X <- c(rep(-100,12), -93, -92, rep(-91,2), -90, -85, -83, -81, -80, -78, -46, -40, -34, 0, 29, 62, 75, 106, 147, 1321) Y <- c(rep(-100,5), -93, -89, -80, -78, -75, -74, -72, -71, -66, -59, -41, -30, -29, -26, -20, -15, 20, 25, 37, 55, 68, 73, 75, 145, 146, 220, 1044) d <- data.frame(gr=factor(c(rep('X',length(X)),rep('Y',length(Y)))), val=c(X,Y)) rnk <- rank(d$val) dd <- data.frame(d,rk=rnk) RX <- dd$rk[dd$gr=='X'] RY <- dd$rk[dd$gr=='Y'] print(sum(RX)) print(sum(RY)) N <- 32+32+1 print(ERY <- 32*N/2) print(VRY <- 32*32*N/12-32*32/(12*(N-2)*(N-1))*(17^3-17+(2^3-2)*5)) print(z0 <- (sum(RY)-ERY-0.5)/sqrt(VRY)) print(2*(1-pnorm(z0,0,1))) wilcox.test(X,Y,exact=F)