I have a dataset with timed observations of an event across the day, in two different places. I am particularly interested in whether the peak in observation is significantly different between the two places. To give more details, we suspect that location 2 has these events happening way later than in location 1.
Here's an hypothetical example of the data:
|Location 1||Location 2|
The way I thought of testing this hypothesis is to the smooth the observation data of two locations using kernel density estimation (KDE). After that I could test whether the two density curves have different modes. However, I can't seem to find any test for differences in modes. Does anybody known of a test for that?
I tough of testing whether the mean time is different between locations, but a increase in mean hour might not represent an increase in mode, especially if the distribution is not symmetric or if it has events concentrated in particular hours with long intervals in between. Does anybody know of an alternative test I can use to test this hypothesis?