I have a set of
n spatial points distributed across the landscape. I have hypothesised that the location of these points is determined by a property of the landscape as measured from the point, such as extent of viewshed (
v). I have used a peturbation simulation to test this hypothesis; for each of the 99 iterations of the simulation the location of each point is randomly moved a given distance before
v is measured.
Next, I calculate the mean value of
v for both the original set of points and each set of points belonging to each iteration of the simulation. When all 100 mean
v values are ranked by size, the original dataset shows the highest value, leading me to reject the null hypothesis that the position of the points in the original dataset was determined by chance alone.
However, when I rank
v for each point individually (i.e. compare each original point's
v value against all 99 peturbated
v values for this point), I see that for most of the original points the original
v rarely ranks highest, and often ranks somewhere in the middle of all
v values derived from peturbated points. Only in a select few cases does the original
v value rank highly compared to all simulated examples.
It would seem that, individually, the location of each point is not optimised to maximimise
v in comparison to 99 nearby peturbated locations. Yet, when viewed as a set, the mean
v value across the original points is higher than in any of the peturbated sets. Is it still fair to use the overall mean to reject the null hypothesis? What are the implications of the above staticially?