# Random Sequence of Heads and Tails: For R Users

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Rick Wicklin on the SAS blog made a post today on how to tell if a sequence of coin flips were random. I figured it was only fair to port the SAS IML code over to R. Just like Rick Wicklin did in his example this is the Wald-Wolfowitz test for randomness. I tried to match his code line-for-line.

flips = matrix(c('H','T','T','H','H','H','T','T','T','T','T','T','T','H','H','H','T','H','T','H','H','H','T','H','H','H','T','H','T','H')) RunsTest = function(flip.seq){ u = unique(flip.seq) # unique value (should be two) d = rep(-1, nrow(flip.seq)*ncol(flip.seq)) # recode as vector of -1, +1 d[flip.seq==u[1]] = 1 n = sum(d > 0) # count +1's m = sum(d < 0) # count -1's dif = c(ifelse(d[1] < 0, 2, -2), diff( sign(d) )) # take the lag and find differences R = sum(dif==2 | dif==-2) # count up the number of runs ww.mu = 2*n*m / (n+m) + 1 # get the mean ww.var = (ww.mu-1)*(ww.mu-2)/(n+m-1) # get the variance sigma = sqrt(ww.var) # standard deviation # compute test statistics if((n+m) > 50){ Z = (R-ww.mu) / sigma } else if ((R-ww.mu) < 0){ Z = (R-ww.mu+0.5) / sigma } else { Z = (R-ww.mu-0.5)/sigma } pval = 2*(1-pnorm(abs(Z))) # compute a two-sided p-value ret.val = list(Z=Z, p.value=pval) return(ret.val) } runs.test = RunsTest(flips) runs.test > runs.test $Z [1] -0.1617764 $p.value [1] 0.8714819

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