Hi there,
I am doing multiple comparisons for data that is not normally distributed.
For this purpose I tried both functions kruskal{agricolae} and
kruskalmc{pgirmess}. It confuses me that these functions do not yield the
same results although they are doing the same thing, don't they? Can anyone
tell my why this happens and which function I can trust?
kruskalmc() tells me that there are no differences between any of the groups
(i.e. the "difference" column of the results is filled only with FALSE).
kruskal() tells me that there are indeed differences (between group 4 and
11).
Here is my data and code:
x <- structure(c(-0.089, 0.093, -0.125, -0.253, 0.053, 0.029, 0.429,
0.139, 0.153, -0.035, 0.721, 0, -0.271, -0.014, 0.038, 0.107,
-0.064, -0.178, 0, -0.065, 0.232, 0, -0.036, 0.107, -0.018, -0.632,
0.189, -0.247, -0.982, 0.161, 0.307, 0.146, 0.21, -0.043, -0.029,
0.107, -0.043, -0.178, 0.036, 0.511, 0, 0.307, 0.389, -0.754,
0.152, -0.129, 0.65, 0.411, 0, 0.539, -0.122, 0.514, -0.15, -1.19,
-0.032, 0.103, 0, -0.522, -0.857, -0.036, 0.104, -0.357, 0.114,
-0.054, 0.04, 0.036, 0.086, 0.736, -0.097, 0.784, 0.053, 0.007,
-0.646, 0.185, 0.107, -0.115, 0, -0.036, -0.082, -0.113, -0.032,
0.354, -0.095, -0.328, -0.215, -0.036, 0, 0.357, 0, 0.108, -0.014,
0.307, -0.053, 0.318, -0.058, 0.268, -0.067, 0.071, 0.261, -0.018,
0.054, 0.086, 1.107, -0.617, 0.286, 0.072, 0.036, 0.179, -0.096,
0.143, 0.45, -0.21, 0.372, 0.061, -0.218, -0.214, 0.272, 0.108,
0.175, -0.017, 0.473, -0.575, 0.083, 0.025, 0.25, -0.843, -0.054,
-0.775, 0.036, -0.297, 0.8, 0.004, 0.189, 0.005, 0.103, 0.289,
-0.107, -0.096, 0, 0.015, -0.035, -0.125, 0.125, -0.071, -0.029,
-0.643, -0.008, 0.184, 0.303, 0, -0.164, 0.047, -0.062, -0.164,
-0.604, -0.178, 0.233, -0.154, -0.107, -0.14, -0.207, 0.211,
0.175, 0.714, 0, 0.286, -0.143, 0.018, 0.643, -0.036, 0.357,
0.071, 0.186, 0.104, -0.086, -0.611, -0.028, -0.025, 0.179, -0.032,
0.058, 0.04, -0.428, 0.447, 0.178, -0.061, 0.167, -0.071, 0.321,
0.082, 0.532, -0.22, 0.086, -0.107, 0.118, -0.139, 0.03, -0.228,
0.008, 0.178, -0.3, 0.018, -0.025, -0.329, 0.136, 0.304, 0.085,
-0.014, 0.07, 0.136, -0.218, 0.071, -0.178, 0.012, 0.229, 0.268,
-0.535, 0.164, -0.15, 0.097, 0.125, -0.536, 0.214, 0.222, -0.089,
-0.121, -0.155, -0.286, -0.282, -0.443, 0.071, -0.05, -0.04,
-0.075, -0.03, -0.357, -0.071, 0.641, 0.007, 0, 0.018, -0.573,
0.132, -0.33, -0.279, -0.639, -0.093, -0.5, -0.197, 0.303, 0.322,
-0.071, -0.071, 0.165, 0, 0, 0, 0, 0.054, -0.321, 0.093, 0.268,
-0.511, -0.3, 0.202, 0.328, -0.24, 0.871, -0.021, 0.211, 0.118,
-0.157, -0.357, 0.107, 0, 0.072, -0.357, 0.003, 0.147, 0.057,
-0.315, 0.053, 0.35, -0.107, 0.036, -0.143, 0.168, 0, 0.172,
0.321, 0.178, -0.526, -0.035, 0.247, 0.557, 0.168, 0.143, 0,
-0.432, 0.072, -0.065, 1, 0, 0.179, 0.218, 0.196, -0.122, -0.457,
0.072, 0, 0.247, -0.296, -0.118, 0.107, 0.136, 0.029, -0.058,
0.25, 0.139, -0.057, 0.15, 0.042, -0.703, -0.018, -0.318, -0.011,
-0.321, -0.6, -1.189, 0.225, -0.143, -0.112, 0.09, -0.071, -0.015,
0.828, 0.124, 0.582, 0.689, -0.107, 0.017, -0.15, 0.057, 0.143,
0.107, -0.204, -0.118, 0.021, 0.067, -0.035, -0.357, -1.015,
-0.039, 0.046, -0.036, 0.072, 0.204, 0.05, -0.038, 0, 0.057,
-0.05, 0.41, 0.143, -0.325, 0.332, -0.153, 0.157, -0.185, 0.206,
-0.086, -0.204, 0, 0.271, -0.143, 0, -0.357, 0.218, 0.036, 0.179,
-0.45, 0.072, 0.018, -0.259, 0, -0.53, -0.018, -0.054, 0.435,
0.378, 0.221, -0.921, -0.375, -0.54, 0.25, -0.16, 0, -0.007,
-0.357, 0.204, 0.129, 0, -0.45, 0, 0, 0.571, 0.392, 0, -0.465,
0.072, 0.072, -0.257, -0.007, 0.039, 0, 0.299, -0.526, 0.268,
-0.05, -0.45, 0.178, 0.025, 0.072, 0.107, 0.195, 0.089, 0.115,
0, 0.189, -0.036, -0.337, -0.45, -0.34, -0.065, 0.343, -0.071,
0.107, -0.111, 0, -0.411, -1.012, -0.108, -0.036, -0.036, 0.243,
-0.118, 0.045, 0.018, -0.607, 0.196, -0.425, -0.174, 0.068, -0.886,
-0.075, 0.143, 0.09, 0.482, -0.058, -0.2, 0.341, -0.014, 0.068,
0.107, 0.078, 0.107, -0.25, 0.382, -0.122, -0.466, -0.471, 0.046,
0.229, 0.329, 0.043, -0.207, 0.357, 0.029, 0.107, 0.286, 0, -0.15,
-0.389, -0.261, -0.135, 1.028, 0.384, 0.136, -0.147, -0.143,
0.486, -0.075, -0.036, 0.04, -0.214, 0, 0.286, 0.071, 0.25, 0.115,
1, 7, 5, 1, 1, 1, 11, 8, 3, 11, 9, 4, 9, 2, 1, 1, 4, 2, 2, 4,
2, 1, 1, 6, 4, 4, 8, 1, 4, 1, 9, 1, 11, 9, 3, 10, 1, 4, 1, 5,
2, 1, 1, 1, 1, 3, 7, 11, 1, 1, 2, 1, 1, 2, 1, 1, 8, 2, 1, 1,
1, 1, 1, 10, 3, 4, 1, 10, 2, 1, 1, 6, 5, 1, 1, 11, 1, 11, 3,
1, 1, 2, 11, 2, 1, 6, 7, 1, 9, 1, 3, 8, 1, 1, 4, 2, 5, 2, 1,
1, 3, 1, 1, 1, 10, 5, 3, 1, 1, 11, 4, 1, 1, 10, 1, 1, 6, 2, 1,
1, 5, 1, 2, 4, 9, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 11, 5, 1, 1,
1, 1, 1, 1, 2, 1, 10, 1, 1, 9, 9, 1, 11, 1, 1, 1, 4, 2, 3, 1,
11, 1, 4, 1, 1, 1, 5, 1, 1, 4, 1, 1, 1, 1, 8, 2, 1, 1, 1, 1,
1, 7, 2, 2, 2, 2, 1, 11, 1, 8, 1, 1, 8, 2, 1, 1, 5, 1, 5, 1,
1, 2, 10, 7, 8, 1, 9, 1, 5, 6, 9, 11, 2, 1, 1, 1, 1, 3, 1, 1,
1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 11, 1, 1, 5, 5, 5, 11, 10,
3, 1, 8, 1, 1, 1, 6, 1, 1, 6, 1, 11, 1, 4, 1, 1, 8, 11, 8, 1,
3, 1, 1, 1, 1, 11, 11, 5, 9, 1, 1, 5, 5, 7, 11, 4, 3, 1, 10,
5, 8, 1, 1, 7, 1, 5, 1, 1, 1, 6, 5, 4, 1, 2, 1, 7, 1, 3, 7, 1,
8, 7, 1, 1, 2, 11, 1, 1, 1, 1, 1, 10, 1, 1, 1, 11, 3, 3, 1, 1,
9, 1, 1, 1, 11, 1, 11, 1, 1, 1, 11, 7, 1, 6, 1, 1, 1, 11, 10,
3, 4, 3, 4, 1, 1, 1, 11, 1, 8, 6, 1, 6, 5, 11, 1, 2, 1, 4, 1,
1, 1, 10, 1, 1, 6, 1, 1, 2, 1, 1, 1, 7, 2, 1, 8, 8, 1, 1, 1,
1, 5, 1, 11, 1, 1, 1, 9, 4, 1, 2, 2, 8, 1, 1, 6, 3, 1, 2, 1,
1, 1, 1, 1, 10, 9, 4, 1, 1, 6, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1,
1, 1, 2, 10, 1, 6, 2, 1, 1, 1, 1, 1, 1, 1, 10, 10, 6, 11, 1,
1, 1, 1, 11, 1, 1, 1, 1, 2, 1, 1, 1, 7, 6, 1, 1, 1, 9, 1, 7,
11, 4, 1, 1, 1, 1, 8, 1, 1, 6, 1, 2, 1, 3, 1, 11, 1, 5, 1, 6,
1, 1, 11, 6, 1, 1, 1, 2, 1, 1, 2, 6, 7, 7, 1, 8, 3, 1, 1, 1,
7, 1, 1), .Dim = c(500L, 2L))
#Now perform the kruskalmc() test.
require(pgirmess)
kruskalmc(x[,1], x[,2])
#Multiple comparison test after Kruskal-Wallis
#p.value: 0.05
#Comparisons
# obs.dif critical.dif difference
#1-2 8.4929415 82.16065 FALSE
#1-3 2.6363784 104.15270 FALSE
#1-4 22.5503277 102.13541 FALSE
#1-5 13.2511610 100.24365 FALSE
#1-6 0.8574104 108.62307 FALSE
#[..........]
#8-9 17.8228070 165.54197 FALSE
#8-10 9.5230263 162.62538 FALSE
#8-11 26.2159443 137.28174 FALSE
#9-10 27.3458333 172.25281 FALSE
#9-11 8.3931373 148.56074 FALSE
#10-11 35.7389706 145.30369 FALSE
require(agricolae)
kruskal(x[,1], x[,2])
# [ ... ]
#Means with the same letter are not significantly different
#Groups, Treatments and mean of the ranks
#a 11 304.4
#ab 9 296
#ab 7 286.6
#ab 8 278.2
#ab 10 268.7
#ab 2 250.6
#ab 6 242.9
#ab 1 242.1
#ab 3 239.4
#ab 5 228.8
#b 4 219.5
--
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