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Uh oh... I think you're interpreting the probability incorrectly. Shouldn't this be "if we assume that a and b take the same amount of time, then there's a 5%
by kevinwang 6y ago
Uh oh... I think you're interpreting the probability incorrectly. Shouldn't this be "if we assume that a and b take the same amount of time, then there's a 5% chance that we would see this result?".
Can't actually speak to the probability that a is faster than b without some kind of assumed prior distribution for a and b
- saeranv 6y agoYes, this is correct.
- contravariant 6y agoIt should also be pointed out that the one thing you're ruling out is that they have the same distribution. In particular it only provides weak evidence that the mean, mode, median of A is any faster than B's. In the worst case A happens to be a lot slower than B, but with very low probability.
- bo1024 6y agoYep. It gets at, what is the meaning of "faster?" Implicitly we are saying the average runtime of A is smaller than the average of B. But if for example, B always halts in 10 seconds, and A halts in 1 second 99.99% of the time but A runs for 10 years 0.01% of the time, then A is "slower" but you'd need 10,000 trials to notice.