R help - Jan 2004 - repeated measurements with R

Hello All,
I have a more statistical question, and how this is implemented in R.

The problem is the following:
We have 2 different solutions (samples), which are filtered and then
the concentration of the filtrate is measured.

We want to evaluate how the filter proces and the concentration
measurement influences the detection of the difference of the two
solutions and which step has which influence. So we filter the 2
solutions each 6 times and get 12 filterd solutions. each of this
filtrate is measured 8 times, so we get 12 *8 96 conc. values. i get a
data table of:

solution nr.filter nr.measures conc.
1 or 2    1 till 6  1-till 8    96 values
because the concentrations are "repeated measurements" as i was told
by a statistician (i am not) it is not allowed to make a anova with
the formula: conc~solution+nr.filter+nr.measures.

my question is: 
how can i solve this in R?

thanks
Nicolaas Busscher

-- 
Dr.Nicolaas Busscher Universit?t GH Kassel
Nordbahnhofstrasse: 1a, D-37213 Witzenhausen
Phone: 0049-(0)5542-98-1715, Fax: 0049-(0)5542-98-1713

>
>
>The problem is the following:
>We have 2 different solutions (samples), which are filtered and then
>the concentration of the filtrate is measured.
>
>We want to evaluate how the filter proces and the concentration
>measurement influences the detection of the difference of the two
>solutions and which step has which influence. So we filter the 2
>solutions each 6 times and get 12 filterd solutions. each of this
>filtrate is measured 8 times, so we get 12 *8 96 conc. values. i get a
>data table of:
>
>solution nr.filter nr.measures conc.
>1 or 2    1 till 6  1-till 8    96 values
>because the concentrations are "repeated measurements" as i was
told
>by a statistician (i am not) it is not allowed to make a anova with
>the formula: conc~solution+nr.filter+nr.measures.
>
>my question is: 
>how can i solve this in R?
>
R can handle some repeated measurements designs with the 'Error' term in
the formula provided to aov.
(see the section on multistratum models in MASS)
(if you can read French, some examples are provided  in a small tutorial 
about R available at 
http://www.pallier.org/ressources/stats_with_R/stats_with_R.pdf (work in 
progress)).

More complex designs can be analysed with lme (described in the book 
Mixed Effects models in S and S-PLUS by Pinheiro and Bates)
 
But, you should first precise your questions, that is make clear what is 
the unit of analysis, and wether
 'solution', 'nr.filter' and 'nr.measures'  are random
or fixed factors.

*Maybe* your problem can be desribed in the following way (?)

you had twelve samples (=filtered solutions) which came from two 
solutions and you applied the same 6 different filtering processes to each
of these samples. Solution and nr.filter are fixed factors, and you are 
interested in assessing their main effects and interaction.

If this is indeed the structure of your problem, then you should define 
a new factor 'sample' with 12 levels equal to
'solution:nr.measure', and
use the following formula for the anova:

summary(aov(conc~solution*nr.filter+Error(sample/nr.filter)))

Do not use this if you do not understand the hypotheses underlying this 
approach.
For example, if you believe that there is an effect of the time at which 
the samples
were taken from the solution, then this approach is not valid.

If solution and/or filter are  random factors, then the analysis will 
also differ...

Christophe Pallier
www.pallier.org

Dear List Members,
Chistophe Pallier was so kind to help getting my question more clear,
so:

I have the following problem , which is a so called gauge R&R
(repeatebility & reproducibility) question. To get things clear (also
for myself) i draw a small graph, which i attached. 

To describe it short: we have grain samples grown under different
conditons which we process all in the same way . for this processed
grain we have a measurement procedure from which we get a value. we do
this measurement process 6 time (repeated measurements) foreach
processed sample . the process is done 6 time for each sample, we have
two different samples. the data plot looks like: sample proces values
1       1       8.0 7.8 9.0 6,5 5.5 8.9
1       2       ...
...
2       7      ...
and so on

sample is a fixed factor (we alllways use the sample from the same
bag), while process and value are random factors.

the question we have is:
1. how significant can we see the difference between sample 1 and 2,
by generating as much variation as possible, by doing 6 times the
process and each processed sample "measuring" 6 times as far as i
understand it this means: aov(value~sample+Error(proces)) Is this ok
for this kombination of fixed and random factors? from the data types
in R value is a float number, while sample and process are factors. is
that ok?

i have to generate the process information from different data,
because we combine the data from different days. as far as i
understand the Error() function, it reduces the influence of repeated
measurements on the degree of freedom , so the significance is not so
high as without.

if we would expect that there would be a time influence in the process
data (f.e. a degradation of the samples), how could we check this in
terms of this formula?

2. for our development of the complete process : is the variation from
process bigger or from values? do we get this from
aov(value~sample/process)?

the following i get out of my data, process is gathering 4 groups of
repeated measurements, (for a start i take the date of the day of the
experiment), we did the process more than one time a day.>
>     print(summary(aov(value~sample+Error(process))))
Error: process
          Df Sum Sq Mean Sq F value  Pr(>F)  
sample     1  36726   36726  6.1457 0.04787 *
Residuals  6  35855    5976                  
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` '
1

Error: Within
           Df Sum Sq Mean Sq F value    Pr(>F)    
sample      1  35596   35596  39.086 2.040e-09 ***
Residuals 223 203092     911                      
---

Does this mean that from the Error:process line we get the
information, that sample is with one * significant , taking into
account that values are repeated measurents? what means Eror:within,
where can i read about this , beside Peinhiero/Bates and the MASS book
from Venables/Ripley?

Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` '
1 
>     print(summary(aov(value~sample/process)))
                Df Sum Sq Mean Sq F value    Pr(>F)    
sample           1  34068   34068  41.719 6.872e-10 ***
sample:process  14 100812    7201   8.818 4.271e-15 ***
Residuals      216 176389     817                      
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` '
1
are here the f values more interesting? 
F sample ist 41, so it has a stronger influence as process, whos F is
8. so the process has a weaker influence as sample?

thanks
Nicolaas Busscher

-- 
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Dr.Nicolaas Busscher Universit?t GH Kassel
Nordbahnhofstrasse: 1a, D-37213 Witzenhausen
Phone: 0049-(0)5542-98-1715, Fax: 0049-(0)5542-98-1713