Assessing marine plankton community structure from long-term monitoring data with multivariate autoregressive (MAR) models: a comparison of fixed station versus spatially distributed sampling data

We examined how marine plankton interaction networks, as inferred by multivariate autoregressive (MAR) analysis of time-series, differ based on data collected at a fixed sampling location (L4 station in the Western English Channel) and four similar time-series prepared by averaging Continuous Plankton Recorder (CPR) datapoints in the region surrounding the fixed station. None of the plankton community structures suggested by the MAR models generated from the CPR datasets were well correlated with the MAR model for L4, but of the four CPR models, the one most closely resembling the L4 model was that for the CPR region nearest to L4. We infer that observation error and spatial variation in plankton community dynamics influenced the model performance for the CPR datasets. A modified MAR framework in which observation error and spatial variation are explicitly incorporated could allow the analysis to better handle the diverse time-series data collected in marine environments.

Simple shade plots aid better long-term choices of data pre-treatment in multivariate assemblage studies

Shade plots, simple visual representations of abundance matrices from multivariate species assemblage studies, are shown to be an effective aid in choosing an overall transformation (or other pre-treatment) of quantitative data for long-term use, striking an appropriate balance between dominant and less abundant taxa in ensuing resemblance-based multivariate analyses. Though the exposition is entirely general and applicable to all community studies, detailed illustrations of the comparative power and interpretative possibilities of shade plots are given in the case of two estuarine assemblage studies in south-western Australia: (a) macrobenthos in the upper Swan Estuary over a two-year period covering a highly significant precipitation event for the Perth area; and (b) a wide-scale spatial study of the nearshore fish fauna from five divergent estuaries. The utility of transformations of intermediate severity is again demonstrated and, with greater novelty, the potential importance seen of further mild transformation of all data after differential down-weighting (dispersion weighting) of spatially clumped' or schooled' species. Among the new techniques utilized is a two-way form of the RELATE test, which demonstrates linking of assemblage structure (fish) to continuous environmental variables (water quality), having removed a categorical factor (estuary differences). Re-orderings of sample and species axes in the associated shade plots are seen to provide transparent explanations at the species level for such continuous multivariate patterns.

Summary statistics, educational achievement gaps and the ecological fallacy

Summary statistics continue to play an important role in identifying and monitoring patterns and trends in educational inequalities between differing groups of pupils over time. However, this article argues that their uncritical use can also encourage the labelling of whole groups of pupils as ‘underachievers’ or ‘overachievers’ as the findings of group-level data are simply applied to individual group members, a practice commonly termed the ‘ecological fallacy’. Some of the adverse consequences of this will be outlined in relation to current debates concerning gender and ethnic differences in educational attainment. It will be argued that one way of countering this uncritical use of summary statistics and the ecological fallacy that it tends to encourage, is to make much more use of the principles and methods of what has been termed ‘exploratory data analysis’. Such an approach is illustrated through a secondary analysis of data from the Youth Cohort Study of England and Wales, focusing on gender and ethnic differences in educational attainment. It will be shown that, by placing an emphasis on the graphical display of data and on encouraging researchers to describe those data more qualitatively, such an approach represents an essential addition to the use of simple summary statistics and helps to avoid the limitations associated with them.

Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.