Find out which mean gains are significantly different than zero.

[moorepants]

For a given speed, gait phase percentage, and perturbation type the gains have a distribution of values from all 11 subjects. I computed the one-sample Student's T Test from each of the sets of 11 values to see which gains are significantly different than zero (p=0.05). Before doing this, I plot the qqplots to see if the samples are normally distributed. It seems none of them are normally distributed across subjects. I find the T statistic anyways and it seems that something like 150 out of 240 gain values are significantly different than zero for each speed.

[moorepants]

I've updated these plots that show the mean gains across subjects for each speed. Now a colored marker (blue/red) is used if the mean value is significantly different than zero and a black marker if not. I use the simple one-sample t test as described above for each scheduled gain value. The results are not very clear to me. Some of the values seem like they should be colored and some seem like they shouldn't. I'm not sure if this adds any clarity to the results. It is worth noting that in Rouse 2014 he was able to compute a very high VAF and his variation among subjects is less than ours. He found that his damping value wasn't significantly different than zero but that his stiffness and inertia were.

[tvdbogert]

"Some of the values seem like they should be colored and some seem like they shouldn't". I agree. If your colored area represents the SD and N=15 subjects, there seem to be way too many black dots.

But also I think we don't need to do this test for significance. In Rouse's work, it made sense to see whether or not a damping is needed in the model. Here, if a gain is not significantly different from zero, we would not set it to zero when we use the identified controller. We use all parts of the result, significant or not.

Nobody will wonder whether these results are reproducible. It's very good that you show left and right in the same plot. They have the same pattern even though they come from separate raw data (markers and force plate). So clearly these patterns are not random. Certain small gain values may not be significant or reproducible, but they are small so don't do any harm if you use them anyway. The entire curve is what matters.