Let's say that we're testing a coin to see if it's unfairly biased towards heads. The null hypothesis is that it's a fair coin. Test 1 consists of flipping the coin twice and seeing if both times it comes up heads; p = 0.25. Test 2 consists of flipping it once and seeing if it comes up heads; p = 0.5. The chance that a fair coin would fail both tests is 1/8 for a p-value of 0.125. Your formula gives 1/4 * (2*1/2 - 1/4) = 3/16 = 0.1875. Am I missing something? Charles Greathouse Analyst/Programmer Case Western Reserve University On Tue, Nov 11, 2014 at 12:09 PM, Warren D Smith <warren.wds@gmail.com> wrote:
Perhaps this nicely typeset page will help you understand the problem:
http://rangevoting.org/CombinedTestFail.html
The answer is NOT a*b*c*...* despite the tests being independent. This is a trap too many fall into. Indeed, if there were N uniform(0,1) independent randoms, and somebody told you "there exists an ordering such that x_j<j/N for each j=1,2,3,...,N" you do NOT want to be an idiot and conclude "my god, that is an amazingly exponentially improbable miracle." Actually, it is quite likely even for N=100. Eh? So hopefully I've piqued your interest now.
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun