Software SMP_________

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

Purpose

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

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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

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