Date:         Wed, 22 Dec 1999 16:14:33 -0600
Reply-To:     "Nichols, David" <nichols@SPSS.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         "Nichols, David" <nichols@SPSS.COM>
Subject:      Re: Simple contrasts

Lary's right about the general scheme and about the last set of .500 values
being -.500, but it's not the case that the rows of the basis or design
matrix must sum to 0, and only in certain schemes is it the case that the
columns will sum to 0. They will not do so for INDICATOR contrasts (the
contrast matrix rows they produce will sum to 0, aside from the intercept,
of course).

David Nichols
Principal Support Statistician and
Manager of Statistical Support
SPSS Inc.

> -----Original Message-----
> From: Lary Jones [mailto:ljones@BINGHAMTON.EDU]
> Sent: Monday, December 20, 1999 9:24 AM
> To: SPSSX-L@LISTSERV.UGA.EDU
> Subject: Re: [SPSSX-L] Simple contrasts
>
>
> At 12:48 AM 12/19/99 EST, SPL95001 UConnVM wrote:
> >I am trying to interpret simple contrasts for a MANOVA for
> sex (1,2) and
> >age category (1,3).
> >
> >From the parameter codings I get:
> >
> >     parameter  1      2     3    4     5     6
> >
> >level 1      1.000   .500  .667 -.333  .333 -.167
> >level 2      1.000   .500 -.333  .667 -.167  .333
> >level 3      1.000   .500 -.333 -.333 -.167 -.167
> >level 4      1.000   .500  .667 -.333 -.333  .167
> >level 5      1.000   .500 -.333  .667  .167 -.333
> >level 6      1.000   .500 -.333 -.333  .167  .167
>
> >... What I don't understand is in the parameter codings,
> where are the
> >.667s, .333s, and .167s coming from? Why not .5's and 1's?
>
> First, a 2 X 3 design naturally breaks down into weights
> involving a thirds
> and sixths.  Secondly, the coefficients must sum to 0 (zero)
> across each
> row, and down each column (except the first).  The parameter
> matrix as you
> present it is not quite right.  I would expect if you look at
> your output
> more closely that it will say that the coefficients for
> parameter 2 are .5,
> .5, .5, -.5, -.5, -.5  -- a contrast for the main effect of "sex."
>
> Parameters 3 & 4 are partitions of the main effect for age, comparing
> (3) age 1 vs. ages 2 & 3 , and
> (4) age 2 vs. ages 1 & 3
>
> Parameters 5 & 6 are contrasts for the interaction
> (5) +a1b1 -a1b2 -a1b3 and -a2b1 -a2b2 +a2b3           (a=sex, b=age)
>         (Hi-->Lo)             (Lo-->Hi)
> (6) -a1b1 +a1b2 -a1b3 and +a2b1  -a2b2  +a2b3
>        (Lo, Hi, Lo)          (Hi, Lo, Hi)
>
> -lary jones
> _______________________________________________________
> Lary Jones          %     Statistical Computing Analyst
> Computing Services     %     ..........................
> Binghamton University    %        LJones@Binghamton.EDU
> Binghamton, NY 13902-6000   %            (607) 777-2614
>