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How to calculate the HSD (or LSD?) value using Tukey?


Community Member


Mar 20, 2015

Can anyone help me calculate/get this value? I want to include it in graphs, but I can't figure out how to do it. An old post tried to explain how to do it:

"After you've run your "Fit Model" dialog, go to the "Effect Details" tab, and expand that.  You'll find there a tab for each of the factors you've included in the model, each of which has a red triangle on the tab.  Click on that red triangle, and you'll get a menu from which you can select either "LSMeans Student's t" or "LSMeans Tukey HSD". If you do that you'll get two tables: the first one shows the SED, lower confidence limit and upper confidence limits (from which you can calculate the LSD)..." But they failed to explain HOW to calculate the LSD value.

HELP please!


Community Trekker


Jun 5, 2014

Hi, cgva!

Thank you for asking this question!  John Wilder Tukey is one of my favorite personal heros, and your question led me to re-reading a number of references about his vast contributions to science.  In particular, his contributions to the methodology of multiple comparisons was so huge...he really set the stage for lots of subsequent work.  Perhaps unfortunately for you, all my enjoyable re-reading (and diversionary trips down other Tukey rabbit holes! ) took about four days.  I apologize for the tardy response, but I was having some fun.

Interestingly, his seminal work entitled "The Problem of Multiple Comparisons" was informally released in 1953, and was only available by request in mimeograph for quite a while.  It can now be found in The Collected Works of John W Tukey: Multiple Comparisons, Volume VIII by Braun from Chapman Hall/CRC Press.  It is a tour de force, like all the other volumes.

If you are unlucky enough to not have a copy of TCWoJWT, there are many references online that detail the calculation of HSD itself, for instance the NIST/SEMATECH Engineering Statistics Handbook has a section here.  If you want to grab the HSD results from a report, generate the report and right-click on the graph and choose Edit -> Show Tree Structure and note the object that holds the results you desire.  For a model of the TYPING DATA sample dataset, for instance, the picture below shows that the HSD confidence interval values are reported in CrosstabBox(1), nested in several other display type boxes:

8419_Show Tree Structure.jpg

The Scripting Guide has a number of examples on how to extract information from reports once you locate the specific information in the report's Tree Structure.  SAS Press has some books on JSL that may prove helpful too.

As an aside: JMP has added False Detection Rate methodologies of Benjamini and Hochberg (1995) recently, and John W. Tukey, as he studied multiple comparison throughout his life, once wrote (Williams, Jones, & Tukey, 1999) that he "...believes that the Benjamini-Hochberg procedure is the best available choice" for multiple comparisons.  High praise, indeed!

Thanks again for the fun Discussion question!