# Hypothesis testing when you have the entire population?

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?

1. 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).

2. 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)

3. 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.

• Three different types of critters, or just three individual critters? – Jay Schyler Raadt Nov 13 '18 at 11:52
• i am not exactly sure how the question in the heading relates to the questions in the body. some months ago i researched the heading question you and found this compelling answer: researchgate.net/post/… – Winfried Nov 13 '18 at 12:33
• Title: When you have entire population, there is no statistical analysis. – user158565 Nov 13 '18 at 14:32