# One cannot conclude from the variances of pre/post values on the variance of the pre-post difference # without knowing/making assumptions about the correkation. # Example: pre-values x, post values y x <- c(0,0.5,1) y <- c(2,1.5,1) mean(x) var(x) sd(x) mean(y) var(y) sd(y) # Changes d.yx d.yx <- y-x mean(d.yx) var(d.yx) sd(d.yx) # Permutation of the post values provides other post values with the same mean and variance: z <- c(1,1.5,2) mean(z) var(z) sd(z) # New changes d.zx have the same mean, but different variance: d.zx <- z-x mean(d.zx) var(d.zx) sd(d.zx) # The reason is the that the correlation differs: cor(x,y) # negative correlation cor(x,z) # positive correlation opar <- par(mfrow=c(1,2),pty="s") plot(c(1,2),c(x[1],y[1]),type="n", main="Pre- and post values", xlab=" ",ylab=" ",ylim=c(0,2)) for (i in 1:3){ lines(c(1,2),c(x[i],y[i])) } legend(1,2,bty="n",expression(paste("Negative Correlation: ",rho," = -0.25"))) plot(c(1,2),c(x[1],z[1]),type="n", main="Pre- and post values", xlab=" ",ylab=" ",ylim=c(0,2)) for (i in 1:3){ lines(c(1,2),c(x[i],z[i])) } legend(1,2,bty="n",expression(paste("Perfect positive Correlation: ",rho," = 1"))) par(opar)