Complex multiple t tests in a data frame with several id factors

The concentrations of the different metals within an animal are
correlated, so that doing as you suggest will almost certainly result
in nonsense P values. So I suggest you seek local statistical help or,
failing that, post on a statistical forum like stats.stackexchange.com
?.

There are ?various multivariate packages -- check e.g. the ChemPhys
and Multivariate task views -- that may be pertinent, but your post
suggests that you probably need some help to use them. Ergo my
suggestion above.

Cheers,
Bert

On Sun, Dec 4, 2011 at 7:36 AM, Kaiyin Zhong <kindlychung at gmail.com> wrote:

I have assayed the concentrations of various metal elements in
different anatomic regions of two strains of mice. Now, for each
element, in each region, I want to do a t test to find whether there
is any difference between the two strains.

Here is what I did (using simulated data as an example):

# create the data frame

elemconc = data.frame(expand.grid(id=1:3, geno=c('exp', 'wt'), region=c('brain', 'spine'), elem=c('fe', 'cu', 'zn')), conc=rnorm(36, 10))
elemconc

? id geno region elem ? ? ?conc
1 ? 1 ?exp ?brain ? fe ?8.497498
2 ? 2 ?exp ?brain ? fe ?9.280944
3 ? 3 ?exp ?brain ? fe ?9.726271
4 ? 1 ? wt ?brain ? fe 11.556397
5 ? 2 ? wt ?brain ? fe 10.992550
6 ? 3 ? wt ?brain ? fe ?9.711200
7 ? 1 ?exp ?spine ? fe 11.168603
8 ? 2 ?exp ?spine ? fe ?9.331127
9 ? 3 ?exp ?spine ? fe 11.048226
10 ?1 ? wt ?spine ? fe ?8.480867
11 ?2 ? wt ?spine ? fe ?8.887062
12 ?3 ? wt ?spine ? fe ?8.329797
13 ?1 ?exp ?brain ? cu 10.242652
14 ?2 ?exp ?brain ? cu ?9.865984
15 ?3 ?exp ?brain ? cu ?9.163728
16 ?1 ? wt ?brain ? cu 11.099385
17 ?2 ? wt ?brain ? cu ?9.364261
18 ?3 ? wt ?brain ? cu ?9.718322
19 ?1 ?exp ?spine ? cu 10.720157
20 ?2 ?exp ?spine ? cu 11.505430
21 ?3 ?exp ?spine ? cu ?9.499359
22 ?1 ? wt ?spine ? cu ?9.855950
23 ?2 ? wt ?spine ? cu 10.120489
24 ?3 ? wt ?spine ? cu ?9.526252
25 ?1 ?exp ?brain ? zn ?9.736196
26 ?2 ?exp ?brain ? zn 11.938710
27 ?3 ?exp ?brain ? zn ?9.668625
28 ?1 ? wt ?brain ? zn ?9.961574
29 ?2 ? wt ?brain ? zn 10.461621
30 ?3 ? wt ?brain ? zn ?9.873667
31 ?1 ?exp ?spine ? zn ?9.708067
32 ?2 ?exp ?spine ? zn 10.109309
33 ?3 ?exp ?spine ? zn 10.973387
34 ?1 ? wt ?spine ? zn ?8.406536
35 ?2 ? wt ?spine ? zn ?7.797746
36 ?3 ? wt ?spine ? zn 11.127984

# use tapply to aggregate

tapply(elemconc$conc, elemconc[c('elem', 'region')], function(x) x)

? ?region
elem brain ? ? spine
?fe Numeric,6 Numeric,6
?cu Numeric,6 Numeric,6
?zn Numeric,6 Numeric,6

# check whether the order of data has been preserved after aggregation

x['fe', 'brain']

[[1]]
[1] ?8.497498 ?9.280944 ?9.726271 11.556397 10.992550 ?9.711200

# create an external factor for strain grouping

tmpgeno = rep(c('exp', 'wt'), each=3)
tmpgeno

[1] "exp" "exp" "exp" "wt" ?"wt" ?"wt"

# do the t test using the grouping factor

x = tapply(elemconc$conc, elemconc[c('elem', 'region')], function(x) t.test(x~tmpgeno) )
x

? ?region
elem brain ?spine
?fe List,9 List,9
?cu List,9 List,9
?zn List,9 List,9

I believe I have made no mistakes so far, but I wonder is there a
better way of doing this?


--
Kaiyin Zhong
------------------------------------------------------------------------------------------------------------------
Neuroscience Research Institute, Peking University, Beijing, P.R.China 100038

--

Bert Gunter
Genentech Nonclinical Biostatistics

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