- #1

fog37

- 1,568

- 108

I am still slightly confused about the meaning of the p-value. Here my current understanding:

- There is a population. We don't know its parameters but we want to estimate them.

We collect a possibly large sample of size ##n## from it.

We formulate the hypotheses ##H0## and ##H1##, set a significance level ##\alpha##, and perform a hypothesis test to either fail to reject ##H0## or reject ##H0## in favor ##H1##. - The p-value is the probability, ASSUMING H0 is correct, of the calculated sample statistic.
- A low p-value leads to rejecting H0: it means that the calculated sample statistic would have been really too rare, under the assumption that H0 is correct, for it actually happen. But it happened. The sample statistic, given its low p-value probability, is to be considered rare,
__but it happened.__This means that it cannot be ascribed to just being a random fluke. Just sampling error would have not generated such a low probability statistic value. Something deeper must be going on. This leads us to believe that H0 is not so reliable. - The p-value is also called "the probability of chance" because it should be the value we would expect if only chance was at work, as it happens in random sampling. The fact that the sample statistic happened regardless of its low chances, must be attributed to something other than chance.

The procedure above is based on analyzing a

__single, large sample__. What if we repeated the procedure above with another simple random sample and this time the p-value was larger than the set threshold ##\alpha##? That would mean that we would fail to reject H0...So how many samples do we need to analyze to convince ourselves that ##H0## must be rejected or not?

It seems reasonable to explore multiple random samples and determine the p-value before drawing conclusions of what to do with H0.

THANK YOU!