Earlier quoted context omitted.
Okay, why do you think the null is crappy? In the absence of any information whatsoever, the idea that an analysis pipeline produces false positives at or below its nominal rate seems pretty reasonable. But, they have some prior information. Let's look at the E1 paradigm (2 sec on, 6 sec off). In the NeuroImage Paper (Figure 1A, 2A), the FWER on voxel tests is statistically indistinguishable from 5%. In other words,…
>"Okay, why do you think the null is crappy?" Because their goal is to determine if some sort of treatment has an effect. If the null is false for other reasons, then statistical significance can't be used to support the existence of a treatment effect. So these would be pointless, pedantic calculations.
I see a few ways this could come about: perhaps the way we record and model activity doesn't conform to the distribution we assume (I'm not sure if they assume a normal distribution here - or if that even makes sense given the nature of the data) -- or perhaps the issue is with taking 3d/4d data and "turning it into" an easy-to-model statistical model (like the normal distribution)?
At any rate, it does seem that they're saying we can't tell that one individual at rest, measured twice, is in the same (rest) state both times? Hence, they're null hypothesis is bunk?