Software SMP_________
  1. Technical Information
  2. Purpose
  3. References


SMP. Technical information

  Version: 2.1  (2000)  
  Authors:  Silvia Mato
 A. Martín Andrés
  Download: File name: SMP.EXE  
File size: 70 Kb
File type: executable



The program provides the unconditional p-value for comparing two independent binomial proportions. 

If  xi ~ B(ni; pi),  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) = åCR 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: 

Ha º p1< p2  if  x1/n1 < x2/n2



   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