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Priorities in statistics, the sensitive feet of elephants, and don’t transform data

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Abstract

In spite of the widespread use of statistics in plant ecology, some misunderstandings are widespread. Lájer’s warning against non-random sampling in the field is well taken, but non-randomization is probably more common than we realize in experimental work too, and a frequent cause of inexplicable “significant” results. However, in the placement of quadrats/samples, restricted randomization is always preferable to plain random. The main purpose of randomization, as R.A. Fisher made clear, is to obtain a valid estimate of the error. Random placement does not, as Fisher realized, ensure independence of samples because of spatial autocorrelation, which is present in all ecological work. If we forget this, we can end up concluding that elephants carefully select moss cushions to tread on. Although a normal distribution is often formally required, tests such as the Analysis of Variance are fairly robust against departures. Obsession with normality leads to the use of inappropriate transformations, for example a log transformation when the author had no intention of a multiplicative model. Even worse is the use of a log (x + 1) transformation, which gives answers in neither additive nor multiplicative terms, and in a way unrelated to the means presented. There are several solutions to this, including randomization tests. After all this, we should not take the arbitrary value of 0.05 too seriously. Many statisticians do not.

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Correspondence to J. Bastow Wilson.

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Bastow Wilson, J. Priorities in statistics, the sensitive feet of elephants, and don’t transform data. Folia Geobot 42, 161 (2007). https://doi.org/10.1007/BF02893882

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Keywords

  • Normality
  • Pseudoreplication
  • Randomization
  • Restricted randomization
  • Spatial autocorrelation
  • Stratified randomization
  • Transformation