This bug has been fixed for Release 14 SP1 (R14SP1). For previous releases, please read below for any possible workarounds:
Our documentation staff will look into adding documentation on this function function in a future release of the Statistics Toolbox. Currently, the intervals in BOXPLOT are not described adequately. They are 95% comparison intervals. Two group medians are significantly different if their intervals are disjoint, and are not significantly different if the intervals overlap. There is no control over the 95% level, and the intervals should not be interpreted as confidence intervals.
More information on Boxplots can be found below:
The original source for the notched boxplots is McGill, Tukey, and Larsen (1978), "Variations of Boxplots", The American Statistician, 32:12-16. Books on exploratory data analysis (EDA) should also cover them, we happen to have on hand Velleman and Hoaglin (1981), "Applications, Basics, and
Computing of Exploratory Data Analysis", Duxbury Press.
A journal article that gives a good explanation of why the individual CIs are not at 95% confidence, but the "overlap test for difference of medians" is at 95% significance is Nelson, L.S., (1989), "Evaluating
Overlapping Confidence Intervals", Journal of Quality Technology, 21:140-141.
