Abstract
The reporting and graphing of ecological data and statistical results often leave a lot to be desired. One reason can be a misunderstanding or confusion of some basic concepts in statistics such as standard deviation, standard error, margin of error, confidence interval, skewness of distribution and correlation. The implications of having small sample sizes are also often glossed over. In several situations, statistics and associated graphical representations are made for comparing groups of samples, where the issues become even more complex. Here, I aim to clarify these basic concepts and ways of reporting and visualizing summaries of variables in ecological research, both for single variables and for pairs of variables. Specific recommendations about better practice are made, for example describing precision of the mean by the margin of error and bootstrapping to obtain confidence intervals. The role of the logarithmic transformation of positive data is described, as well as its implications in the reporting of results in multiplicative rather than additive form. Comments are also made about ordination plots derived from multivariate analyses, such as principal component analysis and canonical correspondence analysis, with suggested improvements. Some data sets from this Kongsfjord special issue are amongst those used as examples.
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Notes
This same least-squares principle is used in a more general form in multivariate ordination methods, to define closest subspaces to a set of points, to be treated later.
Strictly speaking, for theoretical reasons, the sum of squared distances (i.e. the sum of the squared deviations from the mean) is divided by n − 1, not the sample size n, to obtain the “average”. In practice, this only makes noticeable differences in the case of very small sample sizes.
The lower 0.025 quantile is clearly 0, while the upper 0.975 quantile is based on an interpolation between the 14th and 15th ordered values of 26 and 31, and closer to the 31 than the 26. There are at least nine slightly different ways of computing this interpolation, as detailed in the documentation of the \({\mathsf R}\) function \({\tt quantile}\), the default option of which was used to obtain the estimate of 29.25.
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Acknowledgements
The author would like to express his sincere thanks to Haakon Hop for his encouragement and constant constructive feedback related to this article, also to Markus Molis for our many discussions on this topic, as well as Walter Zucchini for additional comments. Thanks are also due to Kim Huenerlage, Andrey Voronkov and Henk Bolhuis for their cooperation in being able to use some of their data from this special Kongsfjorden issue of Polar Biology.
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This article belongs to the special issue on the “Kongsfjorden ecosystem—new views after more than a decade of research”, coordinated by Christian Wiencke and Haakon Hop.
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Video S1
Video animation of the three-dimensional view of Figure 10, showing the true nature of the separation between the ellipsoidal confidence regions (GIF 1869 kb)
Video S2
Video animation of the CCA ordination of Figure 11 when a third dimension is added. The video pauses when dimension 2 is horizontal and pointing to the right (i.e. Figure 11), and when dimension 3 is horizontal and pointing to the right, which shows that all confidence ellipses overlap on the third dimension (GIF 5084 kb)
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Greenacre, M. Data reporting and visualization in ecology. Polar Biol 39, 2189–2205 (2016). https://doi.org/10.1007/s00300-016-2047-2
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DOI: https://doi.org/10.1007/s00300-016-2047-2