Finding outliers without assuming normal distribution I have small datasets of size 40-50 points. Without assuming that the data is normally distributed I wanted to find out the outliers with 90% confidence at least. I thought boxplot could be a good way to do that but I am not sure.
Any help appreciated.
Also with boxplot implementations I could not find a implementation which besides drawing the plot explicitly spits out the outliers.
 A: This does not directly answer your question, but you may learn something from looking at the outliers dataset in the TeachingDemos package for R and working through the examples on the help page.  This may give you a better understanding of some of the issues with automatic outlier detection.
A: That's because such an algorithm can't exist. You require an assumed distribution in order to be able to classify something as lying outside the range of expected values.
Even if you do assume a normal distribution, declaring data points as outliers is a fraught business. In general, you not only need a good estimate of the true distribution, which is often unavailable, but also a good theoretically supported reason for making your decision (i.e. the subject broke the experimental setup somehow). Such a judgement is usually impossible to codify in an algorithm.
A: R will spit out the outliers as in
dat <- c(6,8.5,-12,1,rnorm(40),-1,10,0)
boxplot(dat)$out

which will draw the boxplot and give
[1]   6.0   8.5 -12.0  10.0

A: As others have said you have stated the question poorly in terms of confidence.  There are statistical tests for outlier's like Grubbs' test and Dixon's ratio test that I have referred to on another post.  They assume the population distribution is normal although Dixon's test is robust to the normality assumption in small samples.  A boxplot is a nice informal way to spot outliers in your data.  Usually the whiskers are set at the 5th and 95th percentile and obsevations plotted beyond the whiskers are usually considered to be possible outliers.  However this does not involve formal statistical testing.
