Confidence Intervals for Skewed right distribution.

#1
We have compiled data and made a histogram where n = 91,800.

The average is 0.14098, the standard deviation is 0.143945, kurtosis is 8.23115, and the median is 0.094845. The histogram is skewed right (positive skew). Like the empirical rule we would like to say that 95% (2 standard deviations) of the data collected fall within x. It is our understanding that the empirical rule only works with a normal distribution. How can this be done with a skewed right distribution?
 

TheEcologist

Global Moderator
#2
We have compiled data and made a histogram where n = 91,800.

The average is 0.14098, the standard deviation is 0.143945, kurtosis is 8.23115, and the median is 0.094845. The histogram is skewed right (positive skew). Like the empirical rule we would like to say that 95% (2 standard deviations) of the data collected fall within x. It is our understanding that the empirical rule only works with a normal distribution. How can this be done with a skewed right distribution?
If really want to stick with using the normal distribution as a model for your data then you can try transforming the data:
Here are some usefull examples
http://www.pfc.forestry.ca/profiles/wulder/mvstats/transform_e.html

Instead of using a parameteric approach you could simply use the 97.5% percentile (of your data) for the upperbound CL and 2.5% percentile for your lower CL.
 

TheEcologist

Global Moderator
#4
I'm not sure if I understand that answer. What statement can I make if I calculate the 2.5th and 97.5th percentiles?
You wanted to know how to get confidence intervals (CI) right? That is one way to get confidence intervals, a very simple way.Its acceptable because your sample distribution approximates the distribution of your population (especially with such a large sample size).

Now you might want to try a more sophisticated way: the bootstrap. In your case that can also get you what you need and the CI might be a bit (or a lot) narrower too.

http://en.wikipedia.org/wiki/Bootstrapping_(statistics)

Good luck,