Message-ID: <CACk-te33TE+V_Sfs3KDCs-QWPH4fnwUmjiNHMmRJkJeQdDWKKw@mail.gmail.com>
Date: 2011-12-11T14:49:03Z
From: Bert Gunter
Subject: multiple comparison of interaction of ANCOVA
In-Reply-To: <4EE49ED0.9050500@yeah.net>
Inline below.
-- Bert
On Sun, Dec 11, 2011 at 4:15 AM, Jinsong Zhao <jszhao at yeah.net> wrote:
> Hi there,
>
> The following data is obtained from a long-term experiments.
>
>> mydata <- read.table(textConnection("
> + ? ? ? ?y year Trt
> + ? ? 9.37 1993 ? A
> + ? ? 8.21 1995 ? A
> + ? ? 8.11 1999 ? A
> + ? ? 7.22 2007 ? A
> + ? ? 7.81 2010 ? A
> + ? ?10.85 1993 ? B
> + ? ?12.83 1995 ? B
> + ? ?13.21 1999 ? B
> + ? ?13.70 2007 ? B
> + ? ?15.15 2010 ? B
> + ? ? 5.69 1993 ? C
> + ? ? 5.76 1995 ? C
> + ? ? 6.39 1999 ? C
> + ? ? 5.73 2007 ? C
> + ? ? 5.55 2010 ? C"), header = TRUE)
>> closeAllConnections()
>
> The experiments is designed without replication, thus I have to use ANCOVA
> or linear mixed effect model to analyze the data. In the model, variable
> year is coded as a continuous variable, and Trt is factor variable.
>
>> mydata.aov <- aov(y~Trt*year, mydata)
>> anova(mydata.aov)
> Analysis of Variance Table
>
> Response: y
> ? ? ? ? ?Df ?Sum Sq Mean Sq ?F value ? ?Pr(>F)
> Trt ? ? ? ?2 140.106 ?70.053 197.9581 3.639e-08 ***
> year ? ? ? 1 ? 0.610 ? 0.610 ? 1.7246 ?0.221600
> Trt:year ? 2 ? 8.804 ? 4.402 ?12.4387 ?0.002567 **
> Residuals ?9 ? 3.185 ? 0.354
> ---
> Signif. codes: ?0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> As you have seen, the interaction effect is significant. I hope to use
> TukeyHSD() or glht() to do multiple comparison on Trt:year. However, for
> variable year is not a factor, they all give error messages.
>
> I try to follow the demo("MMC.WoodEnergy") in HH package, as follwoing:
>
>> library(HH)
>> mca.1993 <- mcalinfct(mydata.aov, "Trt")
>> non.zero <- mca.1993[,5:6] != 0
>> mca.1993[,5:6][non.zero] <- 1993 * sign(mca.1993[,5:6][non.zero])
>> summary(glht(mydata.aov, linfct=mca.1993))
>
> ? ? ? ? Simultaneous Tests for General Linear Hypotheses
>
> Fit: aov(formula = y ~ Trt * year, data = mydata)
>
> Linear Hypotheses:
> ? ? ? ? ? Estimate Std. Error t value Pr(>|t|)
> B - A == 0 ? 2.8779 ? ? 0.5801 ? 4.961 ?0.00215 **
> C - A == 0 ?-2.8845 ? ? 0.5801 ?-4.972 ?0.00191 **
> C - B == 0 ?-5.7624 ? ? 0.5801 ?-9.933 ?< 0.001 ***
> ---
> Signif. codes: ?0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> (Adjusted p values reported -- single-step method)
>
> It can give comparison between levels of Trt within one year, e.g., 1993.
>
> Is it possible to do multiple comparison for the following pairs:
>
> A.1995 - A.1993
> B.1995 - A.1993
> C.1995 - A.1993
>
> Any suggestions or comments will be really appreciated. Thanks in advance!
Graph the data sensibly to figure out what's going on. Statistical
machinationsand anova tables with P values alone are not sufficient
and can be opaque or misleading.
If you do not know what "sensibly" is (or even if you do), consult:
http://addictedtor.free.fr/graphiques/
Cheers,
Bert
>
> Regards,
> Jinsong
>
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
--
Bert Gunter
Genentech Nonclinical Biostatistics
Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm