[R] multiple comparison of interaction of ANCOVA

[Bert Gunter]

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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> and provide commented, minimal, self-contained, reproducible code.



-- 

Bert Gunter
Genentech Nonclinical Biostatistics

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