问题
Related Bounty: 250 reputation points.
I have a question regarding summary.lm() output.
Firstly, here is reproducible code for my data set:
Cond_Per_Row_stats<-structure(list(Participant = structure(c(1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L,
6L, 7L, 8L, 9L, 10L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L,
1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L), .Label = c("21", "22",
"23", "24", "25", "26", "27", "28", "29", "30"), class = "factor"),
Coherence = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L), .Label = c("P0.0", "P3", "P35",
"P4", "P45"), class = "factor"), PrimeType = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L), .Label = c("fp",
"np", "tp"), class = "factor"), PrimeDuration = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("1200ms",
"50ms"), class = "factor"), Condition = structure(c(21L,
21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 22L, 22L, 22L,
22L, 22L, 22L, 22L, 22L, 22L, 22L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 11L,
11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 12L, 12L, 12L,
12L, 12L, 12L, 12L, 12L, 12L, 12L, 25L, 25L, 25L, 25L, 25L,
25L, 25L, 25L, 25L, 25L, 26L, 26L, 26L, 26L, 26L, 26L, 26L,
26L, 26L, 26L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L,
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 15L, 15L, 15L, 15L, 15L,
15L, 15L, 15L, 15L, 15L, 16L, 16L, 16L, 16L, 16L, 16L, 16L,
16L, 16L, 16L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L,
23L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L,
13L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 29L,
29L, 29L, 29L, 29L, 29L, 29L, 29L, 29L, 29L, 30L, 30L, 30L,
30L, 30L, 30L, 30L, 30L, 30L, 30L, 9L, 9L, 9L, 9L, 9L, 9L,
9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L,
10L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 20L,
20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 27L, 27L, 27L,
27L, 27L, 27L, 27L, 27L, 27L, 27L, 28L, 28L, 28L, 28L, 28L,
28L, 28L, 28L, 28L, 28L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 17L, 17L,
17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 18L,
18L, 18L, 18L, 18L, 18L, 18L), .Label = c("P0.0np1200.0",
"P0.0np50.0", "P3np1200.0", "P3np50.0", "P35np1200.0", "P35np50.0",
"P4np1200.0", "P4np50.0", "P45np1200.0", "P45np50.0", "P0.0tp1200.0",
"P0.0tp50.0", "P3tp1200.0", "P3tp50.0", "P35tp1200.0", "P35tp50.0",
"P4tp1200.0", "P4tp50.0", "P45tp1200.0", "P45tp50.0", "P0.0fp1200.0",
"P0.0fp50.0", "P3fp1200.0", "P3fp50.0", "P35fp1200.0", "P35fp50.0",
"P4fp1200.0", "P4fp50.0", "P45fp1200.0", "P45fp50.0"), class = "factor"),
Accuracy = c(0.785398163397448, 0.523598775598299, 0.785398163397448,
0.523598775598299, 0.785398163397448, 0.869122203007293,
0.955316618124509, 0.785398163397448, 0.615479708670387,
0.701674123787604, 1.15026199151093, 1.15026199151093, 0.869122203007293,
0.523598775598299, 0.701674123787604, 0.701674123787604,
0.955316618124509, 0.701674123787604, 0.955316618124509,
0.615479708670387, 0.955316618124509, 0.785398163397448,
0.701674123787604, 0.869122203007293, 0.785398163397448,
0.615479708670387, 0.615479708670387, 0.869122203007293,
0.701674123787604, 0.615479708670387, 1.0471975511966, 0.869122203007293,
0.615479708670387, 0.615479708670387, 0.869122203007293,
0.701674123787604, 0.701674123787604, 0.869122203007293,
0.785398163397448, 0.869122203007293, 1.0471975511966, 0.955316618124509,
0.523598775598299, 1.0471975511966, 0.615479708670387, 0.955316618124509,
0.615479708670387, 0.785398163397448, 0.955316618124509,
0.785398163397448, 0.701674123787604, 0.615479708670387,
0.615479708670387, 0.955316618124509, 0.869122203007293,
0.869122203007293, 1.0471975511966, 0.785398163397448, 0.701674123787604,
0.785398163397448, 1.0471975511966, 0.911738290968488, 1.00028587904971,
0.827113206702756, 0.785398163397448, 1.00028587904971, 1.09681145610345,
1.00028587904971, 1.0471975511966, 1.09681145610345, 1.0471975511966,
0.827113206702756, 1.0471975511966, 0.420534335283965, 0.659058035826409,
1.0471975511966, 0.869122203007293, 1.0471975511966, 0.869122203007293,
0.785398163397448, 1.09681145610345, 0.785398163397448, 0.955316618124509,
0.911738290968488, 0.911738290968488, 1.00028587904971, 1.20942920288819,
1.15026199151093, 1.00028587904971, 1.20942920288819, 1.09681145610345,
1.0471975511966, 0.911738290968488, 0.827113206702756, 1.00028587904971,
0.969532110115768, 1.09681145610345, 1.00028587904971, 0.785398163397448,
1.09681145610345, 1.09681145610345, 0.869122203007293, 0.743683120092141,
0.869122203007293, 0.869122203007293, 1.0471975511966, 1.00028587904971,
1.09681145610345, 1.36522739563372, 1.00028587904971, 1.15026199151093,
0.869122203007293, 0.570510447745185, 1.20942920288819, 1.0471975511966,
0.955316618124509, 0.827113206702756, 1.00028587904971, 1.00028587904971,
1.0471975511966, 0.955316618124509, 0.911738290968488, 0.911738290968488,
0.570510447745185, 0.869122203007293, 1.00028587904971, 0.869122203007293,
0.785398163397448, 0.911738290968488, 0.869122203007293,
0.785398163397448, 0.701674123787604, 1.00028587904971, 0.420534335283965,
0.570510447745185, 0.969532110115768, 0.869122203007293,
0.911738290968488, 1.0471975511966, 0.785398163397448, 0.955316618124509,
0.827113206702756, 0.827113206702756, 0.659058035826409,
0.955316618124509, 0.701674123787604, 0.785398163397448,
0.785398163397448, 1.09681145610345, 1.0471975511966, 0.869122203007293,
0.827113206702756, 0.911738290968488, 0.827113206702756,
0.785398163397448, 0.827113206702756, 1.00028587904971, 0.911738290968488,
1.09681145610345, 0.955316618124509, 0.955316618124509, 1.15026199151093,
0.785398163397448, 0.955316618124509, 0.911738290968488,
1.0471975511966, 0.869122203007293, 0.869122203007293, 0.911738290968488,
0.955316618124509, 0.955316618124509, 0.827113206702756,
0.785398163397448, 0.869122203007293, 0.955316618124509,
0.684719203002283, 0.827113206702756, 1.00028587904971, 0.785398163397448,
0.827113206702756, 1.27795355506632, 1.20942920288819, 1.27795355506632,
1.00028587904971, 0.869122203007293, 1.15026199151093, 1.36522739563372,
1.27795355506632, 1.5707963267949, 1.5707963267949, 1.5707963267949,
1.27795355506632, 1.20942920288819, 0.911738290968488, 0.659058035826409,
1.36522739563372, 1.20942920288819, 1.36522739563372, 1.36522739563372,
1.27795355506632, 1.20942920288819, 1.0471975511966, 1.15026199151093,
1.15026199151093, 0.869122203007293, 1.27795355506632, 1.36522739563372,
1.27795355506632, 1.09681145610345, 1.36522739563372, 1.27795355506632,
1.00028587904971, 1.27795355506632, 1.15026199151093, 1.00028587904971,
1.36522739563372, 1.09681145610345, 1.15026199151093, 1.15026199151093,
1.36522739563372, 1.5707963267949, 1.5707963267949, 0.869122203007293,
1.09681145610345, 1.20942920288819, 1.36522739563372, 1.27795355506632,
1.27795355506632, 1.36522739563372, 1.5707963267949, 1.5707963267949,
1.15026199151093, 0.911738290968488, 1.20942920288819, 1.20942920288819,
1.28403977458335, 1.20942920288819, 1.36522739563372, 1.27795355506632,
1.36522739563372, 1.20942920288819, 0.911738290968488, 1.20942920288819,
1.0471975511966, 0.827113206702756, 1.5707963267949, 1.0471975511966,
1.0471975511966, 1.15026199151093, 1.27795355506632, 1.15026199151093,
1.00028587904971, 1.20942920288819, 0.659058035826409, 0.785398163397448,
1.09681145610345, 1.20942920288819, 0.827113206702756, 1.0471975511966,
1.20942920288819, 1.5707963267949, 0.955316618124509, 1.0471975511966,
1.0471975511966, 0.869122203007293, 1.20942920288819, 1.27795355506632,
1.09681145610345, 1.0471975511966, 1.5707963267949, 1.27795355506632,
0.869122203007293, 1.00028587904971, 0.911738290968488, 0.911738290968488,
1.00028587904971, 1.20942920288819, 1.20942920288819, 1.00028587904971,
1.36522739563372, 1.0471975511966, 1.09681145610345, 0.827113206702756,
1.15026199151093, 1.09681145610345, 1.27795355506632, 1.36522739563372,
1.36522739563372, 1.36522739563372, 1.15026199151093, 1.27795355506632,
0.955316618124509, 0.701674123787604, 1.09681145610345, 1.00028587904971,
1.20942920288819, 1.20942920288819, 1.20942920288819, 1.00028587904971,
1.36522739563372)), .Names = c("Participant", "Coherence",
"PrimeType", "PrimeDuration", "Condition", "Accuracy"), row.names = c(20L,
21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 49L, 50L, 51L, 52L,
53L, 54L, 55L, 56L, 57L, 58L, 78L, 79L, 80L, 81L, 82L, 83L, 84L,
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862L, 863L, 864L, 865L, 866L, 867L, 868L, 869L, 870L), class = "data.frame")
(NB: It is worth noting here that I changed 'Participant' to a factor prior to creating reproducible code. This is in order to ensure the output of aov matches that of a Type III ezANOVA. This does affect the output of aov making it incompatible with summary.lm(). However, this is not avoidable it seems when running a repeated measures with aov. See here for some context.)
I then change the factor levels in Condition like this:
Cond_Per_Row_stats$Condition <- factor (Cond_Per_Row_stats$Condition, levels = c("P0.0np1200.0", "P0.0np50.0",
"P3np1200.0", "P3np50.0",
"P35np1200.0", "P35np50.0",
"P4np1200.0", "P4np50.0",
"P45np1200.0", "P45np50.0",
"P0.0tp1200.0", "P0.0tp50.0",
"P3tp1200.0", "P3tp50.0",
"P35tp1200.0", "P35tp50.0",
"P4tp1200.0", "P4tp50.0",
"P45tp1200.0", "P45tp50.0",
"P0.0fp1200.0", "P0.0fp50.0",
"P3fp1200.0", "P3fp50.0",
"P35fp1200.0", "P35fp50.0",
"P4fp1200.0", "P4fp50.0",
"P45fp1200.0", "P45fp50.0"
))
Cond_Per_Row_stats <- Cond_Per_Row_stats[order(Cond_Per_Row_stats$Condition),]
I run a repeated measures aov:
aovModel <- aov(Accuracy ~ (Coherence * PrimeDuration * PrimeType) + Error(Participant/(Coherence * PrimeDuration * PrimeType)), data = Cond_Per_Row_stats)
summary(aovModel)
With this output:
Error: Participant
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 9 2.045 0.2272
Error: Participant:Coherence
Df Sum Sq Mean Sq F value Pr(>F)
Coherence 4 7.800 1.9499 66.3 4.18e-16 ***
Residuals 36 1.059 0.0294
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: Participant:PrimeDuration
Df Sum Sq Mean Sq F value Pr(>F)
PrimeDuration 1 0.10509 0.10509 10.91 0.00918 **
Residuals 9 0.08668 0.00963
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: Participant:PrimeType
Df Sum Sq Mean Sq F value Pr(>F)
PrimeType 2 0.137 0.06850 0.763 0.481
Residuals 18 1.617 0.08981
Error: Participant:Coherence:PrimeDuration
Df Sum Sq Mean Sq F value Pr(>F)
Coherence:PrimeDuration 4 0.1355 0.03387 2.443 0.0643 .
Residuals 36 0.4992 0.01387
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: Participant:Coherence:PrimeType
Df Sum Sq Mean Sq F value Pr(>F)
Coherence:PrimeType 8 0.1439 0.01798 1.084 0.384
Residuals 72 1.1943 0.01659
Error: Participant:PrimeDuration:PrimeType
Df Sum Sq Mean Sq F value Pr(>F)
PrimeDuration:PrimeType 2 0.0296 0.01481 0.563 0.579
Residuals 18 0.4733 0.02629
Error: Participant:Coherence:PrimeDuration:PrimeType
Df Sum Sq Mean Sq F value Pr(>F)
Coherence:PrimeDuration:PrimeType 8 0.0979 0.01223 0.884 0.534
Residuals 72 0.9965 0.01384
Next I attempt to conduct planned contrasts and that's where I run into problems. First of all I want to use:
summary.lm(aovModel)
But the output from the repeated measures model is not compatible:
Error in if (p == 0) { : argument is of length zero
This isn't a massive issue when I simply want a summary of the model, I can just use summary(aovModel) and inspect the SS, F-values etc there. It is a problem when I want to summarize planned contrasts using summary.lm().
For example, as you can see from the dataframe there are 30 conditions. This is the code I've put together in an attempt to create planned contrasts where the 10 np Conditions are controls and the remaining Conditions are compared to them in contrast1 and then I compare the tp and fp Conditions against each other in contrast2:
contrast1<-c(-20,-20,-20,-20,-20,-20,-20,-20,-20,-20,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10)
contrast2<-c(0,0,0,0,0,0,0,0,0,0,-10,-10,-10,-10,-10,-10,-10,-10,-10,-10,10,10,10,10,10,10,10,10,10,10)
contrasts(Cond_Per_Row_stats$Condition)<-cbind(contrast1, contrast2)
Cond_Per_Row_stats$Condition
aovModelContrastCondition <- aov(Accuracy ~ (Coherence * PrimeDuration * PrimeType) + Error(Participant/(Coherence * PrimeDuration * PrimeType)), data = Cond_Per_Row_stats)
summary.lm(aovModelContrastCondition)
The output for summary.lm() here results in the same error as above.
However, if I run the following code calling a section directly:
summary.lm(aovModelContrastCondition$'Participant:Coherence:PrimeDuration:PrimeType')
I get this output:
Residuals:
Min 1Q Median 3Q Max
-0.23063 -0.08368 -0.02695 0.06902 0.27561
Coefficients:
Estimate Std. Error t value Pr(>|t|)
CoherenceP3:PrimeDuration50ms:PrimeTypenp 0.15288 0.10522 1.453 0.1506
CoherenceP35:PrimeDuration50ms:PrimeTypenp 0.13600 0.10522 1.293 0.2003
CoherenceP4:PrimeDuration50ms:PrimeTypenp 0.07323 0.10522 0.696 0.4887
CoherenceP45:PrimeDuration50ms:PrimeTypenp 0.09476 0.10522 0.901 0.3708
CoherenceP3:PrimeDuration50ms:PrimeTypetp 0.10329 0.10522 0.982 0.3296
CoherenceP35:PrimeDuration50ms:PrimeTypetp 0.22469 0.10522 2.135 0.0361 *
CoherenceP4:PrimeDuration50ms:PrimeTypetp 0.17215 0.10522 1.636 0.1062
CoherenceP45:PrimeDuration50ms:PrimeTypetp 0.10710 0.10522 1.018 0.3122
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1176 on 72 degrees of freedom
Multiple R-squared: 0.08646, Adjusted R-squared: -0.002361
F-statistic: 0.9734 on 7 and 72 DF, p-value: 0.4572
Essentially I'm not entirely sure what I'm seeing here (especially considering how I set up contrast1 and contrast2). Examples of planned contrasts I've seen used between subjects designs and therefore do not address the issue with summary.lm() when conducting a repeated measures ANOVA.
Does anyone have any experience or know-how when it comes to adapting summary.lm() for repeated measures planned contrasts? Or is there another way of viewing the outcome of the planned contrasts in a repeated measures ANOVA using aov?
Thanks in advance.
回答1:
The emmeans package can handle aovlist objects (and many others) and calculate your custom contrasts.
At first we fit the repeated measures ANOVA using orthogonal contrasts.
library("emmeans")
# set orthogonal contrasts
options(contrasts = c("contr.sum", "contr.poly"))
aovModel <- aov(Accuracy ~ Coherence * PrimeDuration * PrimeType +
Error(Participant / (Coherence * PrimeDuration * PrimeType)),
data = Cond_Per_Row_stats)
Now we create an emmGrid object and have a look at the estimated marginal means (EMMs) using the emmeans() function.
emm <- emmeans(aovModel, ~ Coherence * PrimeDuration * PrimeType)
emm
## Coherence PrimeDuration PrimeType emmean SE df lower.CL upper.CL
## P0.0 1200ms fp 0.7330383 0.05433093 91.44 0.6251235 0.8409531
## P3 1200ms fp 0.8654093 0.05433093 91.44 0.7574945 0.9733241
## P35 1200ms fp 0.9813125 0.05433093 91.44 0.8733977 1.0892273
## P4 1200ms fp 1.1298314 0.05433093 91.44 1.0219167 1.2377462
## P45 1200ms fp 1.2569780 0.05433093 91.44 1.1490632 1.3648928
## P0.0 50ms fp 0.8324380 0.05433093 91.44 0.7245232 0.9403528
## P3 50ms fp 0.8061391 0.05433093 91.44 0.6982243 0.9140539
## P35 50ms fp 0.8619138 0.05433093 91.44 0.7539990 0.9698286
## P4 50ms fp 1.0194414 0.05433093 91.44 0.9115266 1.1273562
## P45 50ms fp 1.2212040 0.05433093 91.44 1.1132892 1.3291188
## P0.0 1200ms np 0.7514145 0.05433093 91.44 0.6434997 0.8593293
## P3 1200ms np 0.8640397 0.05433093 91.44 0.7561249 0.9719545
## P35 1200ms np 1.0230695 0.05433093 91.44 0.9151547 1.1309843
## P4 1200ms np 1.1691818 0.05433093 91.44 1.0612670 1.2770966
## P45 1200ms np 1.1809446 0.05433093 91.44 1.0730298 1.2888594
## P0.0 50ms np 0.7943392 0.05433093 91.44 0.6864244 0.9022540
## P3 50ms np 0.9011751 0.05433093 91.44 0.7932603 1.0090898
## P35 50ms np 0.9831985 0.05433093 91.44 0.8752838 1.0911133
## P4 50ms np 1.0755496 0.05433093 91.44 0.9676348 1.1834644
## P45 50ms np 1.1834531 0.05433093 91.44 1.0755383 1.2913679
## P0.0 1200ms tp 0.8285699 0.05433093 91.44 0.7206552 0.9364847
## P3 1200ms tp 0.9410529 0.05433093 91.44 0.8331381 1.0489676
## P35 1200ms tp 0.9957669 0.05433093 91.44 0.8878521 1.1036817
## P4 1200ms tp 1.1742093 0.05433093 91.44 1.0662945 1.2821241
## P45 1200ms tp 1.3174114 0.05433093 91.44 1.2094966 1.4253262
## P0.0 50ms tp 0.7945863 0.05433093 91.44 0.6866715 0.9025010
## P3 50ms tp 0.8516896 0.05433093 91.44 0.7437749 0.9596044
## P35 50ms tp 0.9676721 0.05433093 91.44 0.8597573 1.0755868
## P4 50ms tp 1.1025843 0.05433093 91.44 0.9946695 1.2104990
## P45 50ms tp 1.2553532 0.05433093 91.44 1.1474384 1.3632680
Your contrasts equate to the following hypotheses:
Considering all factor levels and their order in the emmGrid object, we can express these hypotheses equivalently as:
From this we can see the contrast weights you need for contrast1 and contrast2:
contrast1 <- rep(c(-0.5, 1, -0.5) / 10, each = 10)
contrast2 <- rep(c(-1, 0, 1) / 10, each = 10)
To calculate your custom contrasts and get p-values we can now use the contrast() function.
contrast(emm, list(c1 = contrast1,
c2 = contrast2))
## contrast estimate SE df t.ratio p.value
## c1 -0.004193526 0.03670287 18 -0.114 0.9103
## c2 0.052118996 0.04238082 18 1.230 0.2346
If you are only interested in contrasts related to the factor PrimeType it is even easier to construct the emmGrid object as follows:
emm <- emmeans(aovModel, ~ PrimeType)
This implicitly averages over the levels of Coherence and PrimeDuration (which is also indicated by the output).
emm
## PrimeType emmean SE df lower.CL upper.CL
## fp 0.9707706 0.03682466 21.98 0.8943978 1.047143
## np 0.9926366 0.03682466 21.98 0.9162638 1.069009
## tp 1.0228896 0.03682466 21.98 0.9465168 1.099262
##
## Results are averaged over the levels of: Coherence, PrimeDuration
We can then specify the contrast weights for contrast1 and contrast2 by:
contrast1 <- c(-0.5, 1, -0.5)
contrast2 <- c(-1, 0, 1)
The results are equal to the ones we obtained with the "more complex" method.
来源：https://stackoverflow.com/questions/35933702/summary-lm-output-when-using-aov-in-r