I am analyzing data from 3 different gait speeds. For each group/speed, I am determining specific value called "angle". Each group has different sample size. So, I need to compare multimodal distributions and I would like to statistically test following:
- There is significant difference between 3 modes (peaks) within each group
- There is no significant difference between same modes for all three groups (comparing to other 2 modes).
Distributions are shown below, and it is noticable that the 3 modes for each group appear around same value, relative to each other.
I am stucked with this. I have tried KDE, and I got 3 expected clusters. I am not sure how to prove the difference. I have also tried Kruskal-Wallis nonparametric test (for different sample sizes), but the results show significant difference between groups, and I think the distributions are not statistically different (2. point from above).
Another problem is that this is circular problem, since angles are from 0 to 360, so I am not sure if this changes the methods (I have already preprocessed data to deal with this issue).
Can you please help?
Please note that my real data is much larger and I cannot copy it here, so I am giving a toy example below (red violin plots are from real data):
structure(list(speed = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 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), .Label = c("04ms",
"1ms", "2ms"), class = "factor"), angle = structure(c(1L, 16L,
26L, 27L, 4L, 5L, 6L, 17L, 18L, 19L, 28L, 29L, 30L, 2L, 8L, 9L,
12L, 11L, 10L, 22L, 18L, 20L, 28L, 29L, 31L, 15L, 3L, 9L, 7L,
14L, 13L, 14L, 25L, 21L, 22L, 23L, 24L), .Label = c("1", "11",
"12", "120", "121", "123", "125", "13", "130", "132", "133",
"135", "142", "143", "18", "2", "250", "251", "252", "255", "256",
"260", "261", "262", "270", "3", "4", "5", "6", "7", "8"), class = "factor")), class = "data.frame", row.names = c(NA,
-37L))
