Question 158:

Asked on April 18, 2008

Tags: t-distribution , Monte-Carlo , Student-t

1

Answer:

No answer provided yet.

It looks like your standard deviation is sufficiently high enough (a variable sample) and your sample size is sufficiently small enough, that you'll get these impossible negative values. This is often the case with small sample inference. The easiest thing to do is stop the lower-end of your interval at 0. What you won't know though is if you are indeed generating a true 85% or 95% interval (since you've excluded some of it). With that said, there probably as good a chance that even without such abberant values, your intervals are not really 85% or 95% because of deviation from normality. 

A more thorough approach, but one that would take more time is to resample from your sample using a monte-carlo simulation or bootstrap and generate enough permutations to generate your own interval. For example, if you have a sample of 20, then take random samples of 10-15, (which still leaves you with several thousand combinations). Generate the mean for each of of these combinations and see where the interval width lies.