# [R] Standard error of a sum

Kenneth Cabrera krcabrer at epm.net.co
Fri Jul 23 01:27:19 CEST 2004

```If you supose that each mean is independent then

s.err_total_chem <- sqrt(sum(s.err_event^2))

If not you must estimate de var-covariance matrix to find this s.err.
This estimation will be difficult given the scarce data available.

Hope it will helps.

Kenneth

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.
>
>
> 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 <-
>
>
>

--
Kenneth Roy Cabrera Torres
Celular +57 (315) 504 9339

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