Hi

The value of F- Statistic can not be negative. So you can't continiouse in your interoutation for those results.

Hi

The value of F- Statistic can not be negative. So you can't continiouse in your interoutation for those results.

Hello,

Thanks for answering. I understand the problem with the F-statistic, but this is a "pseudo F" as described by Anderson in "A new method for non‐parametric multivariate analysis of variance" [Austral ecology, 26(1), 32-46]. This pseudo F is then permuted to reach a p-value. Since the interaction sum of squares is the largest value, it makes sense in the math that the value is negative:

SSAB =SSTotal – SSA – SSB – SSResidual.

The question would be if this makes sense at all and it is ok in this test to have a negative value for the sum of squares of the interaction term.

Best wishes,

Viviana

Conceptually I don't see how even a pseudo-F can be negative. It is a ratio of two pseudo mean squares each of which is a ratio of SS to df (both positive quantities by definition). Google searches suggest this arise in PAST and PERMANOVA but I'm really not convinced that it makes sense. This suggests either the software has a bug or the approach is flawed.

There is an R implementation:

http://cc.oulu.fi/~jarioksa/softhelp/vegan/html/adonis.html

However, I'd probably consider a different approach such as a Bayesian multivariate analysis that allows you to model the data more flexibly.

Dear Thom,

It is working fine in R. I have a followup question:

I ran the analysis with two factors, no interactions (I am interested in the relative amount of variance explained by the factors, not their interaction, nor their statistical significance over residuals), so I used the formula Y~FactorA+FactorB. Is that correct?

These are my results:

Permutation: free

Number of permutations: 9999

Terms added sequentially (first to last)

Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)

dataset$FactorA 4 0.08279 0.0206972 8.2042 0.14104 1e-04 ***

dataset$FactorB 6 0.06271 0.0104520 4.1431 0.10684 1e-04 ***

Residuals 175 0.44148 0.0025227 0.75212

Total 185 0.58698 1.00000

I am puzzled because the degrees of freedom of FactorA is correct (5 level minus 1), but Factor B has 9 levels, so the degrees of freedom should be 8. I double checked that the data was completely included in the analysis. Am I missing a calculation of the degrees of freedom for the second factor?

Thanks a lot,

Viviana

I don't know this package - but yes you should get 7 df from 8 levels on a factor. I'd check the labelling of the factor and whether there are cases lost for missing data. However, there may be something else going on as I'm not familiar with this procedure.

In terms of model I'd normally include the interaction in a factorial design (because it is orthogonal to the main effects).