Summing Confidence Intervals?


New Member

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.


Point Mass at Zero
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.
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.)