Wappred normal for sensorimotor synchronization task

library(ggplot2)
library(dplyr)
library(circular)

Simulating normal distributions with fixed temporal standard deviation

sim <- expand.grid(freq = seq(.5,5,.5), 
                   stams = seq(30,110, 10),
                   n = 1:10000) %>% 
  group_by(freq, stams, n) %>% 
  mutate(responsems = rnorm(1, 0,stams), 
         responseangle = responsems / 1000 * freq * 4 * pi)

ggplot(sim, aes(x = responsems)) + 
         facet_wrap(~stams) +
         geom_histogram()

Plots for the angle (radians)

ggplot(sim, aes(x = responseangle)) + 
         facet_wrap(~stams) +
         geom_histogram()

Fittting wrapped normals to the response angle and transform them to temporal units

funWrapSim <- function(d){
  sta <- mle.wrappednormal(d$responseangle)$sd
  stamswrap <- sta / (4*pi*first(d$freq))*1000 
  data.frame(stamswrap)
}

simwrap <- sim %>% 
  group_by(freq, stams) %>%
  do(funWrapSim(.))

ggplot(simwrap, aes(x = stams, y = stamswrap, color=factor(freq))) +
  geom_abline(lty = 2) +
         geom_line() +
  labs(x = 'Original sta dev (ms)', y = 'Recovered sta dev (ms)')