From this point of view, the difference between data set 1 and data set 2 is that the closest point pairs in data set 2 seem, in general, to be closer than the closest point pairs of data set 1. If this indeed is the main characteristic of the difference, then the Alternative hypothesis should not be that one closest point pair is closer than expected by chance, but that some summary statistic that the set of closest point pairs for the points of data set 2 has smaller values than the set of the closest point pairs for data set 1. In this case, the test statistic we might consider can be some measure of central location. We consider the arithmetic mean, the harmonic mean, and the geometric mean. We will use a 1% significance level test as before using each kind of mean as our test statistic and we will calculate the misdetect rate of each of the statistics. The table below shows what we find and compares it to the test statistic we tried first, which was the minimum of these interpoint distances.

< Previous >         < Next >