**Date:** Thu, 21 May 1998 11:57:06 -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: RM-ANCOVA
Much of this pertains to general statistical issues as applied to your
specific content area, and for that I'm going to have to let you consult
one or more consulting statisticians familiar with your field. The results
given should be correct for the data as input. You've input 320 total
cases.

My guess is that a statistician familiar with the area is either going to
say that the seedlings are like subjects nested in cells of a normal design
and this analysis is fine, or that you need to treat those within a cell as
likely to be correlated even after fitting this model, in which case you'll
be very limited in options in SPSS. One of those options would be taking
average values to analyze, but that may not be the best way to do things.

David Nichols
Principal Support Statistician and
Manager of Statistical Support
SPSS Inc.
nichols@spss.com

----------
From: rfoster [SMTP:rfoster@LOON.NORLINK.NET]
Sent: Friday, May 15, 1998 10:19 AM
To: SPSSX-L@UGA.CC.UGA.EDU
Subject: RM-ANCOVA

I am looking for advice regarding the analysis of a repeated measures RCBD
with four treatments and four blocks. On each of the 16 plots, a grid of
20 seedlings was established. Four growth variables were measured
annually
on each tree (1 year pre-treatment, then each of the following 4 years
post-treatment).

For simplicity's sake, I first tried a GLM Repeated-Measures using only
one
of the four growth variables as the dependent variable. I used the
pre-treatment values as a covariate and the other 4 years for the
within-subjects variables; block and treatment were the between-subjects
factors.

The resulting ANOVA table for Tests of Between-Subjects Effects is as
follows (edited for brevity):

Source Type III Sum of Squares df Mean Square
F Sig.
Corrected Model 276.118 15 18.408
41.8 .000
Intercept 4086.478 1 4086.478
9293.4 .000
BLOCK 240.392 3 80.131
182.2 .000
TREAT 16.057 3 5.352
12.1 .000
BLOCK * TREAT 19.878 9 2.209 5.0
.000
Error 131.035 304 .440
Total 4555.200 320
Corrected Total 407.153 319

a Computed using alpha = .05
b R Squared = .678 (Adjusted R Squared = .662)

My question is this:
Since the seedlings are really samples (treatments were not randomly
assigned to individual seedlings), I only have 16 true experimental units.
Yet the F test that is reported in the above ANOVA table for TREAT is
F(3,304). Isn't this incorrect, since the Error df reported here is
really
Experimental Error + Sampling Error? Can I use correctly use the MS ratio
of TREAT divided by the interaction of BLOCK*TREAT to get a true test of
signficance i.e. MS = 5.352/2.209 and F(3,9)? If I understand correctly
this is only valid if there is no BLOCK*TREAT interaction, so what should
I
do if there really is a significant interaction?

And can this be extended to the multivariate condition if I wish to test
all four growth variables at the same time?

Alternatively, should I have used the AGGREGATE function to first take the
mean value for the 20 seedlings on each plot, and use those means for
RM-ANOVA?

Any suggestions much appreciated?

Rob Foster