Re: Statistical test for equality ?

[stn021]

Hi,

the wikipedia-article about Likelihood-ratio is a bit too much "mathmatese" for me to be sure. Sounds interesting though. Could someone give a short english explanation?

The example in the wikipedia-article seems to me like the answer to a different question than mine. It is about testing whether two coins having the same probability of coming up heads. That would be chi-square or maybe t_test.

My question is more about testing whether the first toss of coin 1 is identical to the first toss of coin 2. Same for the second toss etc.

I do not want to know if the 2 coins both come up heads 50% of the time. Instead I want to know if they both come up with the same side each time. If coin 1 shows heads then coin 2 should show heads too. Same for tails.

The question is _not_ : are the coins alike ?

Instead it is: is it the same coin ?

I do not think that chi-square will answer this. (Correct me if I'm wrong)

Coins are a bad example though. It is more about continuous variables, for example any (rational) number between 0 and 100. The distribution can be assumed to be normal.

THX

stn

2013/12/24 pathematica <address@hidden>

This answer is based on fading memory of something learned in a course taken
long ago and not subsequently used so please excuse its vagueness. I would
have to revise the method to be more specific.

If your model assumes that each pair of component vectors have been drawn
from the same distribution, then I think you need to use the likelihood
ratio test.

Wikipedia page <http://en.wikipedia.org/wiki/Likelihood-ratio_test>

The test statistic raised by this method follows a chi-squared distribution
(with the appropriate number of degrees of freedom). I note that someone has
already suggested a chi-square test (which is sort of not surprising because
you imply Gaussian noise, which has a distribution that belongs to the
exponential family).



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