Dear Julia peeps,

I am trying to relate brain activity to an amplitude modulated tone stimulus. As in, does the peak of brain activity occur in synchrony with the phase of the modulated tone? HypothesisTests.jl has this function for a Rayleigh Test: ( HypothesisTests.jl/circular.jl at master · JuliaStats/HypothesisTests.jl (github.com)) but I am not sure from the documentation how to use it. Below is the code I’m using to find instantaneous phase of a 2 Hz amplitude modulation wave and relate a series of mock peak latencies to it. I then take the phase as orientation for a series of unit vectors and find the sum of vectors for the length of the resultant vector (vstrength). I want to compare that resultant vector length between conditions and I believe I should be able to do that with the Rayleigh Test. Any help would be appreciated on how to use this function properly.

(I’m using this publication as reference: Auditory Cortex Phase Locking to Amplitude-Modulated Cochlear Implant Pulse Trains (physiology.org))

```
using DSP, FFTW, HypothesisTests
# prep the data which will fluctuate
peaklat1 = Int.(ceil.(rand(100)*100)) # list of fake latencies
peaklat1[peaklat1 .> 50] = peaklat1[peaklat1 .> 50].+150 # create more variance
peaklat2 = Int.(ceil.(rand(100)*100)) # list of fake latencies
clickfreq = 2 # stimulus frequency
sr = 1000 # sampling rate
function getAMwave(clickfreq=2,sr=1000)
t = 0:1/sr:1 # time course
wave = sin.((2*π*clickfreq*t).+3π/2) # AM wave starting at the bottom
return wave
end
# generate the AM wave used and get instantaneous phase
wave = getAMwave(clickfreq,sr) # function above
wavephase = angle.(hilbert(wave)) # Compute phase of wave
# get the phase at each time point of signal peak amplitude
orientation1 = wavephase[peaklat1]
# break vector into components i and j to compute sums, averages, and then the resultant vector
i1 = cos.(orientation1)
j1 = sin.(orientation1)
sumi1 = sum(i1)
sumj1 = sum(j1)
avgi1 = sumi1/length(i1) # average of component i
avgj1 = sumj1/length(j1) # average of component j
vstrength1 = sqrt((avgi1^2)+(avgj1^2)) # find the vector based on i and j components (Pythagorean)
# now the same for the second latency series
orientation2 = wavephase[peaklat2]
i2 = cos.(orientation2)
j2 = sin.(orientation2)
sumi2 = sum(i2)
sumj2 = sum(j2)
avgi2 = sumi2/length(i2)
avgj2 = sumj2/length(j2)
vstrength2 = sqrt((avgi2^2)+(avgj2^2))
# what I feel I should be able to do:
RayleighTest(vstrength1,vstrength2)
# or
RayleighTest([vstrength1,vstrength2],100) # 100 observations per condition
```