I don’t believe you can say the p value would increase, decrease, or stay the same with increasing N. p is just the probability that the observation could be seen at random, regardless of sample size.
There is no sharp cut off line between significant and not significant. The choice of 5% as significant is just a reasonable convention in research that there is a 1 in 20 chance your observation is a fluke.
Different p values apply when the stakes are different. p<5% is fine for research but if you’re building a bridge that won’t do, you want p<0.0000000..001% your bridge will fall down. It all depends on the stakes.
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