Knocking *is* directly related to octane levels, so it's no surprise to find observable correlations there. Also, knocking is not a subtle problem liable to selection bias.
The question is whether *higher* octane gas than required for an engine (engines can be tuned for high octane gas) improves performance. And the gas manufacturers themselves don't claim that. (In their ads, the benefits are all quite nebulous: "better for your engine")
But it's a pretty widespread belief that high octane gasoline has "subtle" improvements (my in-laws swear they get substantially better mileage, including for the month that I was buying regular gas for their car
Yet, because of the general association, it's almost impossible *not* to notice the car performance being better when we think there's "better" fuel in the tank, which is what I was trying to point out.