# Limiting the number of combinations

The final area of the main BEST dialog, headed Permutations, which carries out the *global BEST test* for statistical significance of the best matching combination of variables, is deferred until later in this section. The <ins>Next ></ins> button, under (Method•BIOENV), gives a dialog with a single entry, a choice of (Max num of trial variables/groups: <ins> &nbsp; &nbsp; &nbsp;</ins>  ), for which 5 is the default. This limits the search to $\le$5 (abiotic) variables at a time, and this maximum number should be increased, where feasible. A default of the total number of input variables is not used because the number of combinations of these in an exhaustive search could be very large: for *p* variables there are c = 2$^p$ – 1 combinations, and a practically realistic limit therefore has to be about *p* = 17 (giving c $\approx$ 100,000). The context for Section [13](https://learninghub.primer-e.com/books/primer-v7-user-manual-tutorial/chapter/13-linking-assemblage-to-environment-best-bio-env-linktree) is the matching of subsets of environmental variables to assemblage patterns. Quite often, the number of abiotic variables is then <17 or, if not, the number should probably be pruned before running BEST – so only a full search (BIOENV) will be illustrated now. BVSTEP could be run in much the same way on a larger set, but the reason this is likely to prove unattractive is that, with so many abiotic variables, it is inevitable that they will be strongly inter-correlated. There are then a plethora of equally good solutions and a rather unfocussed interpretation. Deletion of all but one of a highly mutually-correlated set of variables and/or prior reduction to one representative of each different <u>type</u> of environmental variable, may be desirable, just as in multiple linear regression (see the discussion in Chapter 11 of CiMC). In some of the other applications – e.g. when the data matrix is of species variables and *a priori* selection defeats the point of the analysis – the stepwise form (Method•BVSTEP) will be essential, and such an example is seen in Section [14](https://learninghub.primer-e.com/books/primer-v7-user-manual-tutorial/chapter/14-further-matching-of-multivariate-patterns-relate-2stage-best-mvdisp).