[R-sig-eco] stratifying variables in Adonis

[Duncan Mackay]

Hello all,
In the documentation for Adonis in the vegan package, there is an example of a replicated random block design with Nitrate levels as a treatment factor and field as a blocking factor.

The following model is shown :-
### Correct hypothesis test (with strata)
adonis(Y ~ NO3, data=dat, strata=dat$field, perm=1e3)

which results in the following output:-
Call:
adonis(formula = Y ~ NO3, data = dat, permutations = 1000, strata = dat$field) 

          Df SumsOfSqs  MeanSqs F.Model      R2  Pr(>F)  
NO3        1  0.018446 0.018446  1.1241 0.10105 0.03397 *
Residuals 10  0.164090 0.016409         0.89895          
Total     11  0.182536                  1.00000          
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

If we remove the replication by selecting only the first replicate in each block, 
> dat1 <- dat[dat$rep==1,]
we get

> dat1
   rep NO3 field
1    1   0     1
3    1  10     1
5    1   0     2
7    1  10     2
9    1   0     3
11   1  10     3

And
> Y1 <-Y[dat$rep==1,]
> Y1
   Agropyron Schizachyrium
1   3.361260     0.9419159
3   5.579260     1.5222111
5   5.194289     2.7812308
7   6.210538     2.6668505
9   5.916120     4.1912890
11  7.575184     2.1243425

And if we analyze this 
> adonis(Y1 ~ NO3,strata=dat1$field, data=dat1,perm=1000)

Call:
adonis(formula = Y1 ~ NO3, data = dat1, permutations = 1000,      strata = dat1$field) 

          Df SumsOfSqs  MeanSqs F.Model      R2 Pr(>F)
NO3        1  0.022964 0.022964 0.88214 0.18069 0.2418
Residuals  4  0.104128 0.026032         0.81931       
Total      5  0.127091                  1.00000       

My first question is:- Is it OK  to add the stratifying variable (field) in the model statement as below. 
> adonis(Y1 ~ NO3 + field,strata=dat1$field, data=dat1,perm=1000)

Call:
adonis(formula = Y1 ~ NO3 + field, data = dat1, permutations = 1000,      strata = dat1$field) 

          Df SumsOfSqs  MeanSqs F.Model      R2 Pr(>F)
NO3        1  0.022964 0.022964  1.6959 0.18069 0.2358
field      2  0.077045 0.038523  2.8449 0.60622 0.2358
Residuals  2  0.027082 0.013541         0.21309       
Total      5  0.127091                  1.00000  

However, my second question is :- How has Adonis has come up with a P-value here for field?  I thought that all shuffling of data was occurring within fields and therefore that the field totals (and F-ratios) would be the same for each permutation?

Thanks for any help,
Duncan

______________________________________________________________________________
Dr. Duncan Mackay
School of Biological Sciences
Flinders University
GPO Box 2100
Adelaide
S.A.  5001
AUSTRALIA

Phone    61-8-82012627
FAX          61-8-82013015

http://www.flinders.edu.au/science_engineering/biology/our-school/staff-postgrads/academic-staff/mackay-duncan.cfm