[R] gauge R&R and repeated measurements with R

[Nicolaas Busscher]

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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