Pearson's correlation coefficient #Enter data x=c(8,24,17,18,16,12,15,13,5,3,12,20,28,6,6,34,6,17,68,7,4,33,23,5,9,46,14,17,18,17,5,10,5,27,17) y=c(12.5,20.8,11.8,16.7,18.7,8.33,20,23.1,0,0,0,10,25,0,0,14.7,0,23.5,14.7,14.2,0,3,17.4,0,0,23.9,21.4,5.9,38.9,11.8,0,10,0,33.3,29.4) #Permutation test R=5000 ; df=length(x)-1 x=(x-mean(x))/sd(x); y=(y-mean(y))/sd(y) # standardise x & y Q=sum(x*y)/df # observed corr. coeff. q=r=0; while(r < R){r=r+1 q[r]=sum(x*sample(y)/df)} # corr.coef. where x&y randomly assigned p=(sum(q > Q)+sum(q==Q)/2)/r # upper-tail mid-p p=.5-abs(p-.5) # convert to 2 tailed mid-p plot(q,rank(q)/r) abline(v=Q) Q p # give 2-tailed mid-p #Parametric test assuming x&y normal cor.test (x,y,method = "pearson")

The R output for the Pearson correlation test and the permutation test are as follows:

#Permutation test > Q [1] 0.4487518 > p # give 2-tailed mid-p [1] 0.0048 #Parametric test Pearson's product-moment correlation data: x and y t = 2.8846, df = 33, p-value = 0.006853 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.1358158 0.6802677 sample estimates: cor 0.4487518