Taking the average p value from a set of simulated p values I have 149 locations that are lined up from east to west. I have the geographical distances between each location and the adjacent location going west. I want to test whether the locations are randomly distributed or not. Therefore, I take the furthest west location and the furthest east location, and generate 145 random locations within this space and find the distance between each consecutive location (again from east to west). I then test the actual distribution of distances against the randomly generated distribution of distances using Kolmogorov Smirnov to get a p value.
However, if I then decide to do 1000 simulations, does it make sense to just calculate the average (or median) p value of the 1000 KS tests and report this?
 A: See here for the documentation of R's implementation of the Kolmogorov-Smirnov test. The important thing is that you can choose a wide variety of distributions as your null hypothesis in the KS test, like the exponential distribution as you mentioned in a comment.
For your original question, it does not make sense to average p-values because an average p-value has no useful interpretation for your needs (or for anything that I am aware of). What you are trying to do, test whether the distances between locations follow some distribution, is exactly what the KS test does. 
As an example, suppose you believe distances between the 145 locations in your data set follow a $U(0,1000)$ distribution.  Then if your 145 distances are in a vector named $\tt{x}$ in R, run
ks.test(x, punif, min=0, max=1000)

For the hypothesis that the data follows an exponential distribution with mean 2, the code is
ks.test(x, pexp, rate=0.5)

A: Actually you can combine p values using fisher's method. It's not a straight average, it is described here. http://en.wikipedia.org/wiki/Fisher%27s_method 
and probably many other places. This is assuming that the p values are independent though.
