I have done a lot of linear modeling for my thesis, however one of the unsolved stat problems I have should be a pretty basic issue. I am testing to see if an animal is moving from its nest to the stream by following the shortest path or the decline in slope. I drew a straight distance line, and a line that follows the slope as if water was poured from the nest using ArcGIS. I then measured the distance from each animal's waypoint to both lines. So far I used a studen'ts paired t-test to test the significance between the distance from the slope line and the straight line (acting as a null). One of my reviewers mentioned this may be incorrect as the student's paired t-test is usually used for before and after a treatment, such as administering a drug. It has been awhile since I have ran basic stat test, and I greatly appreciate any feedback and advice. Thanks!

Hi,
the paired t-test calculates the difference between the two values making up the pair and tests hypothesises referring to this difference.

So one test could be that the difference between the distance to the slope path and the distance to the linear path is < 0. This would mean that the animal generally keeps closer to the linear path then to the slope path but imho it will not tell you that its is following that path. In fact it could follow any number of alternatives and stillll be on the average closer to one path then to the other, without beeing close to any of them.

This sounds like a job for the sum of the squares of distances from one path compared to the other one. If the sum of squares of the distances from one of the path is small enough it would mean that the animal is actually following that path. Off the top of my head I do not know how to test the different sum of squares for significance though, but that would be the direction I would be looking.