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Science Forum Index » Statistics - Math Forum » Proper test for equality of binomial parameters in...
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| Jacob JKW... |
 Posted: Mon Jul 21, 2008 7:11 pm |
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What's the proper test to use for testing the equality of two binomial
parameters across sample?
For example, in sample a, X_a successes are observed out of N_a
trials, while in sample b, X_b successes are observed out of N_b
trials. If P_a and P_b represent the two binomial parameters, how
would one test H_0: P_a = P_b given small samples? |
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| Jack Tomsky... |
| Posted: Tue Jul 22, 2008 4:57 am |
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Quote: What's the proper test to use for testing the
equality of two binomial
parameters across sample?
For example, in sample a, X_a successes are observed
out of N_a
trials, while in sample b, X_b successes are observed
out of N_b
trials. If P_a and P_b represent the two binomial
parameters, how
would one test H_0: P_a = P_b given small samples?
The UMP unbiased test is the (randomized) conditional test based on the hypergeometric distribution.
P(X_b = xb|X_a + X_b = t) = C(N_a,t-xb)*C(N_b,xb)/C(N_a+N_b,t),
where C(a,b) = a!/[b!(a-b)!].
The acceptance rule of H_0 depends on whether the alternative hypothesis is one-sided or two-sided. Typically, the nonrandomized test is used where the boundary points are put in the acceptance region.
Jack |
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| Jacob JKW... |
| Posted: Tue Jul 22, 2008 5:30 am |
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On Jul 22, 10:57 am, Jack Tomsky <jtom... at (no spam) ix.netcom.com> wrote:
Quote: What's the proper test to use for testing the
equality of two binomial
parameters across sample?
For example, in sample a, X_a successes are observed
out of N_a
trials, while in sample b, X_b successes are observed
out of N_b
trials. If P_a and P_b represent the two binomial
parameters, how
would one test H_0: P_a = P_b given small samples?
The UMP unbiased test is the (randomized) conditional test based on the hypergeometric distribution.
P(X_b = xb|X_a + X_b = t) = C(N_a,t-xb)*C(N_b,xb)/C(N_a+N_b,t),
where C(a,b) = a!/[b!(a-b)!].
The acceptance rule of H_0 depends on whether the alternative hypothesis is one-sided or two-sided. Typically, the nonrandomized test is used where the boundary points are put in the acceptance region.
Thanks, Jack. Much appreciated. |
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