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Date:         Wed, 19 Feb 1997 10:42:48 -0600
Reply-To:     "Nichols, David" <nichols@SPSS.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         "Nichols, David" <nichols@SPSS.COM>
Subject:      Re: Post-hoc query

>---------- >From: William B. Ware[SMTP:wbware@EMAIL.UNC.EDU] >Sent: Wednesday, February 19, 1997 6:15 AM >To: Multiple recipients of list SPSSX-L >Subject: Re: Post-hoc query > >On Thu, 20 Feb 1997, John Reece wrote: > >> A simple query: Is the Tukey B post-hoc test the same as the post-hoc test >> often called the Tukey-Kramer? If _not_, then what is the preferred method >> for analysing post-hoc when sample sizes are unequal (sometimes wildly)? >> Does it involve taking a harmonc mean of all groups? > >The Tukey B procedure is a compromise between the Tukey A procedure and >the studentized Newman-Keuls procedure... The Tukey A uses the same >critical value for each pairwise contrast, no matter how many means are in >the "range." The SNK is based on a "layered" approach, where the critical >value varies with the number of means in the range. The Tukey B procedure >uses the average of Tukey B and SNK. For example, consider the >"manufactured" example below... > >#means in range 2 3 4 > >Tukey A 4 4 4 > >SNK 4 5 6 > >Tukey B 4 4.5 5.0 > >********** > >In my opinion, the most appropriate is Tukey A. As for the Tukey-Kramer, >it is a modification of the Tukey A. It uses the harmonic mean of the >samples sizes of the two groups being contrasted, rather than the harmonic >mean of all sample sizes. It is the default in SPSS when you run Tukey's >A. > > >_____________________________________________________________________________ >_ > >William B. Ware, Professor and Chair Educational Psychology >CB# 3500 EMAIL: > >University of North Carolina PHONE: >(919)-966-5266 >Chapel Hill, NC 27599-3500 FAX: >(919)-962-1533 > >URL: >_____________________________________________________________________________ >_

Bill's explanation is accurate. To elaborate, the default method in pre-7.x releases of SPSS, using the individual cell sizes or their harmonic mean rather than the harmonic mean of all cell sizes, is also known as the Tukey-Kramer method, and it is to be generally recommended in opposition to other variants on Tukey methods. What Bill refers to here as Tukey A is sometimes called Tukey's HSD (Honestly Significant Difference), and I think we refer to it that way in some of our documentation. In Release 7.0 and above, we actually give two forms of results for the Tukey approach. One does all pairwise comparisons using the Tukey A/HSD or Tukey-Kramer approach for unequal N, while the other gives homogeneous subsets based on the harmonic mean approach. For the Tukey-B option, we give only the homogeneous subsets results, since the test is by definition a sequential test.

David Nichols Senior Support Statistician SPSS Inc.

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