How to address unintended confounding in an experiment I am conducting a study looking at the effects of 3 different footwear conditions on energy expenditure during running. This will be a repeated measures study. I want to control for the effects of shoe mass in my analysis. This would normally be an ANCOVA - however the mass of the shoes in each condition will be the same value, thus I don't think this approach will be appropriate. Are there any other approaches that could be used to solve this issue, i.e., co-variate values which are identical for each participant?
 A: Unfortunately, your manipulation is confounded with shoe mass.  Using Wikipedia's scheme, you have "procedural confounding".  To differentiate the effect of other aspects of footwear from the mass of the footwear, you need to find footwear for your participants in which the aspects you care about vary independently of the mass.  Ideally, you would find footwear in which the mass was identical from one shoe type to the next.  If that isn't possible, the less correlated these attributes are the better.  
None of that helps you now, of course.  At present, you are mostly stuck, I'm sorry to say.  If you are willing to assume that the effect of mass is perfectly linear, and that there is no interaction between the other aspects of the footwear and their mass, you can see how the conditions deviate from a straight line.  However, this is likely to have low power, and if you do find an effect, your conclusions are completely contingent on those assumptions, which are at least somewhat implausible and impossible to check.  
(Note that the repeated measures nature of your data is unrelated to the issues here.) 
