One way dan Two way MANOVA
Fazila Azra Anggina
2024-10-27
DATASET ONE WAY
Kanker payudara adalah kanker yang paling umum terjadi pada wanita di dunia. Kanker ini menyumbang 25% dari semua kasus kanker, dan mempengaruhi lebih dari 2,1 juta orang pada tahun 2015 saja. Kanker ini dimulai ketika sel-sel dalam payudara mulai tumbuh di luar kendali. Sel-sel ini biasanya membentuk tumor yang dapat dilihat melalui sinar-X atau dirasakan sebagai benjolan di area payudara.
data1 <- read.csv("data1.csv")
head(data1)## id diagnosis radius_mean texture_mean perimeter_mean area_mean
## 1 842302 M 17.99 10.38 122.80 1001.0
## 2 842517 M 20.57 17.77 132.90 1326.0
## 3 84300903 M 19.69 21.25 130.00 1203.0
## 4 84348301 M 11.42 20.38 77.58 386.1
## 5 84358402 M 20.29 14.34 135.10 1297.0
## 6 843786 M 12.45 15.70 82.57 477.1
## smoothness_mean compactness_mean concavity_mean concave.points_mean
## 1 0.11840 0.27760 0.3001 0.14710
## 2 0.08474 0.07864 0.0869 0.07017
## 3 0.10960 0.15990 0.1974 0.12790
## 4 0.14250 0.28390 0.2414 0.10520
## 5 0.10030 0.13280 0.1980 0.10430
## 6 0.12780 0.17000 0.1578 0.08089
## symmetry_mean fractal_dimension_mean radius_se texture_se perimeter_se
## 1 0.2419 0.07871 1.0950 0.9053 8.589
## 2 0.1812 0.05667 0.5435 0.7339 3.398
## 3 0.2069 0.05999 0.7456 0.7869 4.585
## 4 0.2597 0.09744 0.4956 1.1560 3.445
## 5 0.1809 0.05883 0.7572 0.7813 5.438
## 6 0.2087 0.07613 0.3345 0.8902 2.217
## area_se smoothness_se compactness_se concavity_se concave.points_se
## 1 153.40 0.006399 0.04904 0.05373 0.01587
## 2 74.08 0.005225 0.01308 0.01860 0.01340
## 3 94.03 0.006150 0.04006 0.03832 0.02058
## 4 27.23 0.009110 0.07458 0.05661 0.01867
## 5 94.44 0.011490 0.02461 0.05688 0.01885
## 6 27.19 0.007510 0.03345 0.03672 0.01137
## symmetry_se fractal_dimension_se radius_worst texture_worst perimeter_worst
## 1 0.03003 0.006193 25.38 17.33 184.60
## 2 0.01389 0.003532 24.99 23.41 158.80
## 3 0.02250 0.004571 23.57 25.53 152.50
## 4 0.05963 0.009208 14.91 26.50 98.87
## 5 0.01756 0.005115 22.54 16.67 152.20
## 6 0.02165 0.005082 15.47 23.75 103.40
## area_worst smoothness_worst compactness_worst concavity_worst
## 1 2019.0 0.1622 0.6656 0.7119
## 2 1956.0 0.1238 0.1866 0.2416
## 3 1709.0 0.1444 0.4245 0.4504
## 4 567.7 0.2098 0.8663 0.6869
## 5 1575.0 0.1374 0.2050 0.4000
## 6 741.6 0.1791 0.5249 0.5355
## concave.points_worst symmetry_worst fractal_dimension_worst X
## 1 0.2654 0.4601 0.11890 NA
## 2 0.1860 0.2750 0.08902 NA
## 3 0.2430 0.3613 0.08758 NA
## 4 0.2575 0.6638 0.17300 NA
## 5 0.1625 0.2364 0.07678 NA
## 6 0.1741 0.3985 0.12440 NAUJI KLASIK
UJI NORMALITAS
Uji normalitas multivariat merupakan uji yang mengasumsikan bahwa variabel terikat terdistribusi secara normal multivariat dalam setiap kelompok.
data1_fix <- data.frame(cbind(data1$smoothness_mean,data1$compactness_mean))
data1_fix## X1 X2
## 1 0.11840 0.27760
## 2 0.08474 0.07864
## 3 0.10960 0.15990
## 4 0.14250 0.28390
## 5 0.10030 0.13280
## 6 0.12780 0.17000
## 7 0.09463 0.10900
## 8 0.11890 0.16450
## 9 0.12730 0.19320
## 10 0.11860 0.23960
## 11 0.08206 0.06669
## 12 0.09710 0.12920
## 13 0.09740 0.24580
## 14 0.08401 0.10020
## 15 0.11310 0.22930
## 16 0.11390 0.15950
## 17 0.09867 0.07200
## 18 0.11700 0.20220
## 19 0.09831 0.10270
## 20 0.09779 0.08129
## 21 0.10750 0.12700
## 22 0.10240 0.06492
## 23 0.10730 0.21350
## 24 0.09428 0.10220
## 25 0.11210 0.14570
## 26 0.11860 0.22760
## 27 0.10540 0.18680
## 28 0.09440 0.10660
## 29 0.10820 0.16970
## 30 0.09847 0.11570
## 31 0.10640 0.18870
## 32 0.11090 0.15160
## 33 0.11970 0.14960
## 34 0.09401 0.17190
## 35 0.10400 0.15590
## 36 0.09610 0.13360
## 37 0.09823 0.10980
## 38 0.08983 0.03766
## 39 0.09387 0.05131
## 40 0.10160 0.12550
## 41 0.08162 0.06031
## 42 0.12270 0.12180
## 43 0.09081 0.21900
## 44 0.10410 0.14360
## 45 0.09714 0.10470
## 46 0.10990 0.16860
## 47 0.08600 0.05943
## 48 0.11580 0.12310
## 49 0.10310 0.09092
## 50 0.08752 0.07698
## 51 0.08637 0.04966
## 52 0.07685 0.06059
## 53 0.08261 0.04751
## 54 0.11480 0.14850
## 55 0.09056 0.07081
## 56 0.09524 0.05473
## 57 0.10530 0.12670
## 58 0.11370 0.13650
## 59 0.08060 0.03789
## 60 0.09752 0.05272
## 61 0.11340 0.08061
## 62 0.12430 0.08963
## 63 0.10490 0.20080
## 64 0.07721 0.08751
## 65 0.11220 0.12620
## 66 0.11720 0.14790
## 67 0.10440 0.07773
## 68 0.08139 0.04701
## 69 0.10660 0.14130
## 70 0.09831 0.05234
## 71 0.09009 0.10290
## 72 0.09783 0.15310
## 73 0.10710 0.18300
## 74 0.10070 0.12800
## 75 0.09172 0.06829
## 76 0.09168 0.08424
## 77 0.12910 0.10470
## 78 0.10650 0.21460
## 79 0.12860 0.34540
## 80 0.09934 0.09546
## 81 0.11020 0.09362
## 82 0.10780 0.15350
## 83 0.10630 0.26650
## 84 0.12150 0.17910
## 85 0.09723 0.07165
## 86 0.09874 0.10530
## 87 0.09444 0.09947
## 88 0.09029 0.12060
## 89 0.08772 0.09445
## 90 0.11320 0.13390
## 91 0.08974 0.08606
## 92 0.09200 0.10360
## 93 0.07355 0.05055
## 94 0.10220 0.08165
## 95 0.10390 0.15530
## 96 0.09078 0.13130
## 97 0.10450 0.07057
## 98 0.10240 0.05301
## 99 0.08983 0.07525
## 100 0.09752 0.11410
## 101 0.09488 0.08511
## 102 0.11700 0.07568
## 103 0.08013 0.04038
## 104 0.10050 0.09697
## 105 0.09989 0.08578
## 106 0.13980 0.17650
## 107 0.11420 0.10170
## 108 0.08477 0.06815
## 109 0.13260 0.27680
## 110 0.08759 0.06575
## 111 0.10370 0.08404
## 112 0.09933 0.12090
## 113 0.07837 0.22330
## 114 0.11220 0.13030
## 115 0.11500 0.08201
## 116 0.09768 0.07849
## 117 0.09462 0.12430
## 118 0.11620 0.16490
## 119 0.11550 0.17520
## 120 0.08402 0.06722
## 121 0.09373 0.06685
## 122 0.10540 0.11000
## 123 0.14470 0.28670
## 124 0.11010 0.10990
## 125 0.07115 0.07325
## 126 0.08785 0.06136
## 127 0.09258 0.07862
## 128 0.08217 0.08028
## 129 0.11500 0.18070
## 130 0.10150 0.15890
## 131 0.10660 0.09509
## 132 0.10920 0.12230
## 133 0.10080 0.12840
## 134 0.09462 0.09462
## 135 0.09430 0.09709
## 136 0.09055 0.05761
## 137 0.10510 0.06095
## 138 0.09639 0.06889
## 139 0.11670 0.13050
## 140 0.11640 0.11360
## 141 0.09250 0.04102
## 142 0.09721 0.11370
## 143 0.10920 0.09486
## 144 0.08677 0.09509
## 145 0.07793 0.05139
## 146 0.11520 0.12960
## 147 0.10910 0.17000
## 148 0.08138 0.11670
## 149 0.09970 0.10210
## 150 0.07944 0.06376
## 151 0.11350 0.07589
## 152 0.09405 0.13050
## 153 0.10720 0.15990
## 154 0.09754 0.05113
## 155 0.09384 0.08498
## 156 0.08654 0.06679
## 157 0.11150 0.16650
## 158 0.07445 0.07223
## 159 0.09311 0.05241
## 160 0.07515 0.03718
## 161 0.10890 0.11410
## 162 0.08694 0.11850
## 163 0.11200 0.16660
## 164 0.10120 0.10150
## 165 0.08439 0.11450
## 166 0.08421 0.05352
## 167 0.09594 0.05736
## 168 0.08865 0.09182
## 169 0.10490 0.16030
## 170 0.09855 0.07885
## 171 0.10280 0.06981
## 172 0.09048 0.06288
## 173 0.12570 0.15550
## 174 0.10060 0.05743
## 175 0.08792 0.04302
## 176 0.09138 0.04276
## 177 0.09699 0.12940
## 178 0.09831 0.15560
## 179 0.06251 0.01938
## 180 0.08739 0.03774
## 181 0.10940 0.19140
## 182 0.11410 0.28320
## 183 0.09597 0.08799
## 184 0.09059 0.08155
## 185 0.09057 0.10520
## 186 0.09267 0.04695
## 187 0.08588 0.08468
## 188 0.09774 0.06141
## 189 0.10070 0.05562
## 190 0.08080 0.07253
## 191 0.10750 0.24130
## 192 0.08749 0.06601
## 193 0.06950 0.02344
## 194 0.10340 0.13530
## 195 0.10440 0.19800
## 196 0.07941 0.05366
## 197 0.12000 0.12670
## 198 0.07371 0.08642
## 199 0.08523 0.14280
## 200 0.09872 0.12060
## 201 0.09586 0.08087
## 202 0.08968 0.11980
## 203 0.11410 0.20840
## 204 0.13230 0.17680
## 205 0.09965 0.10580
## 206 0.08876 0.09588
## 207 0.10890 0.07232
## 208 0.08772 0.07304
## 209 0.10020 0.14830
## 210 0.08182 0.06230
## 211 0.09090 0.13480
## 212 0.08871 0.06900
## 213 0.11420 0.15160
## 214 0.10060 0.11460
## 215 0.09463 0.13060
## 216 0.10260 0.15170
## 217 0.09363 0.11540
## 218 0.08054 0.05907
## 219 0.09383 0.13060
## 220 0.08420 0.11300
## 221 0.09646 0.08711
## 222 0.10510 0.11920
## 223 0.10610 0.08502
## 224 0.10250 0.12040
## 225 0.08445 0.04994
## 226 0.09906 0.07624
## 227 0.10530 0.07722
## 228 0.08371 0.10960
## 229 0.07903 0.07529
## 230 0.10880 0.17990
## 231 0.11410 0.15720
## 232 0.06883 0.03813
## 233 0.07780 0.03574
## 234 0.09159 0.10740
## 235 0.08464 0.04087
## 236 0.09070 0.06945
## 237 0.09509 0.16820
## 238 0.08355 0.08348
## 239 0.08223 0.10390
## 240 0.09812 0.12980
## 241 0.09423 0.06630
## 242 0.07926 0.03393
## 243 0.09592 0.13250
## 244 0.08043 0.06807
## 245 0.10270 0.15580
## 246 0.10700 0.05971
## 247 0.07215 0.04524
## 248 0.08760 0.13460
## 249 0.09657 0.07234
## 250 0.10130 0.07808
## 251 0.10070 0.16060
## 252 0.09345 0.05991
## 253 0.10620 0.18490
## 254 0.10080 0.10410
## 255 0.10350 0.11880
## 256 0.10960 0.12790
## 257 0.09260 0.20630
## 258 0.13350 0.22840
## 259 0.11090 0.31140
## 260 0.10630 0.16390
## 261 0.10000 0.10880
## 262 0.08662 0.06290
## 263 0.08999 0.12730
## 264 0.07840 0.05616
## 265 0.09726 0.08995
## 266 0.09469 0.11430
## 267 0.09688 0.11470
## 268 0.07956 0.08259
## 269 0.09425 0.06219
## 270 0.10820 0.12890
## 271 0.06429 0.02675
## 272 0.09834 0.07608
## 273 0.09401 0.19610
## 274 0.09037 0.04689
## 275 0.08855 0.07027
## 276 0.12250 0.07210
## 277 0.09379 0.03872
## 278 0.08923 0.05884
## 279 0.07948 0.04052
## 280 0.09516 0.07688
## 281 0.10200 0.14530
## 282 0.07813 0.04340
## 283 0.10370 0.14420
## 284 0.10660 0.18020
## 285 0.07818 0.09580
## 286 0.08393 0.04216
## 287 0.08605 0.10110
## 288 0.06955 0.03729
## 289 0.08020 0.11810
## 290 0.08713 0.05008
## 291 0.08757 0.16760
## 292 0.08992 0.09823
## 293 0.10050 0.07943
## 294 0.08372 0.05642
## 295 0.09667 0.08393
## 296 0.09198 0.06221
## 297 0.08518 0.04721
## 298 0.09968 0.05914
## 299 0.06576 0.05220
## 300 0.10150 0.06797
## 301 0.11500 0.16420
## 302 0.08451 0.10140
## 303 0.10800 0.18380
## 304 0.10680 0.06678
## 305 0.08853 0.07694
## 306 0.07474 0.05688
## 307 0.08511 0.05251
## 308 0.07005 0.03116
## 309 0.07376 0.03614
## 310 0.08352 0.03735
## 311 0.08814 0.05253
## 312 0.07618 0.03515
## 313 0.08794 0.07948
## 314 0.08597 0.05969
## 315 0.10740 0.05847
## 316 0.08511 0.03834
## 317 0.07734 0.03212
## 318 0.09746 0.11170
## 319 0.09968 0.19720
## 320 0.07557 0.03454
## 321 0.10610 0.11110
## 322 0.08020 0.08564
## 323 0.11340 0.08834
## 324 0.11700 0.18750
## 325 0.08673 0.06545
## 326 0.10280 0.07664
## 327 0.09309 0.05306
## 328 0.07683 0.03892
## 329 0.11690 0.13190
## 330 0.11650 0.12830
## 331 0.09491 0.13710
## 332 0.09579 0.11250
## 333 0.10540 0.06779
## 334 0.08306 0.04458
## 335 0.08313 0.04202
## 336 0.11190 0.10560
## 337 0.09462 0.09965
## 338 0.09116 0.14020
## 339 0.10070 0.07326
## 340 0.10690 0.12830
## 341 0.09751 0.11390
## 342 0.08481 0.09228
## 343 0.10330 0.09097
## 344 0.09797 0.13390
## 345 0.11500 0.07281
## 346 0.09882 0.09159
## 347 0.08386 0.05794
## 348 0.08875 0.07780
## 349 0.09076 0.05886
## 350 0.11580 0.12060
## 351 0.07561 0.03630
## 352 0.12430 0.23640
## 353 0.11490 0.23630
## 354 0.10240 0.09769
## 355 0.07274 0.06064
## 356 0.08760 0.10380
## 357 0.10820 0.13040
## 358 0.08743 0.05492
## 359 0.08293 0.07698
## 360 0.10090 0.05956
## 361 0.07436 0.02650
## 362 0.08582 0.06373
## 363 0.09676 0.07952
## 364 0.09686 0.08468
## 365 0.07937 0.05696
## 366 0.09150 0.11310
## 367 0.09905 0.16690
## 368 0.09231 0.07175
## 369 0.09384 0.08562
## 370 0.10630 0.19540
## 371 0.09742 0.14970
## 372 0.07963 0.06934
## 373 0.10010 0.15150
## 374 0.09446 0.10760
## 375 0.08302 0.06374
## 376 0.09880 0.14380
## 377 0.09073 0.16600
## 378 0.07517 0.04726
## 379 0.08268 0.07548
## 380 0.12160 0.21540
## 381 0.12370 0.11110
## 382 0.07987 0.07079
## 383 0.06935 0.10730
## 384 0.10420 0.12970
## 385 0.08363 0.08575
## 386 0.08682 0.06636
## 387 0.08108 0.07823
## 388 0.07026 0.04831
## 389 0.08365 0.11140
## 390 0.10100 0.13180
## 391 0.09996 0.07542
## 392 0.10390 0.07428
## 393 0.11600 0.15620
## 394 0.11670 0.20870
## 395 0.10290 0.09758
## 396 0.08045 0.05361
## 397 0.10590 0.11470
## 398 0.08044 0.08895
## 399 0.07741 0.04768
## 400 0.09087 0.06232
## 401 0.12300 0.25760
## 402 0.08872 0.05242
## 403 0.07351 0.07899
## 404 0.09879 0.08836
## 405 0.08682 0.04571
## 406 0.10040 0.07460
## 407 0.09495 0.08501
## 408 0.07551 0.08316
## 409 0.10360 0.13040
## 410 0.08685 0.06526
## 411 0.08858 0.05313
## 412 0.10770 0.07804
## 413 0.07969 0.06053
## 414 0.08515 0.10250
## 415 0.08320 0.04605
## 416 0.09773 0.08120
## 417 0.10440 0.06159
## 418 0.11200 0.15710
## 419 0.08785 0.05794
## 420 0.10180 0.05978
## 421 0.08546 0.07722
## 422 0.10310 0.18360
## 423 0.10880 0.11680
## 424 0.09057 0.11470
## 425 0.10750 0.08333
## 426 0.08117 0.03912
## 427 0.09816 0.10130
## 428 0.08801 0.05743
## 429 0.08151 0.03834
## 430 0.07896 0.04522
## 431 0.09947 0.22250
## 432 0.10540 0.13160
## 433 0.11330 0.14890
## 434 0.10180 0.13890
## 435 0.08924 0.07074
## 436 0.10600 0.11330
## 437 0.09136 0.07883
## 438 0.08458 0.05895
## 439 0.08684 0.06330
## 440 0.07966 0.05581
## 441 0.08915 0.11130
## 442 0.08331 0.11090
## 443 0.08817 0.06718
## 444 0.08142 0.04462
## 445 0.08947 0.12320
## 446 0.10300 0.09218
## 447 0.09997 0.13140
## 448 0.09179 0.08890
## 449 0.08388 0.07800
## 450 0.09684 0.11750
## 451 0.06613 0.10640
## 452 0.10320 0.09871
## 453 0.08437 0.06450
## 454 0.10990 0.09242
## 455 0.08583 0.05430
## 456 0.09245 0.07426
## 457 0.09357 0.08574
## 458 0.08791 0.05205
## 459 0.08369 0.05073
## 460 0.07984 0.04626
## 461 0.09898 0.11100
## 462 0.10840 0.19880
## 463 0.06995 0.05223
## 464 0.08508 0.05855
## 465 0.07466 0.05994
## 466 0.08284 0.12230
## 467 0.08675 0.10890
## 468 0.08311 0.05428
## 469 0.09289 0.20040
## 470 0.11750 0.14830
## 471 0.08946 0.06258
## 472 0.08752 0.06000
## 473 0.08098 0.08549
## 474 0.07699 0.03398
## 475 0.10070 0.10690
## 476 0.09040 0.08269
## 477 0.08931 0.11080
## 478 0.06828 0.05319
## 479 0.10460 0.08228
## 480 0.10260 0.18930
## 481 0.09087 0.07838
## 482 0.07991 0.05326
## 483 0.10710 0.11550
## 484 0.09950 0.07957
## 485 0.10430 0.12990
## 486 0.09514 0.15110
## 487 0.08641 0.06698
## 488 0.10890 0.14480
## 489 0.11280 0.09263
## 490 0.07497 0.07112
## 491 0.08192 0.05200
## 492 0.07838 0.06217
## 493 0.10010 0.12890
## 494 0.07372 0.04043
## 495 0.07335 0.05275
## 496 0.09587 0.08345
## 497 0.10760 0.13340
## 498 0.08928 0.07630
## 499 0.10120 0.13170
## 500 0.10850 0.16440
## 501 0.09883 0.13640
## 502 0.11620 0.16810
## 503 0.11580 0.10850
## 504 0.09342 0.12750
## 505 0.16340 0.22390
## 506 0.12550 0.22040
## 507 0.10960 0.11520
## 508 0.11940 0.10710
## 509 0.09427 0.06712
## 510 0.11830 0.18700
## 511 0.08099 0.09661
## 512 0.08472 0.05016
## 513 0.11060 0.14690
## 514 0.09832 0.08918
## 515 0.09215 0.08597
## 516 0.10490 0.08499
## 517 0.10680 0.12480
## 518 0.10370 0.13100
## 519 0.12180 0.16610
## 520 0.11250 0.11170
## 521 0.13710 0.12250
## 522 0.10300 0.21060
## 523 0.08511 0.04413
## 524 0.09916 0.10700
## 525 0.09492 0.08419
## 526 0.10360 0.07632
## 527 0.10750 0.11380
## 528 0.09003 0.06307
## 529 0.12480 0.09755
## 530 0.11000 0.09009
## 531 0.10730 0.09713
## 532 0.10160 0.09453
## 533 0.09277 0.07255
## 534 0.09156 0.13130
## 535 0.09687 0.09752
## 536 0.10460 0.17390
## 537 0.10380 0.11540
## 538 0.12360 0.15520
## 539 0.08098 0.04878
## 540 0.08668 0.11990
## 541 0.09984 0.11200
## 542 0.08837 0.12300
## 543 0.08275 0.07214
## 544 0.08671 0.06877
## 545 0.09578 0.10180
## 546 0.09246 0.06747
## 547 0.09434 0.04994
## 548 0.08877 0.08066
## 549 0.08491 0.05030
## 550 0.08192 0.06602
## 551 0.07431 0.04227
## 552 0.09566 0.08194
## 553 0.08276 0.04234
## 554 0.09240 0.05605
## 555 0.08123 0.05824
## 556 0.09030 0.07658
## 557 0.10030 0.07504
## 558 0.08123 0.04971
## 559 0.08473 0.13300
## 560 0.09261 0.10210
## 561 0.09929 0.11260
## 562 0.07449 0.03558
## 563 0.10480 0.20870
## 564 0.10990 0.22360
## 565 0.11100 0.11590
## 566 0.09780 0.10340
## 567 0.08455 0.10230
## 568 0.11780 0.27700
## 569 0.05263 0.04362library(MVN)## Warning: package 'MVN' was built under R version 4.3.3test = mvn(data1_fix, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq")
test## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 183.764023308911 1.15899340618412e-38 NO
## 2 Mardia Kurtosis 10.3892333316892 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk X1 0.9875 1e-04 NO
## 2 Shapiro-Wilk X2 0.9170 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th Skew
## X1 569 0.09636028 0.01406413 0.09587 0.05263 0.1634 0.08637 0.1053 0.4539207
## X2 569 0.10434098 0.05281276 0.09263 0.01938 0.3454 0.06492 0.1304 1.1838556
## Kurtosis
## X1 0.8244671
## X2 1.6088967
Secara eksploratif, dapat terlihat bahwa terdapat penyimpangan yang cukup besar antara titik-titik data dengan garis. Selain itu, hasil tes Mardia juga menunjukkan bahwa data tidak berdistribusi normal multivariat. Oleh karena itu, akan dilakukan transformasi data.
X1 <- log(data1$smoothness_mean)
X2 <- log(data1$compactness_mean)
data2_fix <- data.frame(cbind(X1,X2))
data2_fix## X1 X2
## 1 -2.133687 -1.281574
## 2 -2.468168 -2.542875
## 3 -2.210918 -1.833207
## 4 -1.948413 -1.259133
## 5 -2.299590 -2.018911
## 6 -2.057289 -1.771957
## 7 -2.357781 -2.216407
## 8 -2.129472 -1.804845
## 9 -2.061209 -1.644029
## 10 -2.131999 -1.428784
## 11 -2.500305 -2.707700
## 12 -2.332014 -2.046394
## 13 -2.328929 -1.403237
## 14 -2.476819 -2.300587
## 15 -2.179483 -1.472724
## 16 -2.172434 -1.835711
## 17 -2.315974 -2.631089
## 18 -2.145581 -1.598498
## 19 -2.319630 -2.275943
## 20 -2.324933 -2.509732
## 21 -2.230264 -2.063568
## 22 -2.278869 -2.734600
## 23 -2.232127 -1.544118
## 24 -2.361486 -2.280824
## 25 -2.188364 -1.926206
## 26 -2.131999 -1.480166
## 27 -2.249993 -1.677717
## 28 -2.360214 -2.238672
## 29 -2.223774 -1.773723
## 30 -2.318003 -2.156755
## 31 -2.240550 -1.667597
## 32 -2.199126 -1.886510
## 33 -2.122767 -1.899790
## 34 -2.364354 -1.760842
## 35 -2.263364 -1.858541
## 36 -2.342366 -2.012905
## 37 -2.320444 -2.209095
## 38 -2.409836 -3.279157
## 39 -2.365844 -2.969870
## 40 -2.286712 -2.075450
## 41 -2.505681 -2.808257
## 42 -2.098013 -2.105375
## 43 -2.398986 -1.518684
## 44 -2.262403 -1.940724
## 45 -2.331602 -2.256656
## 46 -2.208184 -1.780226
## 47 -2.453408 -2.822956
## 48 -2.155891 -2.094758
## 49 -2.272056 -2.397775
## 50 -2.435888 -2.564210
## 51 -2.449115 -3.002555
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## 53 -2.493625 -3.046815
## 54 -2.164564 -1.907170
## 55 -2.401743 -2.647755
## 56 -2.351355 -2.905343
## 57 -2.250942 -2.065933
## 58 -2.174192 -1.991431
## 59 -2.518257 -3.273068
## 60 -2.327698 -2.942760
## 61 -2.176834 -2.518133
## 62 -2.085057 -2.412065
## 63 -2.254748 -1.605446
## 64 -2.561226 -2.436002
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## 502 -2.152442 -1.783196
## 503 -2.155891 -2.221005
## 504 -2.370650 -2.059639
## 505 -1.811554 -1.496556
## 506 -2.075450 -1.512311
## 507 -2.210918 -2.161086
## 508 -2.125276 -2.233992
## 509 -2.361592 -2.701273
## 510 -2.134532 -1.676647
## 511 -2.513430 -2.337073
## 512 -2.468404 -2.992537
## 513 -2.201835 -1.918003
## 514 -2.319528 -2.417098
## 515 -2.384338 -2.453757
## 516 -2.254748 -2.465222
## 517 -2.236797 -2.081043
## 518 -2.266253 -2.032558
## 519 -2.105375 -1.795165
## 520 -2.184802 -2.191939
## 521 -1.987045 -2.099644
## 522 -2.273026 -1.557795
## 523 -2.463811 -3.120615
## 524 -2.311021 -2.234926
## 525 -2.354721 -2.474679
## 526 -2.267218 -2.572820
## 527 -2.230264 -2.173313
## 528 -2.407612 -2.763510
## 529 -2.081043 -2.327390
## 530 -2.207275 -2.406946
## 531 -2.232127 -2.331705
## 532 -2.286712 -2.358838
## 533 -2.377632 -2.623479
## 534 -2.390761 -2.030270
## 535 -2.334385 -2.327698
## 536 -2.257612 -1.749275
## 537 -2.265289 -2.159351
## 538 -2.090705 -1.863041
## 539 -2.513553 -3.020435
## 540 -2.445532 -2.121097
## 541 -2.304186 -2.189256
## 542 -2.426223 -2.095571
## 543 -2.491931 -2.629147
## 544 -2.445186 -2.676988
## 545 -2.345701 -2.284745
## 546 -2.380979 -2.696072
## 547 -2.360850 -2.996933
## 548 -2.421707 -2.517512
## 549 -2.466163 -2.989750
## 550 -2.502012 -2.717798
## 551 -2.599510 -3.163678
## 552 -2.346955 -2.501768
## 553 -2.491810 -3.162023
## 554 -2.381628 -2.881511
## 555 -2.510471 -2.843183
## 556 -2.404618 -2.569419
## 557 -2.299590 -2.589734
## 558 -2.510471 -3.001549
## 559 -2.468286 -2.017406
## 560 -2.379358 -2.281803
## 561 -2.309710 -2.183914
## 562 -2.597090 -3.335972
## 563 -2.255702 -1.566857
## 564 -2.208184 -1.497897
## 565 -2.198225 -2.155028
## 566 -2.324831 -2.269150
## 567 -2.470412 -2.279846
## 568 -2.138767 -1.283738
## 569 -2.944469 -3.132240test = mvn(data2_fix, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq")
test## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 5.38450637342627 0.250069526119044 YES
## 2 Mardia Kurtosis 1.47864509793058 0.139235192870837 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk X1 0.9971 0.4096 YES
## 2 Shapiro-Wilk X2 0.9965 0.2533 YES
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## X1 569 -2.350210 0.1455718 -2.344762 -2.944469 -1.811554 -2.449115 -2.250942
## X2 569 -2.380518 0.4944591 -2.379142 -3.943514 -1.063052 -2.734600 -2.037149
## Skew Kurtosis
## X1 -0.06745920 0.3644211
## X2 -0.03390649 -0.3788768
Setelah melalui transformasi, dapat terlihat bahwa titik-titik data sudah tidak menyimpang secara jauh lagi dengan garis. Selain itu, hasil tes Mardia juga menunjukkan bahwa data telah berdistribusi normal multivariat. Sehingga, uji asumsi normalitas terpenuhi.
UJI HOMOGENITAS
Uji homogenitas digunakan untuk menguji apakah dua atau lebih kelompok memiliki matriks kovarians yang sama untuk beberapa variabel terikat.
library(biotools)## Warning: package 'biotools' was built under R version 4.3.3## Loading required package: MASS## ---
## biotools version 4.2Y <- data1$diagnosis
boxM(data = data2_fix, grouping = Y)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data2_fix
## Chi-Sq (approx.) = 21.951, df = 3, p-value = 6.679e-05Berdasarkan hasil uji Box’s M, didapatkan hasil p-value < alpha sehingga H0 ditolak. Oleh karena itu, terdeteksi gejala heteroskedastisitas dalam data dan data perlu ditransformasi.
library(dplyr)## Warning: package 'dplyr' was built under R version 4.3.3##
## Attaching package: 'dplyr'## The following object is masked from 'package:MASS':
##
## select## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionnum <- data.frame(diagnosis=c("M","B"))
num <- data1 %>%
mutate(numerik=recode(diagnosis,
"M"=0,
"B"=1))
model <- glm(num$numerik~X1+X2, data=data1, family=binomial)
summary(model)##
## Call:
## glm(formula = num$numerik ~ X1 + X2, family = binomial, data = data1)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.5194 2.0659 -2.672 0.00755 **
## X1 1.5689 1.0431 1.504 0.13257
## X2 -4.2320 0.4054 -10.440 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 751.44 on 568 degrees of freedom
## Residual deviance: 500.57 on 566 degrees of freedom
## AIC: 506.57
##
## Number of Fisher Scoring iterations: 5predicted_probabilities <- predict(model,type="response")
Y <- cut(predicted_probabilities,
breaks=c(0,0.627,1.354),
labels=c("B", "M"),
right=TRUE)
boxM(data = data2_fix, grouping = as.factor(Y))##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data2_fix
## Chi-Sq (approx.) = 4.8456, df = 3, p-value = 0.1835Setelah melalui transformasi, diperoleh p-value yang baru yaitu 0.1835 > alpha sehingga H0 diterima. Oleh karena itu, dapat disimpulkan bahwa gejala heteroskedastisitas telah teratasi dan asumsi homoskedastisitas terpenuhi.
ONE WAY MANOVA
data_manova <- data.frame(X1, X2, Y)
owm <- manova(cbind(X1, X2) ~ Y, data=data_manova)
summary(owm)## Df Pillai approx F num Df den Df Pr(>F)
## Y 1 0.67283 581.99 2 566 < 2.2e-16 ***
## Residuals 567
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Berdasarkan hasil analisis varians multivariat tersebut, diperoleh sebuah kesimpulan bahwa terdapat variabel bebas yang memiliki pengaruh signifikan terhadap variabel terikat. Oleh karena itu, perlu dilakukan uji lanjut.
UJI LANJUT
summary.aov(owm)## Response X1 :
## Df Sum Sq Mean Sq F value Pr(>F)
## Y 1 2.8456 2.84561 175.55 < 2.2e-16 ***
## Residuals 567 9.1910 0.01621
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Response X2 :
## Df Sum Sq Mean Sq F value Pr(>F)
## Y 1 91.994 91.994 1112.7 < 2.2e-16 ***
## Residuals 567 46.877 0.083
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Berdasarkan hasil uji lanjut Post Hoc Test tersebut, diperoleh kesimpulan bahwa kedua variabel X1 (Rata-rata smoothness) dan variabel X2(Rata-rata compactness) memiliki pengaruh yang signifikan terhadap Y (Diagnosis Kanker payudara).
DATASET TWO WAY
Dataset ini berisi informasi kesehatan yang luas untuk 2.149 pasien, masing-masing diidentifikasi secara unik dengan ID mulai dari 4751 hingga 6900. Dataset ini mencakup rincian demografis, faktor gaya hidup, riwayat kesehatan, pengukuran klinis, penilaian kognitif dan fungsional, gejala, dan diagnosis Penyakit Alzheimer.
data2 <- read.csv("data2.csv")
head(data2)## PatientID Age Gender Ethnicity EducationLevel BMI Smoking
## 1 4751 73 0 0 2 22.92775 0
## 2 4752 89 0 0 0 26.82768 0
## 3 4753 73 0 3 1 17.79588 0
## 4 4754 74 1 0 1 33.80082 1
## 5 4755 89 0 0 0 20.71697 0
## 6 4756 86 1 1 1 30.62689 0
## AlcoholConsumption PhysicalActivity DietQuality SleepQuality
## 1 13.297218 6.3271125 1.3472143 9.025679
## 2 4.542524 7.6198845 0.5187671 7.151293
## 3 19.555085 7.8449878 1.8263347 9.673574
## 4 12.209266 8.4280014 7.4356041 8.392554
## 5 18.454356 6.3104607 0.7954975 5.597238
## 6 4.140144 0.2110616 1.5849220 7.261953
## FamilyHistoryAlzheimers CardiovascularDisease Diabetes Depression HeadInjury
## 1 0 0 1 1 0
## 2 0 0 0 0 0
## 3 1 0 0 0 0
## 4 0 0 0 0 0
## 5 0 0 0 0 0
## 6 0 0 1 0 0
## Hypertension SystolicBP DiastolicBP CholesterolTotal CholesterolLDL
## 1 0 142 72 242.3668 56.15090
## 2 0 115 64 231.1626 193.40800
## 3 0 99 116 284.1819 153.32276
## 4 0 118 115 159.5822 65.36664
## 5 0 94 117 237.6022 92.86970
## 6 0 168 62 280.7125 198.33463
## CholesterolHDL CholesterolTriglycerides MMSE FunctionalAssessment
## 1 33.68256 162.18914 21.463532 6.518877
## 2 79.02848 294.63091 20.613267 7.118696
## 3 69.77229 83.63832 7.356249 5.895077
## 4 68.45749 277.57736 13.991127 8.965106
## 5 56.87430 291.19878 13.517609 6.045039
## 6 79.08050 263.94365 27.517529 5.510144
## MemoryComplaints BehavioralProblems ADL Confusion Disorientation
## 1 0 0 1.72588346 0 0
## 2 0 0 2.59242413 0 0
## 3 0 0 7.11954774 0 1
## 4 0 1 6.48122586 0 0
## 5 0 0 0.01469122 0 0
## 6 0 0 9.01568628 1 0
## PersonalityChanges DifficultyCompletingTasks Forgetfulness Diagnosis
## 1 0 1 0 0
## 2 0 0 1 0
## 3 0 1 0 0
## 4 0 0 0 0
## 5 1 1 0 0
## 6 0 0 0 0
## DoctorInCharge
## 1 XXXConfid
## 2 XXXConfid
## 3 XXXConfid
## 4 XXXConfid
## 5 XXXConfid
## 6 XXXConfidUJI NORMALITAS
data1_fix2 <- data.frame(cbind(data2$PhysicalActivity,data2$SleepQuality))
data1_fix2## X1 X2
## 1 6.327112474 9.025679
## 2 7.619884540 7.151293
## 3 7.844987791 9.673574
## 4 8.428001350 8.392554
## 5 6.310460689 5.597238
## 6 0.211061631 7.261953
## 7 9.257694910 5.477686
## 8 4.649450668 4.213210
## 9 1.531359788 5.748224
## 10 6.440772687 7.551773
## 11 8.819950351 7.644097
## 12 3.834639382 8.312326
## 13 3.978078872 8.253005
## 14 0.631280727 7.333236
## 15 9.714565829 9.087141
## 16 2.956494729 6.736797
## 17 7.182894555 4.654828
## 18 1.306320412 5.436423
## 19 7.127939893 6.790196
## 20 4.060713917 7.393126
## 21 6.381502407 9.521027
## 22 9.126038218 9.574005
## 23 7.676580404 9.250389
## 24 6.934726371 4.412596
## 25 7.198931183 6.732595
## 26 8.939248659 9.582177
## 27 6.509781497 5.797064
## 28 9.986553927 6.090394
## 29 0.442690864 7.869068
## 30 5.292522976 8.391243
## 31 8.172444166 7.686632
## 32 7.780543611 6.744820
## 33 7.731579822 5.621529
## 34 7.905611793 9.018246
## 35 5.013303852 6.164646
## 36 3.769174562 4.872168
## 37 3.985612824 8.810729
## 38 4.773199920 5.539086
## 39 4.005685760 6.046635
## 40 3.831908858 8.833341
## 41 3.613763603 4.938171
## 42 3.690074973 7.255963
## 43 3.759919282 5.532066
## 44 2.915573105 9.741159
## 45 4.581855185 9.999201
## 46 1.225182426 6.715982
## 47 0.930558096 8.473919
## 48 0.307673697 5.720985
## 49 9.338357919 8.204619
## 50 3.599932511 5.123009
## 51 6.848293354 8.353761
## 52 1.230084068 8.232079
## 53 6.578338283 7.981846
## 54 9.859541546 9.710274
## 55 8.194583994 8.554071
## 56 8.117289817 4.137893
## 57 8.030965822 9.527303
## 58 0.785802296 4.580381
## 59 6.034843146 5.912972
## 60 9.673810277 7.621481
## 61 6.539632391 9.470753
## 62 8.153139134 6.551533
## 63 2.308566553 4.074439
## 64 0.825491352 9.986318
## 65 3.690136810 8.561219
## 66 1.353521832 5.208674
## 67 0.094837670 9.383941
## 68 8.731341357 4.231688
## 69 3.441452426 5.966402
## 70 3.877091637 6.062905
## 71 4.855611503 7.988010
## 72 8.492193835 5.547509
## 73 9.985068848 7.561233
## 74 0.119480851 5.397002
## 75 4.810866399 8.371714
## 76 9.861258410 8.303338
## 77 8.112291312 5.949474
## 78 9.277794334 8.900769
## 79 1.915913436 6.146166
## 80 5.204411588 5.112512
## 81 8.784313445 5.528365
## 82 0.954071963 8.066368
## 83 6.438980427 9.209427
## 84 7.639779986 4.213680
## 85 5.525953087 9.768864
## 86 4.012125565 7.040055
## 87 7.789202728 5.278123
## 88 5.328581148 6.160692
## 89 0.826220365 8.467348
## 90 8.596946094 9.623875
## 91 5.369292726 7.092991
## 92 8.072807244 9.078879
## 93 2.973493710 6.090990
## 94 5.487732366 6.271848
## 95 8.152379678 8.197573
## 96 3.835697960 8.395433
## 97 2.519586929 5.196521
## 98 5.141054570 8.114125
## 99 2.948416556 6.145350
## 100 3.754985346 9.800457
## 101 0.480427759 4.179465
## 102 0.413137686 7.673755
## 103 8.594595563 6.055814
## 104 1.006976654 9.382493
## 105 0.371613269 5.710992
## 106 4.099069626 5.970889
## 107 0.221694561 7.965445
## 108 9.129938879 9.774264
## 109 6.293358538 8.890280
## 110 3.722786069 5.401475
## 111 6.224811709 5.847681
## 112 2.904978948 9.400619
## 113 1.032838031 9.162086
## 114 8.860267774 8.776682
## 115 5.154916287 4.738132
## 116 9.208989544 8.974868
## 117 5.371700899 8.054286
## 118 4.382984750 5.009484
## 119 1.477053154 7.471878
## 120 8.269198501 9.736569
## 121 0.285509630 7.682910
## 122 2.677443039 8.940403
## 123 3.434712218 6.864591
## 124 2.687728983 8.384602
## 125 3.024630635 8.863253
## 126 1.299438892 8.193919
## 127 8.382785448 6.279817
## 128 4.550097986 6.885777
## 129 4.776335486 5.980217
## 130 0.835944539 5.314997
## 131 9.495844194 7.976353
## 132 3.759815129 9.636811
## 133 8.287726559 4.560836
## 134 8.484430438 4.918901
## 135 1.895187761 8.794595
## 136 7.902595613 7.123508
## 137 3.697976576 5.177030
## 138 6.941537038 9.514376
## 139 7.932129774 6.244616
## 140 4.079767747 8.945354
## 141 4.719271867 4.214772
## 142 4.347627047 9.983429
## 143 7.734304948 9.370081
## 144 3.365452018 7.294820
## 145 7.877661114 4.056827
## 146 2.850125099 4.336467
## 147 4.860084547 8.842697
## 148 6.145030222 6.267036
## 149 6.893605137 5.192307
## 150 7.015328513 8.549867
## 151 6.615995912 7.512128
## 152 6.986113659 6.457284
## 153 8.410063363 8.847995
## 154 5.588130079 7.614823
## 155 5.621272926 4.664539
## 156 7.823262493 6.145071
## 157 2.723938104 8.579315
## 158 1.951928614 6.700508
## 159 3.838677524 6.396638
## 160 6.065147916 9.302614
## 161 5.109163018 8.634986
## 162 0.664529148 5.863166
## 163 0.068538626 7.582172
## 164 1.455640024 5.254171
## 165 3.654345179 9.775854
## 166 2.524450734 8.047720
## 167 4.437512568 5.128130
## 168 5.142474585 8.047322
## 169 3.598203487 8.015484
## 170 0.404029098 6.336383
## 171 5.226966648 7.906201
## 172 2.244523115 4.231904
## 173 8.312775801 6.491371
## 174 2.862376937 7.440153
## 175 7.634173993 5.453490
## 176 4.036442044 4.681225
## 177 4.191025868 9.068296
## 178 5.141069382 9.630179
## 179 3.698666792 9.779705
## 180 3.174277087 9.156386
## 181 5.957518976 7.708648
## 182 4.867640414 9.223368
## 183 4.427868031 5.277152
## 184 7.489578800 9.586542
## 185 7.869849736 7.819307
## 186 4.293537665 6.780675
## 187 5.601585140 9.509201
## 188 6.417288761 5.917599
## 189 9.296853839 5.069082
## 190 7.442755354 6.098710
## 191 8.027074916 8.063561
## 192 1.927921477 7.694272
## 193 3.961081178 8.660614
## 194 3.247181265 7.345049
## 195 9.947909587 5.520566
## 196 8.847971683 6.915031
## 197 3.716346849 4.808708
## 198 9.095152050 4.457428
## 199 2.041589327 8.542215
## 200 9.874974891 9.443387
## 201 4.236013001 5.018263
## 202 6.729113936 6.518285
## 203 7.184832376 5.430601
## 204 4.019272802 4.511288
## 205 0.183676594 9.393881
## 206 3.410777046 4.470068
## 207 8.399828228 8.807932
## 208 6.411627158 9.292147
## 209 5.172226479 9.379209
## 210 1.141677173 9.625827
## 211 7.614818072 9.274465
## 212 3.688410293 4.097670
## 213 6.900270615 4.248309
## 214 1.648362186 9.041231
## 215 0.740275029 9.940734
## 216 4.070773396 8.551496
## 217 0.966281971 4.140628
## 218 3.729816632 4.439974
## 219 9.923465322 7.047064
## 220 2.707950018 8.278827
## 221 4.190688672 9.655139
## 222 5.837506161 9.524950
## 223 2.859660320 7.973566
## 224 2.621373480 4.008685
## 225 7.222447762 8.931011
## 226 8.017559021 9.135239
## 227 1.119192741 6.029848
## 228 2.041521316 4.784848
## 229 1.317515769 4.268992
## 230 3.983000505 6.011145
## 231 6.075934125 9.230261
## 232 6.290657010 8.373843
## 233 5.025370305 7.787134
## 234 8.487712387 8.817635
## 235 4.235300492 6.638249
## 236 9.245893310 7.992121
## 237 2.632073566 6.896321
## 238 2.832794424 8.060910
## 239 5.563494029 8.197667
## 240 7.008935605 7.249185
## 241 9.358457010 8.569030
## 242 0.446847864 5.028689
## 243 4.023315615 8.919390
## 244 6.184947663 4.148366
## 245 9.552671528 8.562963
## 246 4.198819059 9.688653
## 247 2.688289164 4.137831
## 248 4.150035356 6.613338
## 249 8.640588167 5.216097
## 250 7.876942742 7.940562
## 251 7.888661863 5.206453
## 252 9.750502979 4.965810
## 253 1.498316208 4.367016
## 254 7.489041573 9.610604
## 255 0.745796035 4.866378
## 256 8.148103768 8.207433
## 257 3.363867347 5.432648
## 258 0.308265500 6.626059
## 259 3.505157794 7.925109
## 260 7.586138268 9.344363
## 261 9.407802748 8.153921
## 262 1.131395574 8.775903
## 263 2.576861920 8.288394
## 264 6.363930513 7.629156
## 265 8.917377808 9.241849
## 266 2.387058891 9.296660
## 267 9.072189895 9.829565
## 268 6.926709494 9.618719
## 269 7.066063337 8.847289
## 270 5.275821942 6.856580
## 271 0.468020995 8.975142
## 272 2.887563401 8.848231
## 273 7.502017763 9.651808
## 274 3.986072147 4.704039
## 275 1.680897189 4.549808
## 276 8.087191249 9.453986
## 277 0.009347662 4.075574
## 278 9.049333575 7.090395
## 279 9.835367342 5.335816
## 280 8.638783743 5.599776
## 281 2.999611702 8.588591
## 282 2.740214504 9.833603
## 283 9.700076963 4.574615
## 284 3.857726756 8.924927
## 285 3.732647165 5.635608
## 286 0.959598869 4.547585
## 287 1.385895652 8.158511
## 288 7.904681843 7.201691
## 289 1.579762747 5.222151
## 290 6.484179432 7.988088
## 291 0.997862219 4.013579
## 292 5.099925362 6.740130
## 293 8.767568664 9.802415
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## 1850 3.170947417 4.346708
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## 1861 6.816821098 4.073752
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## 1870 2.168141581 4.715351
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## 1880 2.979994025 8.558910
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## 1883 6.429221734 5.052315
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## 1888 4.004900056 4.313828
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## 1890 0.135299620 4.152637
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## 1892 7.975633062 9.795459
## 1893 2.386598550 5.585371
## 1894 8.889825595 8.965095
## 1895 0.546067206 4.167289
## 1896 7.302839963 4.337330
## 1897 5.108983593 7.979993
## 1898 0.627307231 6.547717
## 1899 1.561771894 9.022263
## 1900 2.287715799 4.416581
## 1901 8.761610911 4.493132
## 1902 8.841834857 5.351304
## 1903 4.523844504 8.709108
## 1904 7.733203908 7.613761
## 1905 9.188524480 6.342495
## 1906 0.791471674 7.683601
## 1907 7.440545807 9.647424
## 1908 8.139960942 8.636694
## 1909 6.585358779 9.114924
## 1910 0.335384000 9.225077
## 1911 5.131833754 8.908367
## 1912 0.125202683 7.474802
## 1913 5.579025816 5.988642
## 1914 6.451099638 9.417279
## 1915 3.092963977 4.820024
## 1916 2.199039260 9.450911
## 1917 0.912922636 7.859771
## 1918 6.036596687 8.155943
## 1919 5.278284652 6.512568
## 1920 2.539822339 8.114029
## 1921 2.831182590 8.404025
## 1922 7.574256453 6.437041
## 1923 2.649062292 9.873654
## 1924 5.764415317 5.532676
## 1925 4.918256594 8.177995
## 1926 7.284965593 6.981196
## 1927 9.169833031 4.008388
## 1928 2.609147068 9.908633
## 1929 0.205303932 6.462495
## 1930 2.833507280 8.365162
## 1931 4.496116907 5.689445
## 1932 8.754723009 7.080829
## 1933 2.615689770 7.760052
## 1934 7.077613348 9.825681
## 1935 9.925559507 4.743849
## 1936 4.187184062 5.436681
## 1937 7.833811667 5.135683
## 1938 4.144894498 6.779246
## 1939 5.371383973 7.255351
## 1940 4.531173353 8.675551
## 1941 9.302901817 7.156592
## 1942 5.387738889 9.162202
## 1943 8.598759290 7.340570
## 1944 7.009845986 7.127650
## 1945 0.962562004 8.526822
## 1946 5.556923010 8.772479
## 1947 0.314731794 7.683223
## 1948 4.411354457 7.663635
## 1949 9.538424988 8.930221
## 1950 1.541340353 8.319863
## 1951 6.324575046 4.379219
## 1952 9.111274267 7.088391
## 1953 7.529675563 6.632324
## 1954 7.606683884 4.420943
## 1955 0.379227531 5.940909
## 1956 4.035658336 4.979517
## 1957 9.148462476 8.538750
## 1958 5.311993687 5.596701
## 1959 6.420774238 4.955423
## 1960 6.845568462 8.918556
## 1961 8.563196487 9.958887
## 1962 7.957842550 6.554297
## 1963 5.654854675 8.389189
## 1964 9.327890888 6.984167
## 1965 4.258207262 9.582566
## 1966 1.278167997 6.993833
## 1967 8.396567018 7.192876
## 1968 0.291541906 6.362157
## 1969 7.979117719 6.202612
## 1970 2.113722736 4.252143
## 1971 7.310961077 7.847713
## 1972 2.570626476 7.034120
## 1973 2.879838121 7.009335
## 1974 8.363399824 9.146111
## 1975 2.092653352 8.663942
## 1976 7.604209952 6.994537
## 1977 1.683455705 8.128716
## 1978 4.568941172 8.766244
## 1979 1.938666359 9.021964
## 1980 2.176175352 6.489841
## 1981 9.853817133 8.344002
## 1982 0.050560278 8.947572
## 1983 0.331743416 7.113182
## 1984 7.601345060 8.315466
## 1985 8.589238048 8.788732
## 1986 7.680174937 5.323306
## 1987 2.819996480 5.520972
## 1988 7.209136952 5.026449
## 1989 6.979616845 7.681316
## 1990 8.587384148 4.504472
## 1991 1.218963385 7.967169
## 1992 3.583844221 7.161885
## 1993 4.556833538 4.276919
## 1994 2.945723775 6.708658
## 1995 3.107247726 6.932516
## 1996 3.459809889 9.460509
## 1997 9.976581454 4.715534
## 1998 3.438004484 4.260542
## 1999 9.504678301 4.564708
## 2000 9.319172094 6.209636
## 2001 8.305149463 7.862230
## 2002 0.182554696 4.312029
## 2003 3.309847059 6.520243
## 2004 8.767911655 4.527160
## 2005 0.855091948 4.649400
## 2006 8.113952517 9.691701
## 2007 4.608131010 9.712505
## 2008 5.714610279 6.279848
## 2009 9.519231670 8.572455
## 2010 6.130911213 9.749571
## 2011 5.192593567 4.460036
## 2012 7.464692043 5.858770
## 2013 2.576862935 5.798028
## 2014 0.492454430 9.985307
## 2015 8.601466530 5.409637
## 2016 2.373756312 9.160355
## 2017 0.926409610 5.614719
## 2018 9.793562831 6.620672
## 2019 5.657330853 4.323188
## 2020 7.035978807 4.444632
## 2021 7.635473959 9.212180
## 2022 0.022461560 4.544017
## 2023 5.160350902 5.137506
## 2024 0.198637581 7.713025
## 2025 7.741597537 5.336567
## 2026 3.475070744 5.151361
## 2027 1.736418728 9.386881
## 2028 5.418354621 7.115646
## 2029 1.372628033 9.339183
## 2030 8.195905153 6.497990
## 2031 5.584056883 9.214991
## 2032 0.429290543 8.082638
## 2033 5.422803485 9.907700
## 2034 0.710315084 5.629009
## 2035 8.398880413 5.802241
## 2036 9.564388552 4.663711
## 2037 5.099976708 5.743538
## 2038 2.902960253 4.592000
## 2039 6.735203780 9.135464
## 2040 2.617579559 7.164066
## 2041 4.016191285 9.112567
## 2042 4.551224909 7.869491
## 2043 1.659933660 4.645490
## 2044 9.723538361 8.314329
## 2045 9.621395587 7.645894
## 2046 2.005275390 6.370981
## 2047 1.095919251 4.515479
## 2048 7.491242386 5.465014
## 2049 5.140033612 8.819508
## 2050 8.679744241 8.304590
## 2051 8.453190530 5.816467
## 2052 7.465421424 5.364626
## 2053 2.604218197 6.918767
## 2054 0.934962783 7.271949
## 2055 1.768551218 8.050991
## 2056 8.192486044 9.891742
## 2057 8.569750627 9.227229
## 2058 6.487105350 9.789721
## 2059 3.655345857 9.602547
## 2060 6.824674278 9.416989
## 2061 0.593052841 4.153488
## 2062 5.769843844 5.707521
## 2063 7.671327797 9.660031
## 2064 5.669645661 6.679697
## 2065 9.658793963 8.309027
## 2066 4.191477050 4.465378
## 2067 4.544123821 7.062484
## 2068 2.968621221 4.396507
## 2069 8.342139340 9.691204
## 2070 1.731872717 7.529734
## 2071 4.000143699 5.293074
## 2072 5.215282399 8.350396
## 2073 0.482209622 8.094816
## 2074 2.750262774 9.117293
## 2075 3.610386830 6.519889
## 2076 6.295095870 7.922732
## 2077 8.559800172 6.408287
## 2078 4.872265837 6.309326
## 2079 9.369925916 8.798458
## 2080 2.919120665 7.797271
## 2081 9.079687994 7.994295
## 2082 5.703772421 5.027829
## 2083 3.611448691 6.478630
## 2084 5.350638886 9.314261
## 2085 0.498293697 9.277611
## 2086 1.272869576 5.441953
## 2087 9.799702089 7.117649
## 2088 2.584292658 7.897737
## 2089 5.483513139 4.144769
## 2090 5.088933948 7.538554
## 2091 3.144428767 7.783483
## 2092 8.823072463 5.323151
## 2093 9.596895047 7.287440
## 2094 4.733324253 4.496817
## 2095 3.490207196 5.303670
## 2096 7.973018470 7.606749
## 2097 9.464028736 7.296669
## 2098 8.167681553 6.516408
## 2099 9.468334215 7.972071
## 2100 1.109198186 5.797903
## 2101 1.098442027 6.015094
## 2102 4.315767808 8.153123
## 2103 7.044546105 4.180376
## 2104 4.120716307 7.275428
## 2105 7.693043820 9.576382
## 2106 4.593094081 9.866460
## 2107 5.105483724 9.448988
## 2108 4.127906231 7.903963
## 2109 4.043529570 9.999840
## 2110 0.532764611 8.870584
## 2111 8.448133523 4.717674
## 2112 0.958544834 6.759129
## 2113 4.069969216 8.772615
## 2114 5.701564408 4.300610
## 2115 1.658027426 4.565574
## 2116 8.728048828 4.136609
## 2117 2.302765650 4.249376
## 2118 3.850204375 5.203225
## 2119 3.519901645 5.920784
## 2120 4.152669915 8.486049
## 2121 8.702362670 6.653608
## 2122 2.800971731 4.510746
## 2123 0.263901870 5.202338
## 2124 2.590443386 6.977782
## 2125 1.271396048 9.295084
## 2126 4.548318239 8.197806
## 2127 2.604904714 9.506577
## 2128 6.523343707 6.069556
## 2129 3.297674091 7.117036
## 2130 5.289252661 8.336232
## 2131 0.334605261 7.858227
## 2132 0.565121612 9.516258
## 2133 5.235067976 6.681213
## 2134 3.788125456 9.989399
## 2135 3.168538657 5.011026
## 2136 3.430526726 8.412729
## 2137 8.150726658 4.573938
## 2138 2.938590253 6.972506
## 2139 6.830831748 8.642361
## 2140 8.394825679 5.736780
## 2141 0.947567127 4.917760
## 2142 8.181468969 7.088091
## 2143 7.389633240 6.271699
## 2144 4.352401934 9.624312
## 2145 4.049963547 7.535540
## 2146 1.360667029 8.555256
## 2147 9.886002294 5.769464
## 2148 6.354281753 8.322874
## 2149 6.570993383 9.878711test = mvn(data1_fix2, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq")
test## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 3.11366075747284 0.53898797364374 YES
## 2 Mardia Kurtosis -14.0034612145734 0 NO
## 3 MVN <NA> <NA> NO
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk X1 0.9567 <0.001 NO
## 2 Shapiro-Wilk X2 0.9512 <0.001 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## X1 2149 4.920202 2.857191 4.766424 0.003616017 9.987429 2.570626 7.427899
## X2 2149 7.051081 1.763573 7.115646 4.002628660 9.999840 5.482997 8.562521
## Skew Kurtosis
## X1 0.04490983 -1.180940
## X2 -0.06953308 -1.214088
Secara eksploratif, dapat terlihat bahwa terdapat penyimpangan yang cukup besar antara titik-titik data dengan garis. Selain itu, hasil tes Mardia juga menunjukkan bahwa data tidak berdistribusi normal multivariat. Oleh karena itu, akan dilakukan pemotongan data.
data2_p <- data1_fix2[50:100,]
data2_p## X1 X2
## 50 3.59993251 5.123009
## 51 6.84829335 8.353761
## 52 1.23008407 8.232079
## 53 6.57833828 7.981846
## 54 9.85954155 9.710274
## 55 8.19458399 8.554071
## 56 8.11728982 4.137893
## 57 8.03096582 9.527303
## 58 0.78580230 4.580381
## 59 6.03484315 5.912972
## 60 9.67381028 7.621481
## 61 6.53963239 9.470753
## 62 8.15313913 6.551533
## 63 2.30856655 4.074439
## 64 0.82549135 9.986318
## 65 3.69013681 8.561219
## 66 1.35352183 5.208674
## 67 0.09483767 9.383941
## 68 8.73134136 4.231688
## 69 3.44145243 5.966402
## 70 3.87709164 6.062905
## 71 4.85561150 7.988010
## 72 8.49219384 5.547509
## 73 9.98506885 7.561233
## 74 0.11948085 5.397002
## 75 4.81086640 8.371714
## 76 9.86125841 8.303338
## 77 8.11229131 5.949474
## 78 9.27779433 8.900769
## 79 1.91591344 6.146166
## 80 5.20441159 5.112512
## 81 8.78431345 5.528365
## 82 0.95407196 8.066368
## 83 6.43898043 9.209427
## 84 7.63977999 4.213680
## 85 5.52595309 9.768864
## 86 4.01212557 7.040055
## 87 7.78920273 5.278123
## 88 5.32858115 6.160692
## 89 0.82622037 8.467348
## 90 8.59694609 9.623875
## 91 5.36929273 7.092991
## 92 8.07280724 9.078879
## 93 2.97349371 6.090990
## 94 5.48773237 6.271848
## 95 8.15237968 8.197573
## 96 3.83569796 8.395433
## 97 2.51958693 5.196521
## 98 5.14105457 8.114125
## 99 2.94841656 6.145350
## 100 3.75498535 9.800457x1_p <- data2_p[1]
x2_p <- data2_p[2]
data2_fix1 <- data.frame(cbind(x1_p,x2_p))
data2_fix1## X1 X2
## 50 3.59993251 5.123009
## 51 6.84829335 8.353761
## 52 1.23008407 8.232079
## 53 6.57833828 7.981846
## 54 9.85954155 9.710274
## 55 8.19458399 8.554071
## 56 8.11728982 4.137893
## 57 8.03096582 9.527303
## 58 0.78580230 4.580381
## 59 6.03484315 5.912972
## 60 9.67381028 7.621481
## 61 6.53963239 9.470753
## 62 8.15313913 6.551533
## 63 2.30856655 4.074439
## 64 0.82549135 9.986318
## 65 3.69013681 8.561219
## 66 1.35352183 5.208674
## 67 0.09483767 9.383941
## 68 8.73134136 4.231688
## 69 3.44145243 5.966402
## 70 3.87709164 6.062905
## 71 4.85561150 7.988010
## 72 8.49219384 5.547509
## 73 9.98506885 7.561233
## 74 0.11948085 5.397002
## 75 4.81086640 8.371714
## 76 9.86125841 8.303338
## 77 8.11229131 5.949474
## 78 9.27779433 8.900769
## 79 1.91591344 6.146166
## 80 5.20441159 5.112512
## 81 8.78431345 5.528365
## 82 0.95407196 8.066368
## 83 6.43898043 9.209427
## 84 7.63977999 4.213680
## 85 5.52595309 9.768864
## 86 4.01212557 7.040055
## 87 7.78920273 5.278123
## 88 5.32858115 6.160692
## 89 0.82622037 8.467348
## 90 8.59694609 9.623875
## 91 5.36929273 7.092991
## 92 8.07280724 9.078879
## 93 2.97349371 6.090990
## 94 5.48773237 6.271848
## 95 8.15237968 8.197573
## 96 3.83569796 8.395433
## 97 2.51958693 5.196521
## 98 5.14105457 8.114125
## 99 2.94841656 6.145350
## 100 3.75498535 9.800457test = mvn(data2_fix1, mvnTest = "mardia", univariateTest = "SW", multivariatePlot = "qq")
test## $multivariateNormality
## Test Statistic p value Result
## 1 Mardia Skewness 0.528210860172236 0.970697175560602 YES
## 2 Mardia Kurtosis -1.87213603575184 0.0611877856398249 YES
## 3 MVN <NA> <NA> YES
##
## $univariateNormality
## Test Variable Statistic p value Normality
## 1 Shapiro-Wilk X1 0.945 0.0196 NO
## 2 Shapiro-Wilk X2 0.937 0.0094 NO
##
## $Descriptives
## n Mean Std.Dev Median Min Max 25th 75th
## X1 51 5.387357 2.966364 5.369293 0.09483767 9.985069 3.207473 8.114791
## X2 51 7.181405 1.786959 7.561233 4.07443855 9.986318 5.730241 8.510710
## Skew Kurtosis
## X1 -0.1747597 -1.233343
## X2 -0.1103892 -1.328211
Setelah melakukan pemotongan data, dapat terlihat bahwa titik-titik data sudah tidak menyimpang secara jauh lagi dengan garis. Selain itu, hasil tes Mardia juga menunjukkan bahwa data telah berdistribusi normal multivariat. Sehingga, uji asumsi normalitas terpenuhi.
UJI HOMOGENITAS
# Forgetfulness
Y1 <- data2[50:100,33]
boxM(data = data2_fix1, grouping = Y1)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data2_fix1
## Chi-Sq (approx.) = 1.2139, df = 3, p-value = 0.7497# Diagnose
Y2 <- data2[50:100,34]
boxM(data = data2_p, grouping = Y2)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: data2_p
## Chi-Sq (approx.) = 1.3217, df = 3, p-value = 0.724Berdasarkan hasil perhitungan Box’s M, diperoleh kesimpulan bahwa kedua variabel Y1 dan Y2 memiliki gejala homogenitas sehingga asumsi terpenuhi.
TWO WAY MANOVA
fact_Y1 <- as.factor(data2$Forgetfulness[50:100])
fact_Y2 <- as.factor(data2$Diagnosis[50:100])
data2_p <- data.frame(x1_p = unlist(x1_p), x2_p = unlist(x2_p))
manova <- manova(cbind(x1_p, x2_p) ~ fact_Y1 * fact_Y2, data = data2_p)
summary(manova)## Df Pillai approx F num Df den Df Pr(>F)
## fact_Y1 1 0.073648 1.82857 2 46 0.1721
## fact_Y2 1 0.051298 1.24364 2 46 0.2978
## fact_Y1:fact_Y2 1 0.024778 0.58436 2 46 0.5615
## Residuals 47Berdasarkan hasil analisis varians multivariat di atas, diketahui bahwa tidak ada variabel bebas yang berpengaruh signifikan terhadap variabel terikat sehingga tidak perlu dilakukan uji lanjut.