Data transformation and standardization in the multivariate analysis of river water quality

Yong Cao, D. Dudley Williams, Nancy E. Williams

Research output: Contribution to journalArticlepeer-review


Multivariate approaches are being increasingly applied to aquatic studies; however, their ecological relevance has not been adequately addressed. This paper examines the effects of data transformation and standardization on principal-components analysis (PCA) of river water quality. Two currently popular methods, log(x + 1) and standardizing to 0 mean and 1 variance, were evaluated. The choice of the data-handling methods substantially affected the analytic output. However, both methods tested were found to be flawed, with the major problem being disregard for the biological/ecotoxicological significance of water, quality variables and their ranges. We developed a new standardization model, which incorporates water quality standards into data standardization. This provides a mechanism to improve the biological relevance of multivariate analysis. The new model-based PCA yields an assessment of water quality that is more ecologically meaningful than any others tested. We discuss the ecological implications of the new model and of the established methods tested.

Original languageEnglish (US)
Pages (from-to)669-677
Number of pages9
JournalEcological Applications
Issue number2
StatePublished - May 1999
Externally publishedYes


  • Data transformation and standardization
  • Multivariate analysis, ecological relevance
  • Principal-components analysis
  • River pollution
  • Rouge River Basin, southeastern Ontario, Canada
  • Water-quality assessment
  • Water-quality standards

ASJC Scopus subject areas

  • Ecology


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