I just think the proper hypothesis should be that a sample of people can hear a difference between cables or amps.
Well, that's one possible hypothesis. Another possible hypothesis is that one particular individual can hear a difference. That's the equivalent of testing the fairness of one particular coin. Note that the sample size isn't one. It's the number of listening trials/coin flips.
I am only concerned that the choice of the sample size may be determined by what the researcher's intended finding might be.
The choice of sample size isn't what's critical here. The statistical significance is. Granted, larger samples reduce the possibility of false negatives, but it's not as if there have never ever been any ABX tests with large sample sizes. The Stereo Review cables test had a sample size of 165. The possibility of a false negative is very low with a sample that big. (Since you teach statistics, I'll let you do the math.)
And if you think the reason these tests come up negative so often is sample size, you as a "scientist" ought to know how to respond: Do your own experiment. Complaining about other people's data isn't science.
I think it is a far more interesting hypothesis to suggest that those with "better ears" would do better.
Then test it. The SR panel was a pretty audio-savvy bunch, as I recall.
I don't think most audiophile would be convinced or should be convinced that all amps or wires sound the same.
Are you saying they're all close-minded?