On correlation analysis of many-to-many observations: an alternative to Pearson's correlation coefficient and its application to an ecotoxicological study

Elena Moltchanova, Daniel Gerhard, Fathimath Mohamed, Sally Gaw, Chris N. Glover

Research output: Contribution to journalJournal Articlepeer-review

1 Citation (Scopus)

Abstract

Correlation studies are an important hypothesis-generating and testing tool, and have a wide range of applications in many scientific fields. In ecological studies in particular, multiple environmental variables are often measured in an attempt to determine relationships between chemical, physical and biological factors. For example, one may wish to know whether and how soil properties correlate with plant physiology. Although correlation coefficients are widely used, their properties and limitations are often imperfectly understood. This is especially the case when one is interested in correlations between, say, trace element content in sediments and in marine organisms, where no one-to-one correspondence exists. We show that evaluating Pearson's correlation coefficient for either site-specific means or composite samples results in biased estimates, and we propose an alternative estimator. We use simulation studies to demonstrate that our estimator generally has a much smaller bias and mean squared error. We further illustrate its use in a case study of the correlation between trace element content in sediments and in mussels in Lyttelton Harbour, New Zealand.

Original languageEnglish
Pages (from-to)371-387
Number of pages17
JournalAustralian and New Zealand Journal of Statistics
Volume59
Issue number4
DOIs
Publication statusPublished - Dec. 2017

Keywords

  • Pearson's correlation coefficient
  • analysis of variance and covariance
  • ecological science
  • mixed models
  • mussels
  • sediment
  • toxicity
  • trace elements

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