[wisty]

No, almost any sample size can be sufficient, as long as the effect is big enough. Though in psychology, larger samples are often needed, because there's generally smaller effects.

If you want to test whether penicillin can cure a staph infection, you can get statistically significant results with a handful of tests.

[lutusp]

>> Sample size has nothing (not strictly true) to do with whether a result is statistically significant.

>> I hate to rain on your parade, but sample size has everything to do with whether a result is statistically significant.

> No, almost any sample size can be sufficient, as long as the effect is big enough.

Your sentence says "no", but it agrees -- sample size has everything to do with determining statistical significance. The ratio of sample size to population is critical to deciding whether a result is significant: http://classroom.synonym.com/select-statistically-significan...

> Though in psychology, larger samples are often needed, because there's generally smaller effects.

Yes, but many of those kinds of result are insignificant and instantly forgotten regardless of the circumstances, because psychologists generally aren't testing a falsifiable theory, only measuring an "interesting" effect, like whether leaning to the left makes the Eiffel Tower look shorter (the 2012 Ig Nobel Prize winner):

Title: "Leaning to the Left Makes the Eiffel Tower Seem Smaller -- Posture-Modulated Estimation"

Link: http://pss.sagepub.com/content/early/2011/11/23/095679761142...

Ig Nobel Prize announcement: http://www.improbable.com/ig/2012/

[wisty]

Normal distribution of a sample scales with sigma, and inverse to sqrt(n-1), so effect size is more important than sample size. That's all the guy who originally posted was talking about.

I don't think anyone on hn won't know this. Everyone is just quibbling over the wording.

Your new point is very good, and I'd expect someone has used the correlation != causation argument too.