Standard Error; A fairly simple question

#1
Hello All,

Just a little something I am unsure about, I hope you can help!

So, If you have a pile of averages (say stem weight and root weight) and so you have two seperate standard errors. Now I want a standard error for the total weight, can I just add the two standard errors and have my standard error for the total weights?

Cheers,
The_Cat
 

Dason

Ambassador to the humans
#2
It's not quite that simple. We either need to assume that the stem weight and the root weight are independent (which probably isn't the best assumption...) or we would need to know their covariance.

If we assume that they're independent (not the best assumption but it's the slightly easier case) then to get standard error of the sum we could do the following:

Let \( s_w\) be the standard error of the stem weight and \(s_r\) be the standard error of the root weight. Then the standard error of the sum is given by: \( s_{w+r} = \sqrt{s_w^2 + s_r^2}\).
 
#3
Ah ha! Thanks, makes a little more sense now. I won't assume they are independant, but I will go search for co-variance and standard error of the sum. Cheers!