# [R] Standard error of a sum

From: Jim Brennan <jfbrennan_at_rogers.com>
Date: Fri 23 Jul 2004 - 09:35:31 EST

Was just looking at this data and tried this:

> event.var<--tapply(d.1\$chem,factor(d.1\$event),var)
> event.var

1 2 3
-9.022233 -35.385033 -11.884433

Any idea why the variances are coming out negative.

> var(d.1\$chem[1:3])
[1] 9.022233

right number ....

Anyway here is the answer I got if we assume independant means-- and I don't see why not to with the info given.

> sqrt(sum(s.err_event^2))
[1] 4.331732

(sum(event.var/3*-1)^.5)
[1] 4.331732

• Original Message ----- From: "Kenneth Cabrera" <krcabrer@epm.net.co> To: <jahernan@umn.edu>; <r-help@stat.math.ethz.ch> Sent: Thursday, July 22, 2004 7:27 PM Subject: Re: [R] Standard error of a sum

> 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
>
> ______________________________________________
> R-help@stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help