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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
Comments: To: rfoster <rfoster@LOON.NORLINK.NET>

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.

---------- 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

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