1. Technical Information
2. Purpose of the tables
3. References

 

CRB2P. Technical information

Version:	1.0  (2000)
Authors:	Silvia Mato   A. Martín Andrés
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CRB2P. Purpose

The tables provides the unconditional critical region  for comparing two independent binomial proportions. 

If  x_i ~ B(n_i; p_i),  i=1,2, the aim is to test: 
       Ho º  p₁=p₂  (= p unknown) 
       vs Ha º p₁<p₂  or  Ha º p₁>p₂   (one tail) 
       or vs Ha º p₁ ¹ p₂ (two tails) 

Under Ho:  P(x₁, x₂ | n₁, n₂, p)= C(n₁, x₁) C(n₂, x₂) p^a₁ (1-p)^a₂ with a₁ = x₁+x₂ and a₂= n₁+n₂-a₁. For a target error a the critical region is a set, CR, of pairs (x₁, x₂); so the error a is:  a(p) = å_CR P(x₁, x₂ | n₁, n₂, p) and the size of the test will be: a* = Max a(p) in  0<p<1 

This tables gives the CR for the Barnard's test following the optimal procedure. The one-sided Ha considered is that indicate by the data: 

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CRB2P. References