[xaa]

Ultimately the issue is that we somehow got fixated on the p-value, which (roughly and imprecisely speaking) quantifies the probability that there is any effect, even a small one, rather than using effect size estimates which estimate both the magnitude of the observed effect and the uncertainty in that estimate.

Using p-values as our primary metric means an overemphasis on finding small effects (which are usually not clinically relevant anyway) and unduly low focus on things with big effects.

If an effect is real, but very small, that too may well cause replicability problems because it suggests the effect may not be very robust to small changes in experimental conditions, whereas a big effect would be more likely to be robust.

If you think about the really important scientific findings -- the ones that made a big impact and are indisputably true -- statistics usually aren't necessary to prove them, because the effect size is so large it is simply obvious. I'm not against using statistics anyway, of course, but the point is that we should be looking mainly for effects with big effect sizes if we are after important findings, IMO. It is only a major bonus that big effect sizes are most likely to be replicable.