2STAGE for time series and repeated measures

In the context of a 2-factor design, PRIMER makes a 2nd stage matrix very simple to produce but it is less easy to understand what it represents! The structure requires that the factors divide the data into a 2-way layout with no replicates in each cell; the inner factor specifies the patterns to match (spatial, for the Phuket data) and the outer factor is the one displayed (temporal, above). Note that, because of the symmetry of two-way crossed designs, these could be reversed, thus the Phuket data could have matched the inter-annual patterns at each point on the transect. This would remove the ‘main effect’ of differences in (time-averaged) assemblages along the transect, and concentrate on anomalous transect positions – those for which the relationship among years differs. The Clarke, Somerfield, Airoldi & Warwick 2006 paper, referred to above, discusses two further examples in which Analyse>2STAGE is able to match temporal patterns to produce a spatial second-stage matrix. Both have a natural hypothesis testing framework, which extends to repeated measures designs, usually considered problematic even in univariate studies. An inter-annual time series (1973-96) for subtidal macrobenthos, at two sites in each of four different areas in Tees Bay, UK, was met in Section 9, and will be exemplified here, and a repeated measures recolonisation study on macroalgae at Calafuria in the Ligurian Sea (the non-repeated measures data from which was seen in the ANOSIM section) is also discussed in detail as the last example in Chapter 16, CiMC.