Summing Confidence Intervals?

AMac

New Member
#1
Hello,

I have calculated mean concentrations of various environmental chemicals in a population. These chemicals fall into different classes (PCBs, dioxins, etc). There is a 95% CI associated with each mean concentration. I want to sum the mean concentrations for the chemicals in each class (total PCBs, total dioxins, etc). If I sum the means, how do I determine the 95% CI for these summed means? Summing the individual CIs seems incorrect. Any help you can provide would be greatly appreciated.
 

ledzep

Point Mass at Zero
#2
assuming each of the three means are normally distributed, you can work out the distribution of the sum of the means.
They are normally distributed with mean=mean1+mean2+mean3, and variance=var(mean1+mean2+mean3). Assuming independence variance of a sum is the sum of the variance. This will enable you to compute a standard error and then finally the 95% CI.
 
#3
Hopefully these poisonous chemical compounds are at quite low concentrations. So the distributions might be quite skewed.

Then a generalized linear model (glm) with a gamma distributed error structure might be useful. Alternatively the data might be lognormal – take the log of the data and it will be normally distributed.

It might also be that the data are censored in that some data points are below a “detection limits”. This can be dealt with by estimation of censored data. (Don’t replace non-measured values by 1/squarerot-of-detection limit. That’s bad procedure.)