1. Technical Information
2. Purpose
3. References

 

SMP. Technical information

Purpose

The program provides the unconditional p-value 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 program compute that expression for different optimal procedures for obtaining the CR. 

The one-sided Ha considered is that indicate by the data: 

 ---o0o---

References

   For further details see:

1. MARTÍN ANDRÉS, A. (1991). 'A review of classic non-asymptotic methods for comparing two proportions by means of independent samples'. Comm. Stat. -Sim. and Comp. 20 (2&3), 551-583.
2. MARTÍN ANDRÉS, A. (1997). Entry 'Fisher's exact and Barnard's tests'. Encyclopedia of Statistical Sciences. Update Volume 2, 250-8. Ed.: Kotz, Johnson and Read. Wiley-Interscience.
3. MARTÍN ANDRÉS, A. and HERRANZ TEJEDOR, I. (1995). 'Is Fisher's exact test very conservative' Comp. Stat. and Data Anal. 19, 579-591.
4. MARTÍN ANDRÉS, A. and SILVA MATO, A. (1994). 'Choosing the optimal unconditioned test for comparing two independent proportions'. Comp. Stat. and Data Anal. 17, 555-574.
5. MARTÍN ANDRÉS, A.; SANCHEZ QUEVEDO, M. J. and SILVA MATO, A. (1998). 'Fisher's mid-p-value arrangement in 2x2 comparative trials'. Comput. Statis. & Data Anal. 29(1), 107-115.
6. SILVA MATO, A. and MARTÍN ANDRÉS, A. (1995). 'Optimal unconditional tables for comparing two independent proportions'. Biom. Journal 37(7), 821-836.
7. SILVA MATO, A. and MARTÍN ANDRÉS, A. (1997). 'Simplifying the calculation of the P-value for Barnard's test and its derivatives'. Stat. and Comp. 7, 137-143.
8. SILVA MATO, A. and MARTÍN ANDRÉS, A. (1997).SMP.EXE in http://www.jiscmail.ac.uk/files/EXACT-STATS