[R] Error term in aov syntax question

[Petr Pikal]

Hallo all

I went through all files and through some books I have, but still I am not 
completely sure about the correct aov syntax.

Suppose I have a dataset divided to three portions, according to a factor "mereni" 
which is a measurement day. There is another factor named "frakce" (Each 
sample is divided into three distinct fractions according to its particle size). 

samp	frakce	h	mereni
62	0	21.35	1
66	0	21.41	1
70	0	21.42	1
66	0.25	20.93	1
62	1	20.91	1
66	1	21.29	1
70	1	21.22	1
26	0	20.79	2
34	0	20.20	2
26	0.25	20.30	2
37	0.25	20.07	2
71	0.25	21.20	2
26	1	20.73	2
34	1	20.20	2
39	1	19.87	2
49	0	20.01	3
49	0.25	20.05	3
59	0.25	19.78	3
49	1	20.01	3
54	1	20.45	3

The samples are actually taken from one process and the hypotheses to be tested 
are:

**Are all samples same?
It seems that within each measurement they are all the same but:

> summary(aov(h[mereni==3]~vzor[mereni==3]))


                  Df   Sum Sq  Mean Sq F value   Pr(>F)   
vzor[mereni == 3]  2 0.234296 0.117148  224.58 0.004433 **
Residuals          2 0.001043 0.000522                    
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 
 

**Does a measurement day influence the response ("ce","h"),?
It seems that yes.

> summary(aov(h~mereni))


            Df Sum Sq Mean Sq F value    Pr(>F)    
mereni       2 4.3911  2.1956  19.625 3.826e-05 ***
Residuals   17 1.9019  0.1119                      
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1


**Are there some differences in response among fractions?
It seems that yes but only for measurement 1.

> summary(aov(h[mereni==1]~frakce[mereni==1]))

                    Df   Sum Sq  Mean Sq F value  Pr(>F)  
frakce[mereni == 1]  2 0.193038 0.096519  4.5464 0.09334 .
Residuals            4 0.084918 0.021230                  
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 


I know there are not many measurements (only one 0.25 fraction in measurement 
1 and one 0 fraction in measurement 3) in my dataset :-(.

But if I had more data in one measurement (let say three fractions in each of three 
samples),
is the correct aov syntax for such problem like this:

summary(aov(h~frakce+vzor+Error(mereni/(frakce+vzor))))

Thanks a lot

Petr Pikal
Precheza a.s.
Nabø.Dr.E.Beneše 24
750 62 Pøerov
+420641 25 2257 
0724 008 364
petr.pikal at precheza.cz
p.pik at volny.cz


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