I know what significance means, and I also know that getting it from a p-value is nonsensical. > The ~5% improvement reported here might just be an artefact of

I know what significance means, and I also know that getting it from a p-value is nonsensical. > The ~5% improvement reported here might just be an artefact of the data collection or random variation, rather than a consistent repeatable change. You're questioning method or data representativeness, not significance. 250 samples is just about enough to for a 5% difference in NHST (stddev is around .4, so 1.64 sigma is .4/15.8*1.64=0.04 for single sided testing).