I have an experiment that involves testing the route-finding ability of 3 different critters. They have to travel between 5 different points (essentially a travelling salesman problem) and for each organism I measure the total length of the route. The experiment was repeated 16 times for each critter. I want to answer the question: are the crittres choosing routes that are significantly shorter than if they were selecting random routes? I was planning on running an ANOVA (or a a Welch's ANOVA) to compare the critter's route lengths to the 'random' route lengths. My question is: which is the best way to compare the 'random' paths to my organism's paths?
Compare the route lengths of all critters with a column containing all possible routes (24 possibilities). (so an ANOVA with 'Critter 1 path lengths', 'critter 2 path length', 'critter 3 path lengt' and 'all possible routes' as treatments).
Compare critter route lengths to a sample of possible routes, matched to sample size (so subsample 16 out of the 24 possibilities as my sample size for the other critters is 16)
Choose 100 random routes from the 24 possibilities (with replacement)?
I initially thought option 1 was sufficient, then moved towards 2 and am now just confused. Any advice would be greatly appreciated.