What are the significance of ‘n’ and ‘N’ in research and how do they relate to reliability/accuracy/credibility?

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What are the significance of ‘n’ and ‘N’ in research and how do they relate to reliability/accuracy/credibility?

In: Mathematics
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n is a sample size, and N is an entire population. For example, N would be all Americans, and n would be Americans between 18 and 35.

In medical research, n usually refers to the size of the group participating in the trial.

A trial on 2 people may give you a 100% success rate, but because n is so small you wouldn’t consider it a good bit of research – the result could easily be from chance. A trial on 1000 people would be lots more credible, because unlikely / rogue individual results would skew the data much less.

An attempt to quantify this is the p-value of a trial, though there is some abuse of this (relevant [xkcd](https://xkcd.com/882/))