Странные результаты в ANOVA: трехстороннее взаимодействие имеет значение ровно 1

Question

Я выполняю трехстороннее взаимодействие, прогнозируя «суждение» из «фактора_1» (между субъектом, два уровня), «фактора_2» (между субъектом, два уровня) и фактора_3 (в рамках субъекта, два уровня).У меня 120 участников (по 30 на каждом уровне factor_1 и factor_2)

model <- aov(
  judgment ~ factor_1*factor_2*factor_3 +
    Error(participant/factor_3),
  data = MyData)
summary(model)

Я получил странный результат трехстороннего взаимодействия: значения Sum Sq, Mean Sq и F имеют значение (точно) 0и значение p равно 1.

Как это возможно?

Вот мои данные:

MyData = structure(list(participant = structure(c(1L, 1L, 2L, 2L, 3L, 
3L, 4L, 4L, 5L, 5L, 6L, 6L, 7L, 7L, 8L, 8L, 9L, 9L, 10L, 10L, 
11L, 11L, 12L, 12L, 13L, 13L, 14L, 14L, 15L, 15L, 16L, 16L, 17L, 
17L, 18L, 18L, 19L, 19L, 20L, 20L, 21L, 21L, 22L, 22L, 23L, 23L, 
24L, 24L, 25L, 25L, 26L, 26L, 27L, 27L, 28L, 28L, 29L, 29L, 30L, 
30L, 31L, 31L, 32L, 32L, 33L, 33L, 34L, 34L, 35L, 35L, 36L, 36L, 
37L, 37L, 38L, 38L, 39L, 39L, 40L, 40L, 41L, 41L, 42L, 42L, 43L, 
43L, 44L, 44L, 45L, 45L, 46L, 46L, 47L, 47L, 48L, 48L, 49L, 49L, 
50L, 50L, 51L, 51L, 52L, 52L, 53L, 53L, 54L, 54L, 55L, 55L, 56L, 
56L, 57L, 57L, 58L, 58L, 59L, 59L, 60L, 60L, 61L, 61L, 62L, 62L, 
63L, 63L, 64L, 64L, 65L, 65L, 66L, 66L, 67L, 67L, 68L, 68L, 69L, 
69L, 70L, 70L, 71L, 71L, 72L, 72L, 73L, 73L, 74L, 74L, 75L, 75L, 
76L, 76L, 77L, 77L, 78L, 78L, 79L, 79L, 80L, 80L, 81L, 81L, 82L, 
82L, 83L, 83L, 84L, 84L, 85L, 85L, 86L, 86L, 87L, 87L, 88L, 88L, 
89L, 89L, 90L, 90L, 91L, 91L, 92L, 92L, 93L, 93L, 94L, 94L, 95L, 
95L, 96L, 96L, 97L, 97L, 98L, 98L, 99L, 99L, 100L, 100L, 101L, 
101L, 102L, 102L, 103L, 103L, 104L, 104L, 105L, 105L, 106L, 106L, 
107L, 107L, 108L, 108L, 109L, 109L, 110L, 110L, 111L, 111L, 112L, 
112L, 113L, 113L, 114L, 114L, 115L, 115L, 116L, 116L, 117L, 117L, 
118L, 118L, 119L, 119L, 120L, 120L), .Label = c("101", "102", 
"103", "104", "105", "106", "107", "108", "109", "110", "111", 
"112", "113", "114", "115", "116", "117", "118", "119", "120", 
"121", "122", "123", "124", "125", "126", "127", "128", "129", 
"130", "131", "132", "133", "134", "135", "136", "137", "138", 
"139", "140", "141", "142", "143", "144", "145", "146", "147", 
"148", "149", "150", "151", "152", "153", "154", "155", "156", 
"157", "158", "159", "160", "161", "162", "163", "164", "165", 
"166", "167", "168", "169", "170", "171", "172", "173", "174", 
"175", "176", "177", "179", "180", "181", "182", "183", "184", 
"185", "186", "187", "188", "189", "190", "191", "192", "193", 
"194", "195", "196", "197", "198", "199", "200", "201", "202", 
"203", "204", "205", "206", "207", "208", "209", "210", "211", 
"212", "213", "214", "215", "216", "217", "218", "219", "220", 
"221"), class = "factor"), factor_1 = structure(c(2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 
2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 
2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 
2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 
1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 
2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L), .Label = c("L", 
"P"), class = "factor"), factor_2 = structure(c(1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 
2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L), .Label = c("1", 
"2"), class = "factor"), factor_3 = structure(c(1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 
1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L), .Label = c("HighLoss", 
"LowLoss"), class = "factor"), judgment = c(10L, 5L, 10L, 10L, 
5L, 5L, 5L, 1L, 7L, 5L, 8L, 7L, 5L, 5L, 10L, 10L, 3L, 6L, 4L, 
6L, 10L, 10L, 10L, 6L, 10L, 10L, 1L, 1L, 8L, 8L, 6L, 6L, 8L, 
10L, 8L, 1L, 5L, 5L, 4L, 4L, 3L, 3L, 5L, 2L, 10L, 10L, 8L, 8L, 
7L, 5L, 7L, 10L, 10L, 10L, 4L, 4L, 5L, 5L, 5L, 5L, 10L, 10L, 
6L, 6L, 3L, 2L, 6L, 6L, 7L, 5L, 10L, 9L, 8L, 8L, 6L, 5L, 6L, 
6L, 8L, 10L, 6L, 6L, 7L, 7L, 5L, 5L, 10L, 6L, 10L, 10L, 10L, 
6L, 10L, 10L, 10L, 7L, 8L, 8L, 10L, 10L, 9L, 10L, 10L, 10L, 6L, 
8L, 10L, 10L, 6L, 6L, 6L, 3L, 6L, 8L, 5L, 7L, 10L, 10L, 7L, 5L, 
3L, 3L, 6L, 3L, 10L, 10L, 10L, 10L, 10L, 7L, 8L, 10L, 8L, 5L, 
9L, 6L, 6L, 6L, 8L, 8L, 10L, 10L, 10L, 10L, 5L, 5L, 6L, 3L, 9L, 
9L, 2L, 1L, 6L, 6L, 10L, 10L, 8L, 8L, 4L, 8L, 5L, 9L, 10L, 10L, 
10L, 10L, 8L, 8L, 5L, 5L, 8L, 8L, 4L, 3L, 6L, 6L, 1L, 1L, 10L, 
10L, 10L, 10L, 7L, 9L, 8L, 8L, 7L, 7L, 5L, 5L, 6L, 6L, 5L, 5L, 
8L, 8L, 1L, 1L, 2L, 3L, 8L, 6L, 8L, 8L, 8L, 6L, 7L, 9L, 10L, 
10L, 4L, 4L, 10L, 10L, 10L, 10L, 10L, 10L, 5L, 5L, 1L, 1L, 10L, 
10L, 4L, 1L, 10L, 10L, 6L, 6L, 7L, 7L, 7L, 9L, 5L, 5L, 10L, 10L, 
7L, 2L)), class = c("tbl_df", "tbl", "data.frame"), row.names = c(NA, 
-240L), .Names = c("participant", "factor_1", "factor_2", "factor_3", 
"judgment"))