I am trying to evaluate the following formula in R
where,
ni is the number of individuals on patch i, m is the mean of ni and N is the total
number of individuals.
However, when I manually calculate the values vs. calculating it using the covariance function in R, it produces two different answers. I am wondering what the discrepancy is and if someone could suggest if I'm using the incorrect covariance function, or anything else obvious that I'm missing.
nx <- c(1,0,3,2)
ny <- c(3,1,0,1)
mx <- mean(nx)
my <- mean(ny)
Nx <- sum(nx)
covxy.manual <- ((sum(nx * ny)/Nx) - my) * my
covxy.manual # Answer: -0.520
covxy.direct <- cov(nx,ny)/(mx * my)
covxy.direct # Answer: -0.444
As per suggestion, I tried spearmann correlation on a different set, but that doesn't match up either
nx <- c(3,0,3,3)
ny <- c(1,0,1,1)
mx <- mean(nx)
my <- mean(ny)
Nx <- length(nx)
covxy.manual <- ((sum(nx * ny)/(mx * Nx)) - my) * my
covxy.manual
covxy.manual <- ((sum(nx * ny)/(mx * Nx)) - my) * my
covxy.manual
Nx <- sum(nx)
covxy.manual <- ((sum(nx * ny)/Nx) - my) * my
covxy.manual #Answer: 0.1875
covxy.direct <- cov(nx,ny, method = "spearman")/(mx * my)
covxy.direct #Answer: 0.592