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# Re: st: RE: Which test to use?

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Which test to use? Date Thu, 19 May 2011 17:56:55 -0400

```Al--

Or just test whether constants and coefs differ, but it would be
easier to decide among statistical models if there were a theoretical
model in evidence, even a verbal one.   A simulation seems in order,
but what dgp to simulate?  Who knows?

clear
input decision   X      Y
34    1      0
34    1      0
56    0      0
77    0      1
23    0      0
50    0      1
70    0      0
80    0      1
90    0      1
end
biprobit X Y decision
test [X]_cons=[Y]_cons
test [X]decision=[Y]decision, accum
g T=X+2*Y
mlogit T dec
test [0]_cons=[1]_cons
test [0]decision=[1]decision, accum
test [0]decision, accum
test [0]_cons, accum

On Thu, May 19, 2011 at 3:30 PM, Feiveson, Alan H. (JSC-SK311)
<alan.h.feiveson@nasa.gov> wrote:
> 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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