I have no idea what you’re getting at here. The parent pointed out, accurately, that for large effect sizes, N=30 is plenty.
I’m also fairly certain you don’t understand what a “random distribution” is yourself. That’s because there’s no such thing. There’s a normal distribution, binomial distribution, Poisson distribution etc, and they all involve randomness. But there’s no “random distribution”.
So maybe you shouldn’t be quite so quick to judge “novice statisticians”, and what those imaginary people you mention a total of five times may or may not “wrongly assume”, or “don’t know”, or “are limited in”, or “don’t check for”.
And I didn't mean to imply that I'm any better than a novice. I just know enough to know to always check that assumptions for any given test needs to be valid. (It's been a few years since I've had to use any of this in a professional capacity.)
But is 30 plenty? Or is it sufficient?
As I remember, normal distribution usually requires a sample size of N=>30. (As in 30 is the minimum.)
On the other hand, there are so many opportunities for experimental design limiting the applicability of results in mental health experiments, that sample size and distribution doesn't even begin to touch on it. Bottom line: getting a meaningful result that is widely applicable is a horrendously complex undertaking.
I’m also fairly certain you don’t understand what a “random distribution” is yourself. That’s because there’s no such thing. There’s a normal distribution, binomial distribution, Poisson distribution etc, and they all involve randomness. But there’s no “random distribution”.
So maybe you shouldn’t be quite so quick to judge “novice statisticians”, and what those imaginary people you mention a total of five times may or may not “wrongly assume”, or “don’t know”, or “are limited in”, or “don’t check for”.