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On correlation analysis of many‐to‐many observations: an alternative to Pearson's correlation coefficient and its application to an ecotoxicological study
Author(s) -
Moltchanova Elena,
Gerhard Daniel,
Mohamed Fathimath,
Gaw Sally,
Glover Chris N.
Publication year - 2017
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12211
Subject(s) - estimator , pearson product moment correlation coefficient , statistics , correlation coefficient , mathematics , correlation , range (aeronautics) , econometrics , mean squared error , trace (psycholinguistics) , engineering , linguistics , philosophy , aerospace engineering , geometry
Summary 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.