3.2 Results don't match

When we compare the output obtained using the two different pieces of software, we can see that there are fundamental differences in the results (Fig. 1). They don't match!

Fig. 1. Comparison of results for the holdfast data using PERMANOVA in PRIMER and adonis2 in R.

More specifically, although the degrees of freedom and the sums of squares are effectively identical (in this particular case), the pseudo-F statistics and the p-values are not (Fig. 2).

Fig. 2. Pseudo-F ratios and p-values do not match.

Why don't we get the same results as PERMANOVA in PRIMER when we run PERMANOVA using the adonis2 function in R? Unfortunately, the results obtained using adonis2 are incorrect. Basically, adonis2 takes no notice of whether factors are fixed or random. The adonis2 function gives you no way of specifying the types of factors you are dealing with; adonis2 treats all factors as if they are fixed. In contrast, PERMANOVA does the analysis correctly by reference to the full study design specified by the end-user.