Notched Box Plots
A Notched Box Whisker (aka Notched Box Plots) is a graphic way to view data that can be very useful.
The Notch - displays the a confidence interval around the median which is normally based on the median +/- 1.57 x IQR/sqrt of n. According to Graphical Methods for Data Analysis (Chambers, 1983) although not a formal test the, if two boxes' notches do not overlap there is ‘strong evidence’ (95% confidence) their medians differ. Note Here are the pages from the book. Citation Chambers, John M., William S. Cleveland, Beat Kleiner, and Paul A. Tukey. "Graphical Methods for Data Analysis", 62. Belmont, California: Wadsworth International Group;, 1983. ISBN 0-87150-413-8 International ISBN 0-534-98052-X
Note: few software programs can make notched box plots (R and ProUCL for example). The notched box plots in this document were all generated in R which requires time to learn. The following web page allows you to enter data and generate notched box plots but for noncommercial use wessa.net/rwasp_notchedbox1.wasp R can also make notch box plots. Here is how to do it in R. Also ProUCL by the EPA will generate notched box plots.
The image below show the relationship of notched box plot and data distribution, variance, and populations.
The Line - Shows the median of the data
The box shows the interquartile range (IQR). The IQR is the 25 to 75
percentile also known as (aka) Q1 and Q3. The IQR is where the center 50% of your data points will fall (as a 5 foot 8 inch American male this is where I would plot).
The whiskers add 1.5 times the IQR to the 75 percentile (aka Q3) and subtract 1.5 times the IQR from the 25 percentile (aka Q1). The whiskers should include 99.3% of the data if from a normal distribution. So the 6 foot tall man from the example would be inside the whisker but my 6 foot 2 inch girlfriend would be at the top whisker or pass it.
The following image shows the relationship of the box plot to standard deviations. It is from http://en.wikipedia.org/wiki/File:Boxplot_vs_PDF.svg