aov()和ezANOVA输出之间的差异

时间:2016-09-05 09:17:51

标签: r anova

我正在对此数据集运行重复测量ANOVA:

ANOVA1_data<-structure(list(response_time = c(852.3760155, 1126.8859, 771.37418925, 
                                 515.039921, 704.730038, 498.255039538462, 414.674203166667, 1002.95192083333, 
                                 550.903181277778, 967.5577028, 1200.10554377778, 688.62227325, 
                                 568.7093463, 599.644536444444, 599.450236533333, 477.63492625, 
                                 852.6842127, 487.885839, 671.5945855, 1406.254308, 630.157431, 
                                 544.0455392, 952.309923166667, 555.052128285714, 534.940400142857, 
                                 958.7624941, 484.318274461538, 796.669692909091, 1094.1511547, 
                                 644.2667865, 513.026395333333, 578.4711744, 468.296029636364, 
                                 490.760670125, 993.210234181818, 485.081406666667, 784.688966692308, 
                                 994.1911471, 683.231708285714, 489.100872272727, 529.933097166667, 
                                 500.0458643, 502.0769296, 782.131561, 503.106378076923, 873.463863545455, 
                                 954.098663181818, 687.636025714286, 508.866894555556, 609.3654196875, 
                                 569.5037471, 485.838012375, 677.4758566, 490.894644727273, 950.1887905, 
                                 1273.720742, 677.823247, 590.922434416667, 587.083661727273, 
                                 519.520321, 497.9753709, 777.282322444444, 477.434508636364, 
                                 694.656964333333, 894.189973111111, 668.8171375, 492.210069352941, 
                                 633.660594166667, 511.815477066667, 385.2507655, 754.016341833333, 
                                 448.738492071429, 780.0980990625, 1350.88667075, 615.3092625, 
                                 516.4133455, 599.23199475, 528.664191823529, 465.009907142857, 
                                 645.526472, 506.692067461538, 741.007966333333, 1156.59821475, 
                                 739.794313666667, 579.644074272727, 711.2937442, 527.265395333333, 
                                 407.0503579, 679.8124972, 616.782603916667, 790.288266272727, 
                                 1225.061001, 659.54558775, 539.471006666667, 548.871068846154, 
                                 541.776038733333, 593.5888702, 917.187675222222, 634.578, 642.405313916667, 
                                 826.0807324, 557.183927375, 526.966490888889, 602.756101866667, 
                                 476.4600226875, 459.10276, 883.192454111111, 574.848643909091, 
                                 875.407049941176, 1167.006157875, 585.656621714286, 554.222852777778, 
                                 735.8162707, 499.69293775, 556.543906142857, 875.035436571429, 
                                 524.174892722222, 647.455149125, 1087.53515485714, 686.796519, 
                                 506.3197505625, 584.608293222222, 599.938951714286, 548.7216914, 
                                 716.97108425, 485.173967583333, 594.6478585, 1169.579207, 635.1226654, 
                                 576.322667125, 611.906749625, 534.87835075, 542.002233833333, 
                                 832.87268, 551.311072857143, 735.185274142857, 1019.00502225, 
                                 644.710864, 487.586029818182, 588.046562545455, 538.638263, 467.2331068, 
                                 992.040390333333, 447.6888445, 582.810538285714, 770.830189888889, 
                                 545.3166901, 555.4240726, 805.41041225, 485.093444294118, 549.1646476, 
                                 617.863255857143, 545.728531833333, 668.0134345, 988.09201925, 
                                 554.773951428571, 523.983008, 673.102314666667, 512.198864222222, 
                                 525.437858857143, 831.596884111111, 704.2265038, 675.469981090909, 
                                 929.600156857143, 562.595987090909, 528.187944909091, 667.77096975, 
                                 587.682777333333, 739.0132942, 784.1174622, 593.48687, 733.008363, 
                                 967.308045714286, 502.277713666667, 543.780318307692, 741.213556857143, 
                                 485.901219571429, 500.773469166667, 646.677269666667, 579.922640307692, 
                                 670.514432333333, 594.596857055556, 565.1742616, 519.029296666667, 
                                 826.665948, 517.6210813125, 638.896322142857, 842.662615666667, 
                                 608.046112833333, 695.388263090909, 731.689308222222, 614.044796375, 
                                 562.0161665, 676.51305425, 518.815232230769, 505.696347166667, 
                                 811.1939501, 620.4278604, 629.5713655, 886.479992428571, 540.152837090909, 
                                 519.513340125, 741.0639604, 514.0700816, 510.0282582, 652.348294, 
                                 578.9893216, 853.700193571429, 649.196684428571, 506.72766425, 
                                 530.0589578, 1191.7668945, 497.964943, 487.768835, 659.172599142857, 
                                 519.883308375, 862.009397333333, 795.90972425, 630.326232727273, 
                                 592.5958208, 1059.42960416667, 547.5455905, 545.340032125, 668.149378714286, 
                                 536.7357422, 727.936624538462, 826.002796875, 614.638075, 543.432615875, 
                                 1072.87504425, 534.1879206, 558.45495425, 800.5423618, 529.956305125, 
                                 744.011926571429, 717.220530111111, 618.982837166667, 561.909433333333, 
                                 735.876713666667, 528.781302636364, 578.9483135, 831.885292333333, 
                                 526.534026125, 620.34445925, 644.317982714286, 626.278062470588, 
                                 505.169543857143, 558.7303128, 482.935910466667, 520.953098333333, 
                                 776.282798272727, 558.65795325, 618.6108095, 775.767045818182, 
                                 509.158378916667, 519.430281333333, 700.8157985, 533.102873933333, 
                                 526.225282666667, 735.458925444444, 561.294387625, 669.371324125, 
                                 709.557364769231, 530.476736285714, 542.761542333333, 803.686653375, 
                                 547.784239181818, 585.437835125, 700.554143363636, 590.141187153846, 
                                 782.5425745, 612.78272575, 542.874586, 498.931897625, 797.0490638, 
                                 532.9786162, 580.352599555556, 896.370314538462, 529.1135348, 
                                 669.924511461538, 1049.25964625, 489.548872583333, 536.993126142857, 
                                 808.74337, 465.948712125, 476.2053386, 582.2254407, 648.819782777778
), subject_nr = c(0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 
                  2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 
                  0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 
                  7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 
                  5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 
                  3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 
                  1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 
                  9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 
                  6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 
                  4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 
                  2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 
                  0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 
                  7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 
                  5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 
                  3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 
                  1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 
                  9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 
                  6L, 7L, 9L, 0L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 0L, 1L, 2L, 3L, 
                  4L, 5L, 6L, 7L, 9L), Pattern = structure(c(16L, 16L, 16L, 16L, 
                                                             16L, 16L, 16L, 16L, 16L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
                                                             12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 4L, 4L, 4L, 4L, 
                                                             4L, 4L, 4L, 4L, 4L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 
                                                             6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 10L, 10L, 10L, 10L, 10L, 
                                                             10L, 10L, 10L, 10L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 15L, 
                                                             15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 7L, 7L, 7L, 7L, 7L, 7L, 
                                                             7L, 7L, 7L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 3L, 
                                                             3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 13L, 13L, 13L, 13L, 13L, 13L, 
                                                             13L, 13L, 13L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 9L, 9L, 9L, 
                                                             9L, 9L, 9L, 9L, 9L, 9L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 16L, 
                                                             16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 8L, 8L, 8L, 8L, 8L, 8L, 
                                                             8L, 8L, 8L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 4L, 
                                                             4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 14L, 14L, 14L, 14L, 14L, 14L, 
                                                             14L, 14L, 14L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 10L, 10L, 
                                                             10L, 10L, 10L, 10L, 10L, 10L, 10L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
                                                             2L, 2L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 7L, 7L, 
                                                             7L, 7L, 7L, 7L, 7L, 7L, 7L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 
                                                             11L, 11L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 13L, 13L, 13L, 
                                                             13L, 13L, 13L, 13L, 13L, 13L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
                                                             5L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 1L, 1L, 1L, 1L, 1L, 1L, 
                                                             1L, 1L, 1L), .Label = c("RRRR", "ARRR", "RARR", "AARR", "RRAR", 
                                                                                     "ARAR", "RAAR", "AAAR", "RRRA", "ARRA", "RARA", "AARA", "RRAA", 
                                                                                     "ARAA", "RAAA", "AAAA"), class = "factor"), Visual1 = c("one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
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                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "one", 
                                                                                                                                             "one", "one", "one", "one", "one", "one", "one", "one", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two", "two", 
                                                                                                                                             "two", "two", "two", "two", "two", "two", "two", "two")), .Names = c("response_time", 
                                                                                                                                                                                                                  "subject_nr", "Pattern", "Visual1"), row.names = c(1L, 2L, 3L, 
                                                                                                                                                                                                                                                                     4L, 5L, 6L, 7L, 8L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 
                                                                                                                                                                                                                                                                     20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 30L, 31L, 32L, 33L, 
                                                                                                                                                                                                                                                                     34L, 35L, 36L, 37L, 38L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 
                                                                                                                                                                                                                                                                     48L, 50L, 51L, 52L, 53L, 54L, 55L, 56L, 57L, 58L, 60L, 61L, 62L, 
                                                                                                                                                                                                                                                                     63L, 64L, 65L, 66L, 67L, 68L, 70L, 71L, 72L, 73L, 74L, 75L, 76L, 
                                                                                                                                                                                                                                                                     77L, 78L, 80L, 81L, 82L, 83L, 84L, 85L, 86L, 87L, 88L, 89L, 90L, 
                                                                                                                                                                                                                                                                     91L, 92L, 93L, 94L, 95L, 96L, 97L, 99L, 100L, 101L, 102L, 103L, 
                                                                                                                                                                                                                                                                     104L, 105L, 106L, 107L, 109L, 110L, 111L, 112L, 113L, 114L, 115L, 
                                                                                                                                                                                                                                                                     116L, 117L, 119L, 120L, 121L, 122L, 123L, 124L, 125L, 126L, 127L, 
                                                                                                                                                                                                                                                                     129L, 130L, 131L, 132L, 133L, 134L, 135L, 136L, 137L, 139L, 140L, 
                                                                                                                                                                                                                                                                     141L, 142L, 143L, 144L, 145L, 146L, 147L, 149L, 150L, 151L, 152L, 
                                                                                                                                                                                                                                                                     153L, 154L, 155L, 156L, 157L, 159L, 160L, 161L, 162L, 163L, 164L, 
                                                                                                                                                                                                                                                                     165L, 166L, 167L, 169L, 170L, 171L, 172L, 173L, 174L, 175L, 176L, 
                                                                                                                                                                                                                                                                     177L, 179L, 180L, 181L, 182L, 183L, 184L, 185L, 186L, 187L, 189L, 
                                                                                                                                                                                                                                                                     190L, 191L, 192L, 193L, 194L, 195L, 196L, 197L, 199L, 200L, 201L, 
                                                                                                                                                                                                                                                                     202L, 203L, 204L, 205L, 206L, 207L, 209L, 210L, 211L, 212L, 213L, 
                                                                                                                                                                                                                                                                     214L, 215L, 216L, 217L, 219L, 220L, 221L, 222L, 223L, 224L, 225L, 
                                                                                                                                                                                                                                                                     226L, 227L, 229L, 230L, 231L, 232L, 233L, 234L, 235L, 236L, 237L, 
                                                                                                                                                                                                                                                                     239L, 240L, 241L, 242L, 243L, 244L, 245L, 246L, 247L, 249L, 250L, 
                                                                                                                                                                                                                                                                     251L, 252L, 253L, 254L, 255L, 256L, 257L, 259L, 260L, 261L, 262L, 
                                                                                                                                                                                                                                                                     263L, 264L, 265L, 266L, 267L, 269L, 270L, 271L, 272L, 273L, 274L, 
                                                                                                                                                                                                                                                                     275L, 276L, 277L, 279L, 280L, 281L, 282L, 283L, 284L, 285L, 286L, 
                                                                                                                                                                                                                                                                     287L, 289L, 290L, 291L, 292L, 293L, 294L, 295L, 296L, 297L, 299L, 
                                                                                                                                                                                                                                                                     300L, 301L, 302L, 303L, 304L, 305L, 306L, 307L, 309L, 310L, 311L, 
                                                                                                                                                                                                                                                                     312L, 313L, 314L, 315L, 316L, 317L, 319L), class = "data.frame")

我使用库(ez)&amp; AOV():

 ANOVAModel1 <- ezANOVA(data = ANOVA1_data, dv = .(response_time), wid = .(subject_nr), within = .(Pattern, Visual1), type = 1, detailed = TRUE)
 ANOVAModel1

 m.aov2 <- aov(response_time ~ (Pattern * Visual1) +
           Error(subject_nr/(Pattern * Visual1)),
           data = ANOVA1_data)

 summary(m.aov2)

每种方法的输出都不同:

ANOVAModel1:

$ANOVA
           Effect DFn DFd       SSn       SSd         F          p p<.05        ges
1         Pattern  15 120 188752.29  955689.9 1.5800295 0.08915725       0.05636435
2         Visual1   1   8  89415.79 1271189.0 0.5627222 0.47464681       0.02751719
3 Pattern:Visual1  15 120 131635.51  933157.5 1.1285170 0.33871622       0.03999047

m.aov2:

Error: subject_nr
          Df  Sum Sq Mean Sq F value Pr(>F)
Residuals  1 1148803 1148803               

Error: subject_nr:Pattern
        Df Sum Sq Mean Sq
Pattern 15  99658    6644

Error: subject_nr:Visual1
        Df Sum Sq Mean Sq
Visual1  1   4537    4537

Error: subject_nr:Pattern:Visual1
                Df Sum Sq Mean Sq
Pattern:Visual1 15  92056    6137

Error: Within
                 Df  Sum Sq Mean Sq F value   Pr(>F)    
Pattern          15  266386   17759   0.549 0.910425    
Visual1           1  404078  404078  12.488 0.000497 ***
Pattern:Visual1  15  144357    9624   0.297 0.995330    
Residuals       224 7247992   32357                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

但是,如果我跑:

m.aov3 <- aov(response_time ~ (Pattern * Visual1) +
               Error(subject_nr),
             data = ANOVA1_data)

summary(m.aov3)

我得到与ezANOVA输出相同的Sum Square值,但仍然有不同的p值:

Error: subject_nr
          Df  Sum Sq Mean Sq F value Pr(>F)
Residuals  1 1148803 1148803               

Error: Within
                 Df  Sum Sq Mean Sq F value Pr(>F)  
Pattern          15  188752   12583   0.409 0.9759  
Visual1           1   89416   89416   2.905 0.0895 .
Pattern:Visual1  15  131636    8776   0.285 0.9964  
Residuals       255 7849261   30781                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

我的理解是,m.aov2是运行重复测量方差分析的正确方法,但也许我做错了会导致结果的变化?

任何见解都会受到欢迎和赞赏。

1 个答案:

答案 0 :(得分:1)

ezANOVA()警告时,您忘记将subject_nr的班级从integer更改为factor(最好更改Visual1类)。

ANOVA1_data2 <- ANOVA1_data
ANOVA1_data2$subject_nr <- as.factor(ANOVA1_data2$subject_nr)
ANOVA1_data2$Visual1 <- as.factor(ANOVA1_data2$Visual1)

m.aov2.2 <- aov(response_time ~ (Pattern * Visual1) + 
                  Error(subject_nr/(Pattern * Visual1)), 
                data = ANOVA1_data2)            # the same model but the data modified
结果
summary(m.aov2.2)

Error: subject_nr
          Df  Sum Sq Mean Sq F value Pr(>F)
Residuals  8 5838028  729753               

Error: subject_nr:Pattern
           Df Sum Sq Mean Sq F value Pr(>F)  
Pattern    15 188752   12583    1.58 0.0892 .
Residuals 120 955690    7964                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Error: subject_nr:Visual1
          Df  Sum Sq Mean Sq F value Pr(>F)
Visual1    1   89416   89416   0.563  0.475
Residuals  8 1271189  158899               

Error: subject_nr:Pattern:Visual1
                 Df Sum Sq Mean Sq F value Pr(>F)
Pattern:Visual1  15 131636    8776   1.129  0.339
Residuals       120 933157    7776     
p.value的详细信息
p.val <- NA
for(i in 2:4) p.val[i-1] <- summary(m.aov2.2)[i][[1]][[1]][1,5]
  > p.val
   [1] 0.08915725 0.47464681 0.33871622

  > ANOVAModel1[[1]]$p
   [1] 0.08915725 0.47464681 0.33871622    # the same