Determine if the mean gains across subjects are significantly different than those at other gait phase points.

[moorepants]

If we chose a nominal speed and perturbation type we have a distribution of gains across subjects. Rouse 2014 used an ANOVA (I'm guessing) to compute whether the gains are significantly different from the others at different gait phase points. So given the mean scheduled gain (e.g. proportional ankle) across subjects, are the gain values different from those at each schedule. A post hoc analysis can then be used to see which schedules are the same and different.

[tvdbogert]

So this would test whether the identified controller is significantly different from a constant gain controller, in other words, whether gain scheduling is justified.

To me the answer is obvious from looking at the curves, but you could confirm it. I suspect you would get a crazy small p value, which is the probability that these patterns are just random variations around a constant gain level.

I am weak in statistics but you might consider putting everything into a large ANOVA. This seems similar to what Rouse did. The factors would be:

• time in gait cycle (20 levels)
• perturbation (2 levels, yes or no)
• side (2 levels, left or right)
• subject (random factor)

Then you do this for all six dependent variables (P and D gains for the three joints). You would hopefully see:

• significant effect of time in cycle
• significant effect of perturbation (but I think we won't)
• no effect of side
• no significant interactions between factors

Bonferroni would require p<0.05/6 because of doing this for 6 variables.
This would be a way to get all of the statistics done without the messiness of different tests for different questions.