summary.lm output when using aov in R

Asked 11/3, 2016 at 6:31 Answered 3/1, 2019 at 1:26

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, 
85L, 86L, 87L, 107L, 108L, 109L, 110L, 111L, 112L, 113L, 114L, 
115L, 116L, 136L, 137L, 138L, 139L, 140L, 141L, 142L, 143L, 144L, 
145L, 165L, 166L, 167L, 168L, 169L, 170L, 171L, 172L, 173L, 174L, 
194L, 195L, 196L, 197L, 198L, 199L, 200L, 201L, 202L, 203L, 223L, 
224L, 225L, 226L, 227L, 228L, 229L, 230L, 231L, 232L, 252L, 253L, 
254L, 255L, 256L, 257L, 258L, 259L, 260L, 261L, 281L, 282L, 283L, 
284L, 285L, 286L, 287L, 288L, 289L, 290L, 310L, 311L, 312L, 313L, 
314L, 315L, 316L, 317L, 318L, 319L, 339L, 340L, 341L, 342L, 343L, 
344L, 345L, 346L, 347L, 348L, 368L, 369L, 370L, 371L, 372L, 373L, 
374L, 375L, 376L, 377L, 397L, 398L, 399L, 400L, 401L, 402L, 403L, 
404L, 405L, 406L, 426L, 427L, 428L, 429L, 430L, 431L, 432L, 433L, 
434L, 435L, 455L, 456L, 457L, 458L, 459L, 460L, 461L, 462L, 463L, 
464L, 484L, 485L, 486L, 487L, 488L, 489L, 490L, 491L, 492L, 493L, 
513L, 514L, 515L, 516L, 517L, 518L, 519L, 520L, 521L, 522L, 542L, 
543L, 544L, 545L, 546L, 547L, 548L, 549L, 550L, 551L, 571L, 572L, 
573L, 574L, 575L, 576L, 577L, 578L, 579L, 580L, 600L, 601L, 602L, 
603L, 604L, 605L, 606L, 607L, 608L, 609L, 629L, 630L, 631L, 632L, 
633L, 634L, 635L, 636L, 637L, 638L, 658L, 659L, 660L, 661L, 662L, 
663L, 664L, 665L, 666L, 667L, 687L, 688L, 689L, 690L, 691L, 692L, 
693L, 694L, 695L, 696L, 716L, 717L, 718L, 719L, 720L, 721L, 722L, 
723L, 724L, 725L, 745L, 746L, 747L, 748L, 749L, 750L, 751L, 752L, 
753L, 754L, 774L, 775L, 776L, 777L, 778L, 779L, 780L, 781L, 782L, 
783L, 803L, 804L, 805L, 806L, 807L, 808L, 809L, 810L, 811L, 812L, 
832L, 833L, 834L, 835L, 836L, 837L, 838L, 839L, 840L, 841L, 861L, 
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.

Downtime answered 11/3, 2016 at 6:31 Comment(11)

summary.lm is a summary method for an lm object. If you really want to use it, use the lm function instead of anova. aovModel does not inherit the lm class in this case, because you are using the Error function. I am not sure what Error actually does, but one way to fix your issue would be to find a way to replace Error with something usable in lm. The latter should be possible since aov is just a wrapper for lm. – Angleworm 11/3, 2016 at 11:6

@Angleworm thank you very much for your suggestions. I recently asked a question about trying to use the ezANOVA output (which can output aov also) in planned contrasts also & will be adding a bounty to that soon. I suspect there must be a way of using the data that is generated in tandem with planned contrasts. – Downtime 11/3, 2016 at 11:47

Would you mind expanding a little bit on what planned contrasts are? Many different fields use different terminology, and I have never heard of it under this name before, but maybe I can help if I understand better what it means. – Angleworm 11/3, 2016 at 16:36

@Angleworm Planned Contrasts (AKA planned comparisons) are a priori tests that only test specific pairwise comparisons, as compared to Post-hoc tests which test all possible combinations. They are based on predictions of the hypotheses and as such are targeted comparisons. Orthogonal contrasts are the preferred approach. Here's a bit of theoretical background I found: stat.cmu.edu/~hseltman/309/Book/chapter13.pdf – Downtime 11/3, 2016 at 17:22

So, planned contrasts basically refer to group-mean differences for selected groups? And that is why you want to use summary.lm, since it gives you more directly the difference of an individual group from the grand mean? – Angleworm 11/3, 2016 at 17:26

@Angleworm that's basically it. I've added a link to a related Q which has a bounty of 250 I started today BTW if you are interested. – Downtime 11/3, 2016 at 17:32

The issue is, I am not very familiar with anova terminology, and I don't know what Error does. Acc. to the helpfile, it says it is used to specify error strata, and appropriate models are fitted within each error stratum. Indeed, lapply(aovModel, class) shows you that aovModel is 9 different but individual anova models in a list, which makes me wonder if the group comparisons that you are after are actually retrievable from this. – Angleworm 11/3, 2016 at 17:49

@Angleworm That's where my knowledge of the functions fall short I'm afraid. I have no confidence one way or the other on that front. – Downtime 11/3, 2016 at 17:51

@Downtime Does my A solve your problem? – Doyen 27/6, 2019 at 12:41

@Doyen Hi, there. I'll try and make some time to test your answer in the coming days. Cheers. – Downtime 27/6, 2019 at 13:53

Alright. Looking forward to your feedback. – Doyen 1/7, 2019 at 20:41

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.

Doyen answered 3/1, 2019 at 1:26 Comment(0)

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