R help - Mar 2010 - Expected pairwise.student.t and TukeyHSD behavior?

pairwise.t.test is returning NAs when one of the samples only has one entry,
while TukeyHSD returns results (maybe not trustworthy or believable, but
results).

I stumbled on this because I did not realize one of my samples only had one
entry while most of the others had several hundred, so I realize this is not a
desirable situation.  I'm really just curious about the difference between
how pairwise.t.test and TukeyHSD handle this situation, and if this is the
desired result.

As an aside, should, in cases like this, pairwise.t.test return an error or
warning indicating what might be the cause for the NA's being returned?  
Also, should TukeyHSD similarly return a warning about this situation?

Thanks again for any insights and feedback.
 

length_1<-1
mean_1<-0.0
sd_1<-0.0
distribution_1<-rnorm(length_1, mean=mean_1, sd=sd_1)

length_2<-750
mean_2<-0.5
sd_2<-0.0
distribution_2<-rnorm(length_2, mean=mean_2, sd=sd_2)


length_3<-850
mean_3<-0.1
sd_3<-0.65
distribution_3<-rnorm(length_3, mean=mean_3, sd=sd_3)


length_4<-850
mean_4<-0.0
sd_4<-0.65
distribution_4<-rnorm(length_4, mean=mean_4, sd=sd_4)

columns_A<-data.frame(type=c("A"), vals=distribution_1)
columns_B<-data.frame(type=c("B"), vals=distribution_2)
columns_C<-data.frame(type=c("C"), vals=distribution_3)
columns_D<-data.frame(type=c("D"), vals=distribution_4)


combined_columns<-rbind(columns_A, columns_B)
combined_columns<-rbind(combined_columns, columns_C)
combined_columns<-rbind(combined_columns, columns_D)

boxplot(combined_columns$vals ~ combined_columns$type)

a2 <- aov(combined_columns$vals ~ combined_columns$type)
summary(a2)

TukeyHSD(a2)

pairwise.t.test(combined_columns$vals, combined_columns$type, p.adj =
"none")

This is because pairwise.student.t and TukeyHSD use differents estimates for
error term. TukeyHSD use the parameters covariance matrix and t use sample
variance. In this case a treatment with only one value doesn't have sample
variance but has a estimated standard error in a covariance matrix. The
lines below will illustrate the point:

# toy data
da <- data.frame(A=factor(rep(c("a","b","c"),
c(1,5,7))))
da$y <- rnorm(da$A)

# sample variance
tapply(da$y, da$A, var)
pairwise.t.test(da$y, da$A, p.adj="none") # problem!

# model and covariance matriz
m0 <- aov(y~A, da)
vcov(m0)
TukeyHSD(m0) # no problem!

Walmes.



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..ooo0
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..(....)... 0ooo...                              Walmes Zeviani
...\..(.....(.....)...     Master in Statistics and Agricultural
Experimentation
....\_)..... )../....       walmeszeviani at hotmail.com, Lavras - MG, Brasil
............
(_/............................................................................................
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