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# st: RE: Which test to use?

 From "Feiveson, Alan H. (JSC-SK311)" To "statalist@hsphsun2.harvard.edu" Subject st: RE: Which test to use? Date Thu, 19 May 2011 14:30:01 -0500

Here's a shot at answering Toby's question:

One can express the marginal frequencies of X and Y in terms of their joint distribution. Because we are given P(X=1, Y=1) = 0, there are three possible outcomes T:

T=1: (X=0, Y=0) (with probability p1)
T=2: (X=0, Y=1) (with probability p2)
T=3: (X=1, Y=0) (with probability p3)

In general T has a trinomial distribution with cell probabilities (p1, p2 and p3 ), however the
values of p1, p2, and p3 might change with covariates.

So one possible method of addressing Toby's question is to use a multinomial logit (or probit) model. After fitting the model, one can compare P(X = 1) with P(Y = 1); i.e. p3 with p2 for particular values of the covariates (if there are covariates), otherwise directly.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Toby
Sent: Thursday, May 19, 2011 3:12 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Which test to use?

Hello,

I have data of the following character

decision      X      Y
34               1      0
34               1      0
56               0      0
77               0      1
23               0      0

X and Y take the function of categorizing the variable decision. If I
take the mean value of X I get the frequency of decision that could be
classifed as X, the same holds for Y. It could never be that X and Y
take the value 1 at the same time.
Now I want to test whether the frequency of X is significantly
different from the frequency of Y. Can anybody help me figuring out
which statistical test I have to use?

Kind Regards,
Toby
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