Re: Wald-Wolfowitz runs test

*To*: mathgroup at smc.vnet.net*Subject*: [mg53905] Re: Wald-Wolfowitz runs test*From*: "Ray Koopman" <koopman at sfu.ca>*Date*: Wed, 2 Feb 2005 18:10:48 -0500 (EST)*References*: <ctaill$ee8$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Csukas Attila wrote: > Greetings to all > > I would like to ask a little help. Is it possible to do the > Wald-Wolfowitz runs test on the Mathematica? > If so, what is the way to do it. > > Any help is appreciated. > > Thanks in advance. > > Csukas (* sample data *) x = Table[Random[Integer],{n = 25}] {0,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,1,1,0,0} (* number of 1s & 0s, number of runs *) {{n1 = Tr@x, n0 = n - n1}, r = Length@Split@x} {{11, 14}, 13} (* mean & s.d. of the sampling distribution of r *) N@{m = 1 + 2*n0*n1/n, sd = Sqrt[(m-1)(m-2)/(n-1)]} {13.32, 2.41059} (* sampling distribution of r *) f[r_,n0_,n1_] := If[EvenQ@r, With[{k = r/2 - 1},2*Binomial[n0-1,k ]*Binomial[n1-1,k ]], With[{k = (r-1)/2}, Binomial[n0-1,k ]*Binomial[n1-1,k-1] + (**) Binomial[n0-1,k-1]*Binomial[n1-1,k ]]]; rf = Table[{r,f[r,n0,n1]},{r,2,2Min[n0,n1]+Boole[n0!=n1]}] {{2,2}, {3,23}, {4,260}, {5,1365}, {6,7020}, {7,22230}, {8,68640}, {9,145860}, {10,300300}, {11,450450}, {12,648648}, {13,702702}, {14,720720}, {15,566280}, {16,411840}, {17,231660}, {18,115830}, {19,45045}, {20,14300}, {21,3575}, {22,572}, {23,78}} (* divisor to convert the frequencies to probabilities *) {#, # === Tr@rf[[All,2]]}&@Binomial[n,n1] {4457400, True}