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Date:         Mon, 21 Apr 1997 17:11:13 -0500
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: How SPSS uses harmonic means
Comments: To: Jerry Dallal <jerry@MINT.HNRC.TUFTS.EDU>

I never did see this come through to the news group; I guess the demons in the equipment are at it again.

Anyway, what I meant (which may not be anything like universal) by homogeneous subsets is to line up the means in ascending (or descending, but ascending is the custom) order and then specify in some way which ones differ by either drawing lines where each pair of means declared not to differ can be identified by seeing if there is a common line under each member of the pair. Or equivalently, and what SPSS 7.x does, is to line them up from top to bottom and print them in columns, where each set in a column is determined to not differ from each other. When you have unequal sample sizes, it is impossible to do this in all cases, as you can have situations where means 1 and 3, for example, are declared not to differ, but where mean 2 is declared to differ from 1 or 3.

David Nichols Senior Support Statistician SPSS Inc.

>---------- >From: Jerry Dallal[SMTP:jerry@MINT.HNRC.TUFTS.EDU] >Sent: Saturday, April 05, 1997 4:39 PM >To: Multiple recipients of list SPSSX-L >Subject: Re: How SPSS uses harmonic means > > (David Nichols) writes: > >> With unequal N, the Tukey-Kramer method is known to be valid (as you >> point out), but is not guaranteed to give results that are representable >> as homogeneous subsets (see, e.g., Hsu's Multiple Comparisons: Theory >> and Methods). That's why we don't do that for homogeneous subsets >> results. > >I'll have to check Hsu. It appears that "homogenoeus subsets" has a >technical definition that I'm not familiar with. I had been reading >"homogeneous subset" to mean "not significantly different from each >other" as in "Treatments sharing the same superscript are not >significantly different from each other" in which case any MCP could >generate homogeneous subsets. > >Thanks. >

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