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1 Application of Statistics and Management Sep1, 2006 Vol125 No15 : (2006) Permutation Test (11,,226001, ; 21,,210029) : Permutation test,, ;,, ( P ),,,, Permutation, Permutation test,,, : ( ) ; ; ; :R19511 :A The Application of Permutation Test in the Hypothesis Test XUN Peng2cheng,ZHAO Yang, YI Hong2gang (et al,department of Biostatistics,Nanjing medical University,Jiangsu Province) Abstract :Permutation test,a statistical inference methodology,was introduced and illustrated in the practical busi2 ness1 It is sample2based distribution2free method,which makes use of permutation or combination to get the theo2 retical sampling distribution of the constructed statistics,or get the approximate distribution by simulation under the null hypothesis,gets the probability of the sample2at2hand,and draws a conclusion after comparing the probability with the size of the test1 It especially supports small samples without distributional assumptions(e1g1normality) and complex designs for which traditional methods are hard to solve1 In addition,such questions as the meanings of per2 mutation,the characteristics of the permutation test1 the constructing of the statistics,the number of the simula2 tion,and the proceedings of the applications were also discussed1 Key words :Permutation test ;exact probability ;hypothesis test ;distribution2free 0 Permutation test 30,Fisher (1935) Pitman (1937), 80,,, Permutation test : : ( ) 转载

2 , : Permutation Test 617,,! 1 Permutation test :,,, ;, ( P ),, ( ), Exact Permutation Test ( EPT), ( ),,, ( ), Randomized Permutation test (RPT), ( ) EPT Exact Randomization Test ( ), RPT Randomization Test ( ) RPT( ), : (1), H 0 : 1 = 2 ; H 1 : 1 2 ; = 0105 ( ) (2) D, D ( obs),, Permu2 tation test, gx 1 - gx 2 D (3) H 0, D H 0,,, ( ),, Permutation D k ( ) k Permutation D, D (4) P H 0, P D ( ) D ( obs), : P = P( D Ε D ( obs) ) = nu mber ( D Ε D ( obs) ) k k, D Ε D ( bos) (5) 2 Permutation test ( : STA TA 810 )

3 Stata810, ( n 1 = 10) N (0, 1 2 ) ; ( n 2 = 10) N (1,5,1 2 ), : : : gx 1 = s 1 = gx 2 = s 2 = gx 1 - gx 2 D, D ( obs) = ( ) = , RPT ( k) P, P ( D Ε ) P 1 : 1 RPT Table The result of the comparison of two sample means(grouped design) from randomized permutation test under different simulation replications k P , k, P k, P, k 20000, P, , ( 2 = , P = 01842), t, : t = ,P = R PT ( )! : t, Perm utation Test! 2 a Table The distribbution of the relative frequenc of a (numbers of benign tumors in left hemisphere of the brain) a FET Relative frequency RPT : ( Fisherπs ex act test, FE T) R PT ( ), : (1) P : P = ; A T D, R PT ( ) : P = , = , / % = 0108 %,! (2) a

4 , : Permutation Test 619 ( 2) a,, 2 R PT, R PT,, 3 (1) ( tie), n 1 = n 2 = 6, = ,, : A : T A = 26 B : T B = 52 T A 39 D, D (obs) = = - 13 R PT 26-52, P( D Ε 13), 3 3 R PT ( ) Table The result of the analysis of ranked data from randomized permutation test under different simulation replications(without ties) k P , P EPT( ) : ( A ) : C 6 12 = 924, T A Φ26 T A Ε 52 38, : P = P( D Ε 13) = P( T A Φ 26 or T A Ε 52) = 38/ 924 = ,! (2) (tie) : 9 P n 1 = n 2 = 6, T A = 25, T B = 53 (1) RPT P( D Ε 14), 4 : 4 RPT ( ) Table The result of the analysis of ranked data from randomized permutation test under different simulation replications(with ties) 12! 6! (12-6)! = k P , P (1), EPT : P = P ( T Φ25 or T Ε 53) = 24/ 924 = ,?,, ( ),

5 , RPT,,,, (1) (2), Permutation test (tie)! Permutation Permutation,Permutation, Permutation test Permutation :,,,! 312 EPT RPT EPT ( ), ; RPT ( ),, ( k),, EPT,, EPT,, RPT,EPT ( ) ( K )!, K C n 1 n1 + n 2 = ( n 1 + n 2 )! ;, n 1! n 2! K 2 n ( n ) ;, K n! EPT K RPT! 313 RPT?,,, 1000 P 0105,, 1000 ;,, 50000, ,,! 314,, permutation, 315 Permutation test (1) Permutation test, ;,,,,,, (2) Permutation test renksum test Permutation test (Distribution2free),,?, t,,,,

6 , : Permutation Test 621 ; Permutation test ( ),! Permutation test,!, (tie), Permutation test (3) Permutation test bootstrap jackknife Permutation test bootstrap jackknife, bootstrap jackknife, ( ) ; Permutation test,,, Permutation, bootstrap jackknife,! 316 Permutation test,permutation test :, ROC,,,, Permutation test! (,!) [ ] [1 ] H. Onder,M. Sahin,S. Cankaya, Y. Yahtah,Z. Cebeci. Use of t2statistics with permutation test :for small sam2 ple size. Procedings2International Congress on information technology in agriculture,food and environment. http :cebeciz. cu. edu. tr/ documents/ pdf/ Use Of Permutation Tests2Itafe 03. pdf (2003), [ 2 ] Sayan Mukherjee,Polina Golland and Dmitry Panchenko (2003). Permutation Tests for Classification. http :/ / cbcl. mit. edu/ cbcl/ publications/ ai - publications/ 2003/ AIM pdf (2003). [3 ] Wei Pan. On the use of permutation in and the performance of a class of nonparametric methods to detect dif2 ferential gene expression,[j ]. Bioinformatics,2003,19 : [4 ] SEUN G2Ho KAN G,HYUN G W. KIM and CHUL W. AHN. A permutation test for nondependent matched pair data,[j ]. Drug Information Journal,2001,35 : [ 5 ] E. S. Venkatraman. Apermutation test to compare receiver operating characteristic curves, [J ]. Biometrics, 2000,56 : [6 ] Joanna H. Shih,and Michael P. Fay. A class of permutation test for Stratified Data,[J ]. Biometrics,1999,55 : [7 ] Y. WAN,J. COHEN and R. GU ERRA. A permutation test for the robust sib2pair linkage method,[j ]. Ann. Hum. Genet. 1997,61 : [8 ] 1 Stata ( ),[ M ]. :,20031 [9 ].,[ M ]. :,2002. [10 ],,. Bootstrap,[J ].,1997,14 (5) :5.

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