Double factorial in r with letters for differentiation
Dear I am trying to perform a double or two-away anova factor analysis. I would like to know how do I generate the letters of differentiation between treatments for the two factors. This differentiation is common in scientific articles in which it is usually presented in tables, with the lowercase letters differentiating the means in the column and the capital letters in the row.
For this follows the data I used:
data <- structure(list(Parcela = c(1, 8, 14, 19, 2, 9, 15, 17, 3, 10,
13, 18, 4, 6, 12, 20, 5, 7, 11, 16, 40, 35, 29, 23, 39, 34, 30,
25, 38, 32, 26, 21, 37, 33, 28, 22, 36, 31, 27, 24, 41, 47, 51,
59, 42, 55, NA, 60, 43, 48, 52, 57, 44, 46, 54, 58, 45, 50, 53,
56, 80, 71, 67, 62, 79, 73, 68, 64, 78, 72, 69, 61, 77, 74, 70,
63, 76, 75, 66, 65, 81, 90, 93, 99, 82, 86, 91, 96, 83, 89, 92,
97, 84, 88, 95, 100, 85, 87, 94, 98, 120, 114, 106, 102, 119,
111, 110, 101, 118, 115, 109, 103, 117, 113, 108, 105, 116, 112,
107, 104, 121, 128, 134, 136, 122, 129, 131, 137, 123, 127, 132,
140, 124, 126, 135, 139, 125, 130, 133, 138, 160, 155, 146, 143,
159, 154, 148, 142, 158, 152, 150, 145, 157, 153, 147, 141, 156,
151, 149, 144, 161, 170, 174, 176, 162, 168, 172, 180, 163, 167,
171, 178, 164, 169, 175, 179, 165, 166, 173, 177, 201, 206, 212,
219, 202, 207, 215, 217, 203, 209, 211, 218, 204, 210, 213, 216,
205, 208, 214, 220, 240, 234, 227, 222, 239, 235, 228, 224, 238,
232, 230, 225, 237, 233, 229, 223, 236, 231, 226, 221, 241, 246,
254, 260, 242, 247, 251, 256, 243, 250, 255, 257, 244, 248, 253,
259, 245, 249, 252, 258, 280, 275, 267, 263, 279, 274, 269, 265,
278, 273, 270, 264, 277, 272, 268, 262, 276, 271, 266, 261, 281,
286, 294, 299, 282, 289, 295, 297, 283, 287, 292, 300, 284, 288,
291, 298, 285, 290, 293, 296, 320, 314, 307, 301, 319, 313, 308,
305, 318, 311, 309, 302, 317, 315, 306, 304, 316, 312, 310, 303,
321, 327, 335, 337, 322, 326, 332, 340, 323, 328, 333, 336, 324,
330, 334, 338, 325, 329, 331, 339, 360, 355, 346, 341, 359, 354,
349, 345, 358, 351, 348, 344, 357, 353, 350, 342, 356, 352, 347,
343), cul = c("BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO",
"BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO",
"BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO",
"BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO",
"BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO", "BRS 1001IPRO",
"BRS 1001IPRO", "BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO",
"BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO",
"BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO",
"BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO",
"BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO", "BRS 1003IPRO",
"BRS 1003IPRO", "BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO",
"BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO",
"BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO",
"BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO",
"BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO", "BRS 1007IPRO",
"BRS 1007IPRO", "BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO",
"BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO",
"BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO",
"BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO",
"BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO", "BRS 1010IPRO",
"BRS 1010IPRO", "BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO",
"BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO",
"BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO",
"BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO",
"BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO", "BRS 1074IPRO",
"BRS 1074IPRO", "BRS 413RR", "BRS 413RR", "BRS 413RR", "BRS 413RR",
"BRS 413RR", "BRS 413RR", "BRS 413RR", "BRS 413RR", "BRS 413RR",
"BRS 413RR", "BRS 413RR", "BRS 413RR", "BRS 413RR", "BRS 413RR",
"BRS 413RR", "BRS 413RR", "BRS 413RR", "BRS 413RR", "BRS 413RR",
"BRS 413RR", "BRS 388RR", "BRS 388RR", "BRS 388RR", "BRS 388RR",
"BRS 388RR", "BRS 388RR", "BRS 388RR", "BRS 388RR", "BRS 388RR",
"BRS 388RR", "BRS 388RR", "BRS 388RR", "BRS 388RR", "BRS 388RR",
"BRS 388RR", "BRS 388RR", "BRS 388RR", "BRS 388RR", "BRS 388RR",
"BRS 388RR", "BRS 399RR", "BRS 399RR", "BRS 399RR", "BRS 399RR",
"BRS 399RR", "BRS 399RR", "BRS 399RR", "BRS 399RR", "BRS 399RR",
"BRS 399RR", "BRS 399RR", "BRS 399RR", "BRS 399RR", "BRS 399RR",
"BRS 399RR", "BRS 399RR", "BRS 399RR", "BRS 399RR", "BRS 399RR",
"BRS 399RR", "BRB14-211566", "BRB14-211566", "BRB14-211566",
"BRB14-211566", "BRB14-211566", "BRB14-211566", "BRB14-211566",
"BRB14-211566", "BRB14-211566", "BRB14-211566", "BRB14-211566",
"BRB14-211566", "BRB14-211566", "BRB14-211566", "BRB14-211566",
"BRB14-211566", "BRB14-211566", "BRB14-211566", "BRB14-211566",
"BRB14-211566", "BR11-3381", "BR11-3381", "BR11-3381", "BR11-3381",
"BR11-3381", "BR11-3381", "BR11-3381", "BR11-3381", "BR11-3381",
"BR11-3381", "BR11-3381", "BR11-3381", "BR11-3381", "BR11-3381",
"BR11-3381", "BR11-3381", "BR11-3381", "BR11-3381", "BR11-3381",
"BR11-3381", "BR12-511", "BR12-511", "BR12-511", "BR12-511",
"BR12-511", "BR12-511", "BR12-511", "BR12-511", "BR12-511", "BR12-511",
"BR12-511", "BR12-511", "BR12-511", "BR12-511", "BR12-511", "BR12-511",
"BR12-511", "BR12-511", "BR12-511", "BR12-511", "BR10-87465",
"BR10-87465", "BR10-87465", "BR10-87465", "BR10-87465", "BR10-87465",
"BR10-87465", "BR10-87465", "BR10-87465", "BR10-87465", "BR10-87465",
"BR10-87465", "BR10-87465", "BR10-87465", "BR10-87465", "BR10-87465",
"BR10-87465", "BR10-87465", "BR10-87465", "BR10-87465", "BRR12-83021",
"BRR12-83021", "BRR12-83021", "BRR12-83021", "BRR12-83021", "BRR12-83021",
"BRR12-83021", "BRR12-83021", "BRR12-83021", "BRR12-83021", "BRR12-83021",
"BRR12-83021", "BRR12-83021", "BRR12-83021", "BRR12-83021", "BRR12-83021",
"BRR12-83021", "BRR12-83021", "BRR12-83021", "BRR12-83021", "BRR12-53050",
"BRR12-53050", "BRR12-53050", "BRR12-53050", "BRR12-53050", "BRR12-53050",
"BRR12-53050", "BRR12-53050", "BRR12-53050", "BRR12-53050", "BRR12-53050",
"BRR12-53050", "BRR12-53050", "BRR12-53050", "BRR12-53050", "BRR12-53050",
"BRR12-53050", "BRR12-53050", "BRR12-53050", "BRR12-53050", "BRR12-2497",
"BRR12-2497", "BRR12-2497", "BRR12-2497", "BRR12-2497", "BRR12-2497",
"BRR12-2497", "BRR12-2497", "BRR12-2497", "BRR12-2497", "BRR12-2497",
"BRR12-2497", "BRR12-2497", "BRR12-2497", "BRR12-2497", "BRR12-2497",
"BRR12-2497", "BRR12-2497", "BRR12-2497", "BRR12-2497", "BR12-4929",
"BR12-4929", "BR12-4929", "BR12-4929", "BR12-4929", "BR12-4929",
"BR12-4929", "BR12-4929", "BR12-4929", "BR12-4929", "BR12-4929",
"BR12-4929", "BR12-4929", "BR12-4929", "BR12-4929", "BR12-4929",
"BR12-4929", "BR12-4929", "BR12-4929", "BR12-4929", "BR12-10309",
"BR12-10309", "BR12-10309", "BR12-10309", "BR12-10309", "BR12-10309",
"BR12-10309", "BR12-10309", "BR12-10309", "BR12-10309", "BR12-10309",
"BR12-10309", "BR12-10309", "BR12-10309", "BR12-10309", "BR12-10309",
"BR12-10309", "BR12-10309", "BR12-10309", "BR12-10309"), trat = c("Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.",
"Test.", "Test.", "Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.", "Test.", "Test.",
"Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Test.", "Test.", "Test.", "Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.", "Test.", "Test.",
"Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Test.", "Test.", "Test.", "Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.", "Test.", "Test.",
"Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Test.", "Test.", "Test.", "Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.", "Test.", "Test.",
"Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Test.", "Test.", "Test.", "Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.", "Test.", "Test.",
"Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Test.", "Test.", "Test.", "Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.", "Test.", "Test.",
"Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Test.", "Test.", "Test.", "Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.", "Test.", "Test.",
"Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Test.", "Test.", "Test.", "Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Test.", "Test.", "Test.",
"Test.", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)", "Boral 500 SC (1,2)",
"Boral 500 SC (1,2)", "Boral 500 SC (2,4)", "Boral 500 SC (2,4)",
"Boral 500 SC (2,4)", "Boral 500 SC (2,4)", "Sencor 480 (0,75)",
"Sencor 480 (0,75)", "Sencor 480 (0,75)", "Sencor 480 (0,75)",
"Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)", "Sencor 480 (1,5)",
"Test.", "Test.", "Test.", "Test."), rep = c(1, 2, 3, 4, 1, 2,
3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3,
4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 3, 2, 4,
1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1,
2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2,
3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3,
4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4,
1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1,
2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2,
3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3,
4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4,
1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1,
2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2,
3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3,
4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4,
1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1,
2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4), alt = c(87.4,
95.9, 103.3, 94.2, 94.65, 93.2, 98.95, 87.45, 104.4, 103.4, 102.35,
97.9, 96.7, 101.3, 97.95, 96.3, 102, 98.35, 98.8, 97.4, 64.05,
71.8, 69.7, 65.4, 46.5, 37.15, 40.05, 44.2, 95.6, 92.35, 87.8,
87.3, 93.25, 86.4, 93.4, 79.6, 91.3, 92.35, 90.15, 87.3, 82,
81.15, 75.65, 85.35, 80.35, 75.45, 73.6, 72.9, 95.1, 84.75, 80.6,
86.45, 89.8, 81.7, 81.7, 84.55, 92.65, 88.9, 89.7, 82.35, 81.3,
76.55, 92.7, 79.45, 73.25, 42.6, 72.3, 65.6, 102.15, 97, 102.3,
94.65, 103.4, 94.1, 98.2, 91.65, 104.25, 98.25, 104.05, 100.45,
98.35, 106.4, 101.55, 94.9, 98.2, 103.35, 98.3, 101.8, 107.2,
106.85, 104.45, 97.25, 106.2, 100.3, 99.9, 93, 111.15, 102.2,
107.85, 98.65, 80.15, 75.35, 80.3, 72.5, 73.65, 78.5, 70.7, 76.95,
77.55, 81.45, 80.95, 76.5, 78.25, 77.2, 81.5, 79.35, 82.55, 77.75,
83.05, 79.6, 78.1, 78.8, 85.25, 82.25, 79.05, 76.55, 79, 78.85,
86.6, 75.8, 86.1, 79.35, 77.6, 80.3, 80.4, 69.5, 81.95, 79.1,
81.5, 80.6, 56.35, 71.85, 74.1, 63.2, 44.3, 37.1, 44.25, 37.25,
82.65, 84.85, 78, 95.35, 89.15, 82.05, 90.15, 68.95, 89.85, 80.9,
78.55, 85.7, 71.45, 65.4, 70.05, 71.45, 55.2, 44.7, 59.3, 45.2,
80.75, 78.95, 75.25, 79.7, 81.2, 73.85, 84.15, 72.7, 81.2, 88,
80.05, 71.8, 52.35, 69.5, 56.8, 53.2, 29.2, 41.85, 51.75, 37.35,
65.45, 65.15, 66.5, 49.4, 75.5, 78.5, 67.9, 60.85, 69.15, 66.7,
62.9, 63, 86.5, 106.75, 95.2, 99.75, 76.3, 89.35, 90.75, 87.45,
99.8, 110.3, 98.3, 107.15, 99, 104.25, 95.75, 98.75, 102.15,
106.9, 104.65, 97.5, 91.4, 86.3, 77.6, 87.4, 77.9, 79.5, 86.55,
72.6, 89.25, 93.55, 86.15, 84.2, 81.1, 93.85, 77.4, 85.85, 87.15,
96.45, 78.55, 80.4, 72.1, 70.15, 80.8, 77.15, 54.55, 67.7, 76.65,
70.45, 76.5, 75.4, 80.65, 80.35, 74.3, 75.15, 79.75, 79.9, 76.25,
82.45, 77.85, 85.5, 85.95, 90.4, 94.55, 98.3, 84.9, 84.35, 93.75,
77.7, 92.55, 94.15, 100.05, 102.15, 82.55, 91.65, 96.1, 97.4,
100.3, 97.85, 93.9, 97.3, 93.65, 112.15, 108.2, 111.4, 94.3,
97.95, 107, 98.65, 110.9, 112.85, 111.65, 116.45, 100, 109.3,
109.7, 107.4, 106.55, 113.5, 114, 117.8, 107.4, 114, 112.25,
111, 105.7, 107, 114.9, 115.4, 112.8, 115.65, 113.35, 111.4,
108.5, 112.1, 112.55, 113.5, 116.95, 116.65, 121.05, 119.6, 92.1,
100.15, 100.15, 96.35, 91.2, 104.05, 95.7, 92.9, 104.7, 100.3,
97.8, 99.1, 97.95, 103.85, 100.15, 101.55, 100.55, 100.3, 94.8,
99.1)), .Names = c("Parcela", "cul", "trat", "rep", "alt"), row.names = c(NA,
-340L), class = c("tbl_df", "tbl", "data.frame"))
With this data I performed the following operations:
#setup das variaveis
cul <- as.factor(data$cul)
trat <- as.factor(data$trat)
rep <- as.factor(data$rep)
alt <- data$alt
aovalt <- aov(formula=alt ~ cul+trat+cul:trat, data=data)
model.tables(aovalt, "means")
With the command model.tables I can practically get the table that I intend to get, but I lack the letters that demonstrate the differences between cultivars and treatments.
For such I tried:
tukey <- TukeyHSD(aovalt)
tukey$`cul:trat`[,4]
plot(tukey$`cul:trat`[,4])
HSD.test(cul, trt = alt)
But as you can see, a gigantic comparison list is generated, the one below being only a fraction of the list.
BR12-10309:Boral 500 SC (2,4)-BRR12-2497:Boral 500 SC (1,2)
9.580700 e-01
In this sample it is easier to observe the objective of my question: in the first line is the comparison between the cultivar "BR12-10309" treated with "Boral 500 SC (2,4)" compared to the average of the cultivar "BRR12-2497" treated with "Boral 500 SC (1,2)" and the p-value "9.580700 e-01" much less than 0,05 or my question arises how to classify this difference with letters, separating which cultivar obtained the best mean in treatment x,y,z and etc... and within each cultivar what is the best treatment to be applied to it.
Thank you all.
1
Author: Vitor Muller Anunciato, 2018-04-05
1 answers
I recommend using the package emmeans vignette Interaction analysis in emmeans :
library(emmeans)
l1 <- emmeans(aovalt, "cul", "trat") # Cria o objeto emmeans no caso de interação
CLD(l1, Letter="abcdefghij") # Pede a exibição com as letras
trat = Boral 500 SC (1,2):
cul emmean SE df lower.CL upper.CL .group
BR11-3381 57.9625 2.671402 255 52.70168 63.22332 a
BRS 399RR 66.3750 2.671402 255 61.11418 71.63582 ab
BRS 1003IPRO 67.7375 2.671402 255 62.47668 72.99832 ab
BRB14-211566 69.5875 2.671402 255 64.32668 74.84832 abc
BRR12-83021 75.0500 2.671402 255 69.78918 80.31082 bcd
BRS 413RR 77.0750 2.671402 255 71.81418 82.33582 bcd
BRS 1007IPRO 81.0375 2.671402 255 75.77668 86.29832 cde
BRS 388RR 81.1000 2.671402 255 75.83918 86.36082 cde
BRS 1010IPRO 82.5000 2.671402 255 77.23918 87.76082 cdef
BR10-87465 85.6750 2.671402 255 80.41418 90.93582 defg
BRR12-53050 92.3000 2.671402 255 87.03918 97.56082 efgh
BRS 1001IPRO 95.2000 2.671402 255 89.93918 100.46082 fghi
BR12-511 97.0500 2.671402 255 91.78918 102.31082 ghi
BR12-10309 97.1875 2.671402 255 91.92668 102.44832 ghi
BRS 1074IPRO 100.3000 2.671402 255 95.03918 105.56082 hija
BRR12-2497 106.3500 2.671402 255 101.08918 111.61082 ija
BR12-4929 111.1625 2.671402 255 105.90168 116.42332 ja
For each treatment, it makes the comparisons between the "cul". To display the comparisons without displaying the letters, use:
summary(pairs(l1), infer = c(T,T))
trat = Boral 500 SC (1,2):
contrast estimate SE df lower.CL upper.CL t.ratio p.value
BR10-87465 - BR11-3381 27.7125 3.777933 255 14.51235057 40.91264943 7.335 <.0001
BR10-87465 - BR12-10309 -11.5125 3.777933 255 -24.71264943 1.68764943 -3.047 0.1718
BR10-87465 - BR12-4929 -25.4875 3.777933 255 -38.68764943 -12.28735057 -6.746 <.0001
BR10-87465 - BR12-511 -11.3750 3.777933 255 -24.57514943 1.82514943 -3.011 0.1875
BR10-87465 - BRB14-211566 16.0875 3.777933 255 2.88735057 29.28764943 4.258 0.0033
BR10-87465 - BRR12-2497 -20.6750 3.777933 255 -33.87514943 -7.47485057 -5.473 <.0001
BR10-87465 - BRR12-53050 -6.6250 3.777933 255 -19.82514943 6.57514943 -1.754 0.9430
3
Author: Guilherme Parreira, 2018-11-13 11:17:36