[brent]

This is why different communities accept p-values at certain levels (typically <0.05). You have to live with some amount of uncertainty when the data generating mechanism is random... that is unfortunately the nature of the beast.

[arctangent]

I understand this. But let's say I ran some experiments and collected some data in an attempt to disprove theory X. What does it mean for me to say that at the 99% confidence level X is still true, but at the 98% confidence level it is not true? I just find it a bit spooky, is all.