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,
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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,
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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",
"one", "one", "one", "one", "one", "one", "one", "one", "one",
"one", "one", "one", "one", "one", "one", "one", "one", "one",
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"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,
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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：
$ANOVA
Effect DFn DFd SSn SSd F p p<.05 ges
1 Pattern 15 120 188752.29 955689.9 1.5800295 0.08915725 0.05636435
2 Visual1 1 8 89415.79 1271189.0 0.5627222 0.47464681 0.02751719
3 Pattern:Visual1 15 120 131635.51 933157.5 1.1285170 0.33871622 0.03999047
m.aov2：
Error: subject_nr
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 1 1148803 1148803
Error: subject_nr:Pattern
Df Sum Sq Mean Sq
Pattern 15 99658 6644
Error: subject_nr:Visual1
Df Sum Sq Mean Sq
Visual1 1 4537 4537
Error: subject_nr:Pattern:Visual1
Df Sum Sq Mean Sq
Pattern:Visual1 15 92056 6137
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
Pattern 15 266386 17759 0.549 0.910425
Visual1 1 404078 404078 12.488 0.000497 ***
Pattern:Visual1 15 144357 9624 0.297 0.995330
Residuals 224 7247992 32357
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
但是，如果我跑：
m.aov3 <- aov(response_time ~ (Pattern * Visual1) +
Error(subject_nr),
data = ANOVA1_data)
summary(m.aov3)
我得到与ezANOVA输出相同的Sum Square值，但仍然有不同的p值：
Error: subject_nr
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 1 1148803 1148803
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
Pattern 15 188752 12583 0.409 0.9759
Visual1 1 89416 89416 2.905 0.0895 .
Pattern:Visual1 15 131636 8776 0.285 0.9964
Residuals 255 7849261 30781
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
我的理解是，m.aov2是运行重复测量方差分析的正确方法，但也许我做错了会导致结果的变化？
任何见解都会受到欢迎和赞赏。
答案 0 :(得分：1)
在ezANOVA()警告时，您忘记将subject_nr的班级从integer更改为factor（最好更改Visual1类）。
ANOVA1_data2 <- ANOVA1_data
ANOVA1_data2$subject_nr <- as.factor(ANOVA1_data2$subject_nr)
ANOVA1_data2$Visual1 <- as.factor(ANOVA1_data2$Visual1)
m.aov2.2 <- aov(response_time ~ (Pattern * Visual1) +
Error(subject_nr/(Pattern * Visual1)),
data = ANOVA1_data2) # the same model but the data modified
summary(m.aov2.2)
Error: subject_nr
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 8 5838028 729753
Error: subject_nr:Pattern
Df Sum Sq Mean Sq F value Pr(>F)
Pattern 15 188752 12583 1.58 0.0892 .
Residuals 120 955690 7964
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: subject_nr:Visual1
Df Sum Sq Mean Sq F value Pr(>F)
Visual1 1 89416 89416 0.563 0.475
Residuals 8 1271189 158899
Error: subject_nr:Pattern:Visual1
Df Sum Sq Mean Sq F value Pr(>F)
Pattern:Visual1 15 131636 8776 1.129 0.339
Residuals 120 933157 7776
p.val <- NA
for(i in 2:4) p.val[i-1] <- summary(m.aov2.2)[i][[1]][[1]][1,5]
> p.val
[1] 0.08915725 0.47464681 0.33871622
> ANOVAModel1[[1]]$p
[1] 0.08915725 0.47464681 0.33871622 # the same