S3 S4 S5 0.842113 0.859610 0.937237 0.960087 <.0001 <.0001 <.0001 <.0001 S6 0.809118 0.827336 0.897542 0.909447 <.0001 <.0001 <.0001 <.0001 S7 0.796771 0.791740 0.875517 0.887424 <.0001 <.0001 <.0001 <.0001 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 54 S5 S6 S7 S5 1.000000 0.951369 0.916529 <.0001 <.0001 S6 0.951369 1.000000 0.953077 <.0001 <.0001 S7 0.916529 0.953077 1.000000 <.0001 <.0001 E = Error SSCP Matrix TIME_N represents the nth degree polynomial contrast for TIME TIME_1 TIME_2 TIME_3 TIME_1 222.18759 -4.47761 -25.07733 TIME_2 -4.47761 66.13396 10.70779 TIME_3 -25.07733 10.70779 27.83720 TIME_4 12.16620 -12.72198 0.56637 TIME_5 -12.90938 -4.15986 -2.19138 TIME_6 8.90804 -3.15919 0.26587 E = Error SSCP Matrix TIME_N represents the nth degree polynomial contrast for TIME TIME_4 TIME_5 TIME_6 TIME_1 12.16620 -12.90938 8.90804 TIME_2 -12.72198 -4.15986 -3.15919 TIME_3 0.56637 -2.19138 0.26587 TIME_4 37.31676 -0.10095 -1.76903 TIME_5 -0.10095 17.12670 0.58815 TIME_6 -1.76903 0.58815 17.18453 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 4 14:31 Tuesday, August 21, 2001 The GLM Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 54 TIME_1 TIME_2 TIME_3 TIME_4 TIME_5 TIME_6 TIME_1 1.000000 -0.036938 -0.318866 0.133611 -0.209271 0.144163 0.7889 0.0177 0.3308 0.1252 0.2937 TIME_2 -0.036938 1.000000 0.249560 -0.256089 -0.123603 -0.093712 0.7889 0.0661 0.0591 0.3686 0.4962 TIME_3 -0.318866 0.249560 1.000000 0.017572 -0.100362 0.012156 0.0177 0.0661 0.8987 0.4660 0.9298 TIME_4 0.133611 -0.256089 0.017572 1.000000 -0.003993 -0.069858 0.3308 0.0591 0.8987 0.9769 0.6123 TIME_5 -0.209271 -0.123603 -0.100362 -0.003993 1.000000 0.034283 0.1252 0.3686 0.4660 0.9769 0.8038 TIME_6 0.144163 -0.093712 0.012156 -0.069858 0.034283 1.000000 0.2937 0.4962 0.9298 0.6123 0.8038 Sphericity Tests Mauchly's Variables DF Criterion Chi-Square Pr > ChiSq Transformed Variates 20 0.0403737 166.18471 <.0001 Orthogonal Components 20 0.0403737 166.18471 <.0001 Manova Test Criteria and Exact F Statistics for the Hypothesis of no TIME Effect H = Type III SSCP Matrix for TIME E = Error SSCP Matrix S=1 M=2 N=23.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.55848168 6.46 6 49 <.0001 Pillai's Trace 0.44151832 6.46 6 49 <.0001 Hotelling-Lawley Trace 0.79056903 6.46 6 49 <.0001 Roy's Greatest Root 0.79056903 6.46 6 49 <.0001 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 5 14:31 Tuesday, August 21, 2001 The GLM Procedure Repeated Measures Analysis of Variance Manova Test Criteria and F Approximations for the Hypothesis of no TIME*PROGRAM Effect H = Type III SSCP Matrix for TIME*PROGRAM E = Error SSCP Matrix S=2 M=1.5 N=23.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.73167437 1.38 12 98 0.1880 Pillai's Trace 0.28188936 1.37 12 100 0.1943 Hotelling-Lawley Trace 0.34819029 1.40 12 73.199 0.1847 Roy's Greatest Root 0.28259027 2.35 6 50 0.0442 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact. 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 6 14:31 Tuesday, August 21, 2001 The GLM Procedure Repeated Measures Analysis of Variance Tests of Hypotheses for Between Subjects Effects Source DF Type III SS Mean Square F Value PROGRAM 2 419.435262 209.717631 3.07 Error 54 3694.690051 68.420186 Source Pr > F PROGRAM 0.0548 Error 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 7 14:31 Tuesday, August 21, 2001 The GLM Procedure Repeated Measures Analysis of Variance Univariate Tests of Hypotheses for Within Subject Effects Source DF Type III SS Mean Square F Value TIME 6 53.3542637 8.8923773 7.43 TIME*PROGRAM 12 43.0002327 3.5833527 2.99 Error(TIME) 324 387.7867347 1.1968726 Adj Pr > F Source Pr > F G - G H - F TIME <.0001 0.0003 0.0002 TIME*PROGRAM 0.0005 0.0130 0.0104 Error(TIME) Greenhouse-Geisser Epsilon 0.4233 Huynh-Feldt Epsilon 0.4624 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 8 14:31 Tuesday, August 21, 2001 The GLM Procedure Repeated Measures Analysis of Variance Analysis of Variance of Contrast Variables TIME_N represents the nth degree polynomial contrast for TIME Contrast Variable: TIME_1 Source DF Type III SS Mean Square F Value Mean 1 40.5144529 40.5144529 9.85 PROGRAM 2 40.3913623 20.1956812 4.91 Error 54 222.1875850 4.1145849 Source Pr > F Mean 0.0028 PROGRAM 0.0110 Error Contrast Variable: TIME_2 Source DF Type III SS Mean Square F Value Mean 1 10.57713133 10.57713133 8.64 PROGRAM 2 1.42410491 0.71205245 0.58 Error 54 66.13395692 1.22470291 Source Pr > F Mean 0.0048 PROGRAM 0.5626 Error Contrast Variable: TIME_3 Source DF Type III SS Mean Square F Value Mean 1 1.31320035 1.31320035 2.55 PROGRAM 2 0.03999060 0.01999530 0.04 Error 54 27.83720238 0.51550375 Source Pr > F Mean 0.1163 PROGRAM 0.9620 Error 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 9 14:31 Tuesday, August 21, 2001 The GLM Procedure Repeated Measures Analysis of Variance Analysis of Variance of Contrast Variables TIME_N represents the nth degree polynomial contrast for TIME Contrast Variable: TIME_4 Source DF Type III SS Mean Square F Value Mean 1 0.08132173 0.08132173 0.12 PROGRAM 2 0.53719750 0.26859875 0.39 Error 54 37.31675557 0.69105103 Source Pr > F Mean 0.7329 PROGRAM 0.6798 Error Contrast Variable: TIME_5 Source DF Type III SS Mean Square F Value Mean 1 0.69325639 0.69325639 2.19 PROGRAM 2 0.20663265 0.10331633 0.33 Error 54 17.12670068 0.31716112 Source Pr > F Mean 0.1451 PROGRAM 0.7234 Error Contrast Variable: TIME_6 Source DF Type III SS Mean Square F Value Mean 1 0.17490098 0.17490098 0.55 PROGRAM 2 0.40094473 0.20047237 0.63 Error 54 17.18453412 0.31823211 Source Pr > F Mean 0.4617 PROGRAM 0.5365 Error 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 10 14:31 Tuesday, August 21, 2001 Obs SUBJ PROGRAM TIME STRENGTH 1 1 CONT 1 85 2 2 CONT 1 80 3 3 CONT 1 78 4 4 CONT 1 84 5 5 CONT 1 80 6 6 CONT 1 76 7 7 CONT 1 79 8 8 CONT 1 76 9 9 CONT 1 77 10 10 CONT 1 79 11 11 CONT 1 81 12 12 CONT 1 77 13 13 CONT 1 82 14 14 CONT 1 84 15 15 CONT 1 79 16 16 CONT 1 79 17 17 CONT 1 83 18 18 CONT 1 78 19 19 CONT 1 80 20 20 CONT 1 78 21 1 CONT 2 85 22 2 CONT 2 79 23 3 CONT 2 77 24 4 CONT 2 84 25 5 CONT 2 81 26 6 CONT 2 78 27 7 CONT 2 79 28 8 CONT 2 76 29 9 CONT 2 78 30 10 CONT 2 79 31 11 CONT 2 81 32 12 CONT 2 76 33 13 CONT 2 83 34 14 CONT 2 84 35 15 CONT 2 81 36 16 CONT 2 79 37 17 CONT 2 82 38 18 CONT 2 78 39 19 CONT 2 80 40 20 CONT 2 79 41 1 CONT 3 86 42 2 CONT 3 79 43 3 CONT 3 77 44 4 CONT 3 85 45 5 CONT 3 80 46 6 CONT 3 77 47 7 CONT 3 80 48 8 CONT 3 76 49 9 CONT 3 78 50 10 CONT 3 79 51 11 CONT 3 80 52 12 CONT 3 77 53 13 CONT 3 83 54 14 CONT 3 83 55 15 CONT 3 81 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 11 14:31 Tuesday, August 21, 2001 Obs SUBJ PROGRAM TIME STRENGTH 56 16 CONT 3 78 57 17 CONT 3 83 58 18 CONT 3 79 59 19 CONT 3 79 60 20 CONT 3 80 61 1 CONT 4 85 62 2 CONT 4 78 63 3 CONT 4 77 64 4 CONT 4 84 65 5 CONT 4 80 66 6 CONT 4 78 67 7 CONT 4 79 68 8 CONT 4 75 69 9 CONT 4 80 70 10 CONT 4 79 71 11 CONT 4 80 72 12 CONT 4 78 73 13 CONT 4 83 74 14 CONT 4 82 75 15 CONT 4 82 76 16 CONT 4 77 77 17 CONT 4 85 78 18 CONT 4 79 79 19 CONT 4 79 80 20 CONT 4 81 81 1 CONT 5 87 82 2 CONT 5 78 83 3 CONT 5 76 84 4 CONT 5 83 85 5 CONT 5 79 86 6 CONT 5 78 87 7 CONT 5 80 88 8 CONT 5 75 89 9 CONT 5 80 90 10 CONT 5 77 91 11 CONT 5 80 92 12 CONT 5 77 93 13 CONT 5 84 94 14 CONT 5 81 95 15 CONT 5 82 96 16 CONT 5 77 97 17 CONT 5 84 98 18 CONT 5 78 99 19 CONT 5 80 100 20 CONT 5 80 101 1 CONT 6 86 102 2 CONT 6 79 103 3 CONT 6 76 104 4 CONT 6 84 105 5 CONT 6 79 106 6 CONT 6 77 107 7 CONT 6 79 108 8 CONT 6 74 109 9 CONT 6 81 110 10 CONT 6 78 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 12 14:31 Tuesday, August 21, 2001 Obs SUBJ PROGRAM TIME STRENGTH 111 11 CONT 6 81 112 12 CONT 6 77 113 13 CONT 6 83 114 14 CONT 6 79 115 15 CONT 6 82 116 16 CONT 6 78 117 17 CONT 6 83 118 18 CONT 6 77 119 19 CONT 6 80 120 20 CONT 6 79 121 1 CONT 7 87 122 2 CONT 7 78 123 3 CONT 7 77 124 4 CONT 7 85 125 5 CONT 7 80 126 6 CONT 7 74 127 7 CONT 7 81 128 8 CONT 7 74 129 9 CONT 7 80 130 10 CONT 7 79 131 11 CONT 7 82 132 12 CONT 7 77 133 13 CONT 7 83 134 14 CONT 7 78 135 15 CONT 7 80 136 16 CONT 7 78 137 17 CONT 7 82 138 18 CONT 7 77 139 19 CONT 7 80 140 20 CONT 7 80 141 1 RI 1 79 142 2 RI 1 83 143 3 RI 1 81 144 4 RI 1 81 145 5 RI 1 80 146 6 RI 1 76 147 7 RI 1 81 148 8 RI 1 77 149 9 RI 1 84 150 10 RI 1 74 151 11 RI 1 76 152 12 RI 1 84 153 13 RI 1 79 154 14 RI 1 78 155 15 RI 1 78 156 16 RI 1 84 157 1 RI 2 79 158 2 RI 2 83 159 3 RI 2 83 160 4 RI 2 81 161 5 RI 2 81 162 6 RI 2 76 163 7 RI 2 84 164 8 RI 2 78 165 9 RI 2 85 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 13 14:31 Tuesday, August 21, 2001 Obs SUBJ PROGRAM TIME STRENGTH 166 10 RI 2 75 167 11 RI 2 77 168 12 RI 2 84 169 13 RI 2 80 170 14 RI 2 78 171 15 RI 2 80 172 16 RI 2 85 173 1 RI 3 79 174 2 RI 3 85 175 3 RI 3 82 176 4 RI 3 81 177 5 RI 3 82 178 6 RI 3 76 179 7 RI 3 83 180 8 RI 3 79 181 9 RI 3 87 182 10 RI 3 78 183 11 RI 3 77 184 12 RI 3 86 185 13 RI 3 79 186 14 RI 3 77 187 15 RI 3 77 188 16 RI 3 85 189 1 RI 4 80 190 2 RI 4 85 191 3 RI 4 82 192 4 RI 4 82 193 5 RI 4 82 194 6 RI 4 76 195 7 RI 4 83 196 8 RI 4 79 197 9 RI 4 89 198 10 RI 4 78 199 11 RI 4 77 200 12 RI 4 85 201 13 RI 4 80 202 14 RI 4 76 203 15 RI 4 77 204 16 RI 4 85 205 1 RI 5 80 206 2 RI 5 86 207 3 RI 5 83 208 4 RI 5 82 209 5 RI 5 82 210 6 RI 5 76 211 7 RI 5 85 212 8 RI 5 81 213 9 RI 5 88 214 10 RI 5 79 215 11 RI 5 77 216 12 RI 5 86 217 13 RI 5 80 218 14 RI 5 75 219 15 RI 5 75 220 16 RI 5 85 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 14 14:31 Tuesday, August 21, 2001 Obs SUBJ PROGRAM TIME STRENGTH 221 1 RI 6 78 222 2 RI 6 87 223 3 RI 6 83 224 4 RI 6 83 225 5 RI 6 84 226 6 RI 6 76 227 7 RI 6 85 228 8 RI 6 82 229 9 RI 6 85 230 10 RI 6 78 231 11 RI 6 76 232 12 RI 6 86 233 13 RI 6 82 234 14 RI 6 75 235 15 RI 6 75 236 16 RI 6 83 237 1 RI 7 80 238 2 RI 7 87 239 3 RI 7 82 240 4 RI 7 81 241 5 RI 7 86 242 6 RI 7 75 243 7 RI 7 85 244 8 RI 7 81 245 9 RI 7 86 246 10 RI 7 78 247 11 RI 7 76 248 12 RI 7 86 249 13 RI 7 82 250 14 RI 7 76 251 15 RI 7 75 252 16 RI 7 82 253 1 WI 1 84 254 2 WI 1 74 255 3 WI 1 83 256 4 WI 1 86 257 5 WI 1 82 258 6 WI 1 79 259 7 WI 1 79 260 8 WI 1 87 261 9 WI 1 81 262 10 WI 1 82 263 11 WI 1 79 264 12 WI 1 79 265 13 WI 1 83 266 14 WI 1 81 267 15 WI 1 78 268 16 WI 1 83 269 17 WI 1 80 270 18 WI 1 80 271 19 WI 1 85 272 20 WI 1 77 273 21 WI 1 80 274 1 WI 2 85 275 2 WI 2 75 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 15 14:31 Tuesday, August 21, 2001 Obs SUBJ PROGRAM TIME STRENGTH 276 3 WI 2 84 277 4 WI 2 87 278 5 WI 2 83 279 6 WI 2 80 280 7 WI 2 79 281 8 WI 2 89 282 9 WI 2 81 283 10 WI 2 82 284 11 WI 2 79 285 12 WI 2 80 286 13 WI 2 84 287 14 WI 2 81 288 15 WI 2 78 289 16 WI 2 82 290 17 WI 2 79 291 18 WI 2 82 292 19 WI 2 86 293 20 WI 2 78 294 21 WI 2 81 295 1 WI 3 84 296 2 WI 3 75 297 3 WI 3 82 298 4 WI 3 87 299 5 WI 3 84 300 6 WI 3 79 301 7 WI 3 79 302 8 WI 3 91 303 9 WI 3 81 304 10 WI 3 82 305 11 WI 3 80 306 12 WI 3 81 307 13 WI 3 84 308 14 WI 3 82 309 15 WI 3 79 310 16 WI 3 82 311 17 WI 3 79 312 18 WI 3 82 313 19 WI 3 87 314 20 WI 3 80 315 21 WI 3 80 316 1 WI 4 83 317 2 WI 4 76 318 3 WI 4 81 319 4 WI 4 87 320 5 WI 4 85 321 6 WI 4 79 322 7 WI 4 81 323 8 WI 4 90 324 9 WI 4 82 325 10 WI 4 84 326 11 WI 4 81 327 12 WI 4 82 328 13 WI 4 84 329 14 WI 4 84 330 15 WI 4 79 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 16 14:31 Tuesday, August 21, 2001 Obs SUBJ PROGRAM TIME STRENGTH 331 16 WI 4 84 332 17 WI 4 81 333 18 WI 4 82 334 19 WI 4 86 335 20 WI 4 81 336 21 WI 4 81 337 1 WI 5 83 338 2 WI 5 75 339 3 WI 5 83 340 4 WI 5 87 341 5 WI 5 84 342 6 WI 5 80 343 7 WI 5 81 344 8 WI 5 91 345 9 WI 5 82 346 10 WI 5 86 347 11 WI 5 81 348 12 WI 5 83 349 13 WI 5 84 350 14 WI 5 83 351 15 WI 5 78 352 16 WI 5 84 353 17 WI 5 80 354 18 WI 5 81 355 19 WI 5 86 356 20 WI 5 82 357 21 WI 5 81 358 1 WI 6 83 359 2 WI 6 76 360 3 WI 6 83 361 4 WI 6 87 362 5 WI 6 85 363 6 WI 6 79 364 7 WI 6 83 365 8 WI 6 92 366 9 WI 6 83 367 10 WI 6 85 368 11 WI 6 81 369 12 WI 6 82 370 13 WI 6 83 371 14 WI 6 82 372 15 WI 6 79 373 16 WI 6 83 374 17 WI 6 80 375 18 WI 6 81 376 19 WI 6 86 377 20 WI 6 82 378 21 WI 6 82 379 1 WI 7 84 380 2 WI 7 76 381 3 WI 7 82 382 4 WI 7 86 383 5 WI 7 86 384 6 WI 7 80 385 7 WI 7 83 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 17 14:31 Tuesday, August 21, 2001 Obs SUBJ PROGRAM TIME STRENGTH 386 8 WI 7 92 387 9 WI 7 83 388 10 WI 7 87 389 11 WI 7 81 390 12 WI 7 82 391 13 WI 7 83 392 14 WI 7 85 393 15 WI 7 79 394 16 WI 7 84 395 17 WI 7 80 396 18 WI 7 81 397 19 WI 7 86 398 20 WI 7 82 399 21 WI 7 83 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 18 14:31 Tuesday, August 21, 2001 The Mixed Procedure Model Information Data Set WORK.WEIGHT2 Dependent Variable STRENGTH Covariance Structure Variance Components Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values PROGRAM 3 CONT RI WI SUBJ 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 TIME 7 1 2 3 4 5 6 7 Dimensions Covariance Parameters 2 Columns in X 32 Columns in Z 57 Subjects 1 Max Obs Per Subject 399 Observations Used 399 Observations Not Used 0 Total Observations 399 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 2033.88298356 1 1 1420.82019617 0.00000000 Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate SUBJ(PROGRAM) 9.6033 Residual 1.1969 1 EXAMPLE 24. REPEATED MEASURES ANALYSIS: EXERCISE DATA 19 14:31 Tuesday, August 21, 2001 The Mixed Procedure Fit Statistics -2 Res Log Likelihood 1420.8 AIC (smaller is better) 1424.8 AICC (smaller is better) 1424.9 BIC (smaller is better) 1428.9 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F PROGRAM 2 54 3.07 0.0548 TIME 6 324 7.43 <.0001 PROGRAM*TIME 12 324 2.99 0.0005