[R] Standard error of a sum

Spencer Graves spencer.graves at pdf.com
Thu Jul 22 23:00:28 CEST 2004

```The variance of a sum is the sum of all the elements of the
variance-covariance matrix.  If the summands are uncorrelated, then the
variance of the sum is the sum of the variances.  hope this helps.
spencer graves

Jose A. Hernandez wrote:

> Folks,
>
> This is so simple is driving me crazy. It's not really an R question
> is more an Statistics question.
>
> I applied a chemical in 3 different events during a growing season. I
> took 3 samples in each event to estimate mean applied chemical.
>
> Thus, I can easily estimate means and st.err by event. I can then
> estimate the total chemical applied for the whole season by adding the
> 3 means for each event. How can I estimate the standard error of this
> total applied chemical.
>
> Thanks in advance,
>
> Jose
>
>
> event <- c(1,1,1,2,2,2,3,3,3)
> chem <- c(131.75,125.92,130.09,42.67,48.26,54.56,85.05,91.17,90.86)
> d.1 <- data.frame(event,chem)
> attach(d.1)
> s.err <- function(x) sd(x)/(sqrt(length(x)))
>
> print(mean_event <- tapply(d.1\$chem,factor(data.1\$event),mean))
> print(s.err_event <- tapply(d.1\$chem,factor(data.1\$event),s.err))
>
> print(total_chem <- sum(mean_event))
> s.err_total_chem <-
>
>
>

```