3
$\begingroup$

As I understand it aov() is a Type I SS ANOVA. I have followed online advice on how to change its output to Type III.

I have also run a Type III ezANOVA.

My problem is that the F-values and corresponding p-values differ greatly between these two approaches.

Here is reproducible code for my data set:

Cond_Per_Row_stats<-structure(list(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"), 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"), 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"), Participant = c(21L, 22L, 23L, 24L, 25L,
26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L,
29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L,
22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L,
25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L,
28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L,
21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L,
24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L,
27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L,
30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L,
23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L,
26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L,
29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L,
22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L,
25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L,
28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L,
21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L,
24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L,
27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L,
30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L,
23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L,
26L, 27L, 28L, 29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L,
29L, 30L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 21L,
22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L), 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("Coherence",
"PrimeDuration", "PrimeType", "Participant", "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")

Here's the code for ezANOVA Type III:

Cond_Per_Row_stats$Participant <- as.factor(Cond_Per_Row_stats$Participant)
Exp1Model <- ezANOVA(data = Cond_Per_Row_stats, dv = .(Accuracy), wid = .(Participant), within = .(Coherence, PrimeDuration, PrimeType), type=3, detailed = TRUE)

#Exp1Model
Exp1Model$ANOVA

And here is the ezANOVA output:

                            Effect DFn DFd          SSn        SSd            F            p p<.05         ges
1                       (Intercept)   1   9 297.26560885 2.04482984 1308.3682683 4.670956e-11     * 0.973889040
2                         Coherence   4  36   7.79974598 1.05880149   66.2992210 4.175417e-16     * 0.494602047
3                     PrimeDuration   1   9   0.10509137 0.08667666   10.9120771 9.180827e-03     * 0.013014273
4                         PrimeType   2  18   0.13699186 1.61652086    0.7627039 4.808964e-01       0.016898001
5           Coherence:PrimeDuration   4  36   0.13548043 0.49918172    2.4426453 6.426183e-02       0.016714681
6               Coherence:PrimeType   8  72   0.14385084 1.19426233    1.0840646 3.841289e-01       0.017729058
7           PrimeDuration:PrimeType   2  18   0.02961932 0.47325423    0.5632784 5.790571e-01       0.003702594
8 Coherence:PrimeDuration:PrimeType   8  72   0.09786368 0.99646749    0.8838955 5.343856e-01       0.012130069

When I use aov() with advised code to get Type III output:

Cond_Per_Row_stats$Participant <- as.factor(Cond_Per_Row_stats$Participant)
        options(contrasts=c("contr.sum", "contr.poly"))
    aovModel <- aov(Accuracy ~ Coherence * PrimeDuration * PrimeType, data = Cond_Per_Row_stats)
    ## drop1() supposedly spits out Type III results...
    drop1(aovModel,~.,test="F")

I get this output:

    Model:
Accuracy ~ Coherence * PrimeDuration * PrimeType
                                  Df Sum of Sq     RSS      AIC F value  Pr(>F)    
<none>                                          7.9700 -1028.43                    
Coherence                          4    7.7997 15.7697  -831.71 66.0581 < 2e-16 ***
PrimeDuration                      1    0.1051  8.0751 -1026.50  3.5602 0.06025 .  
PrimeType                          2    0.1370  8.1070 -1027.32  2.3204 0.10019    
Coherence:PrimeDuration            4    0.1355  8.1055 -1031.37  1.1474 0.33457    
Coherence:PrimeType                8    0.1439  8.1138 -1039.06  0.6092 0.76998    
PrimeDuration:PrimeType            2    0.0296  7.9996 -1031.32  0.5017 0.60606    
Coherence:PrimeDuration:PrimeType  8    0.0979  8.0679 -1040.77  0.4144 0.91186

As can be seen the outputs for F-values and the corresponding p-values differ quite a bit (apart from coincidental similarity in 'Coherence' factor).

Firstly, does anyone know why the outputs are different considering I followed advice on how to change aov() to Type III output? The sum of squares match but shouldn't everything else also?

Secondly, can anyone suggest how I can ensure aov() outputs the same F-values as ezANOVA?

I've exhausted all avenues that I can find to get to this point. Any advice would be very welcome.

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The reason why you are getting different results, is that you have a within subjects / repeated measures design (at least that is what I concluded from the used ezANOVA function). The way you specified your aov() model uses the predictors as you should do in a between subjects design (with interactions because you used * instead of +).

When you want to specify it as a within subjects design with aov(), you can specify this as follows:

m.aov <- aov(Accuracy ~ (Coherence * PrimeDuration * PrimeType) + 
               Error(Participant/(Coherence * PrimeDuration * PrimeType)), 
            data = Cond_Per_Row_stats)

Now let's compare that to the ezANOVA approach:

library(ez)
m.ez <- ezANOVA(data = Cond_Per_Row_stats, 
                dv = .(Accuracy), 
                wid = .(Participant), 
                within = .(Coherence, PrimeDuration, PrimeType), 
                type = 3, detailed = TRUE)

Looking at the output of summary(m.aov):

> summary(m.aov)

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

you see that you now get the same result compared to the output of m.ez$ANOVA:

                             Effect DFn DFd          SSn        SSd            F            p p<.05         ges
1                       (Intercept)   1   9 297.26560885 2.04482984 1308.3682683 4.670956e-11     * 0.973889040
2                         Coherence   4  36   7.79974598 1.05880149   66.2992210 4.175417e-16     * 0.494602047
3                     PrimeDuration   1   9   0.10509137 0.08667666   10.9120771 9.180827e-03     * 0.013014273
4                         PrimeType   2  18   0.13699186 1.61652086    0.7627039 4.808964e-01       0.016898001
5           Coherence:PrimeDuration   4  36   0.13548043 0.49918172    2.4426453 6.426183e-02       0.016714681
6               Coherence:PrimeType   8  72   0.14385084 1.19426233    1.0840646 3.841289e-01       0.017729058
7           PrimeDuration:PrimeType   2  18   0.02961932 0.47325423    0.5632784 5.790571e-01       0.003702594
8 Coherence:PrimeDuration:PrimeType   8  72   0.09786368 0.99646749    0.8838955 5.343856e-01       0.012130069
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  • $\begingroup$ That looks good so far. I'll check it against my larger data set and select as answered once I've double checked. Thank you very much for that! $\endgroup$
    – Docconcoct
    Mar 10, 2016 at 15:43
  • 1
    $\begingroup$ This is the correct answer. $\endgroup$
    – Henrik
    Mar 10, 2016 at 16:57

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