Wow where to start? As a physical chemist it appears that your units are not comparable as they stand. If you could solve that problem what would such a difference even mean? We would expect some difference between these because of a difference in human physiology most likely would we not? Further the action of the analyte x would seem to have some effect would it not? In this last case the concentration of x itself may not be the important thing because of actions with x as it moves to each final location. If you can answer some questions like these then we could talk about statistical methods to answer your question. If I have missed the important point please tell me. Best wishes David Booth

David Eugene Booth, the scenario described, admittedly, is a hastily-made caricature of a study I am working on. The intention was to provide a context for the key question that serves as the title of the post. The real study that "inspired" this post, nevertheless, has legitimate components and reasoning (of which I am not inclined to share even partially as it is a work in progress with multiple collaborators). While I understand that the domain/subject details are at least as important as the statistical tools to be considered or implemented, I think that this caricature is able to provide necessary context. However, I failed to consider that some people lose sight of the forest for the trees.

Nevertheless, I have already realized a potentially appropriate manner for comparing means of more than two related groups. I am just waiting whether future responses would support or antagonize the tool that I am thinking of.

You have a design for a repeated measures analysis.

If appropriate, a repeated measures analysis of variance would be on option. With modern software, an easy way to take into account the repeated measures nature of your design is to use a mixed-effects model, or hierarchical model, where the subject (Volunteer) is designated as a random effect in the model. You might find information on one-way randomized complete block (RCBD) design, where the block is treated as a random effect. Good software can address the pairwise difference among the groups with least square means (lsmeans) or estimated marginal means (emmeans).

The example you gave is specifically a unreplicated complete block design. With this design, the non-parametric tests Quade Test and Friedman Test are also applicable. There are post-hoc tests designed specifically for these tests to compare among the different levels of the group or treatment variable.

@Aedrian my comments as a professional chemist still stand. While Dr Mangiafico made good comments his methods would not be a good idea without cleaning up the biochemistry as currently described. If you don't wish to share your problem that is your decision but don't expect an answer to a made-up problem to work for your real experiments. It might or might not. Changing to my professional statistician hat. I don't consult with clients that don't tell me the truth. In your original post you implied that the example was a subset of a REAL data set. Now you say that it's not. If graphed to try to understand your data a consultant would have wasted time. Please don't waste other people's time by not telling them the truth. David Booth

Just for the heck of it Salvatore's comment of a repeated measure design may be incorrect. One awful lot of biochemistry can happen to a compound traveling from the eye to the bladder. Notice that he made assumptions about the biochemistry being unimportant. I would suggest you think about that. David Booth

David Eugene Booth , the clue is in the first word of the supporting text: "SUPPOSE..." I do not doubt your aptitude for statistics and physical chemistry but I guess you have to brush up on language context clues. Have a great day.

If you don't intend to do something then don't waste our time..I don't do homework for fun anymore. David Booth