Summary
Ecologists often ‘standardize’ data through the use of ratios and indices. Such measures are employed generally to remove a ‘size effect’ induced by some relatively uniteresting variable. The implications of using the resultant data in correlation and regression analyses are poorly recognized. We show that ratios and indices often provide surprising and ‘spurious’ results due to their unusual properties. As a solution, we advocate the use of randomization tests to evaluate hypotheses confounded by ‘spurious’ correlations. In addition, we emphasize that identifying the appropriate null correlation is of utmost importance when statistically evaluating ratios, although this issue is frequently ignored.
References
Aitchison J (1986) The statistical analysis of compositional data. Chapman and Hall, New York
Atchley WR, Gaskins CT, Anderson D (1976) Statistical properties of ratios: I. Empirical results. Syst Zool 25:137–148
Benson MA (1965) Spurious correlation in hydraulics and hydrology. J Hydraul Div Am Soc Civ Eng 91:3542
Chayes F (1971) Ratio correlation. University of Chicago Press, Chicago
Chayes F, Kruskal W (1966) An approximate statistical test for correlations between proportions. J Geol 74:692–702
Edgington E (1987) Randomization Tests. 2nd. Ed. Marcel Dekker
Green RH (1986) Some applications of linear models for analysis of contaminants in aquatic biota. In: El-Shaarawi AH, Kwiatowski RE (eds) Statistical Aspects of Water Quality Monitoring, Elsevier pp 231–245
Harris HJ, Jr (1970) Evidence of stress response in breeding bluewinged teal. J Wildl Manage 34:747–755
Hills M (1978) On ratios — A response to Atchley, Gaskins, and Anderson. Syst Zool 27:61–62
Jackson DA, Harvey HH, Somers KM (1990) Ratios in aquatic sciences: statistical shortcomings with mean depth and the morphoedaphic index. Can J Fish Aquat Sci 47:1788–1795
Kenney BC (1982) Beware of spurious self-correlations! Water Res. Research 18:1041–1048
Koch GS Jr, Link RF (1971) Statistical Analysis of Geological Data. Volume II. John Wiley and Sons, New York
Long SB (1980) The continuing debate over the use of ratio variables: facts and fiction. In: Schuessler KF (ed) Sociological methodology. Jossey-Bass Publ. pp 37–67
McQuinn H (1989) Identification of spring- and autumn-spawning herring (Clupea harengus harengus) using maturity stages assigned from a gonadosomatic index. Can J Fish Aquat Sci 46:969–980
Meyer SL (1975) Data Analysis for Scientists and Engineers. John Wiley and Sons, New York
Mosimann JE (1962) On the compound multinomial distribution, the multivariate β-distribution, and correlations among proportions. Biometrika 49:65–82
Packard GC, Boardman TJ (1987) The misuse of ratios to scale physiological data that vary allometrically with body size. In: Feder ME, Bennett AF, Burggren WW, Huey RB (eds) New Directions in Ecological Physiology. Cambridge University Press, pp 216–239
Packard GC, Boardman TJ (1988) The misuse of ratios, indices, and percentages in ecophysiological research. Physiol Zool 61:1–9
Pearson K (1897) On a form of spurious correlation which may arise when indices are used in the measurement of organs. Proc R Soc London 60:489–498
Pendleton BF, Newman I, Marshall RS (1983) A Monte Carlo approach to correlation spuriousness and ratio variables. J Statist Comput Simul 18:93–124
Phillips RB (1983) Shape characters in numerical taxonomy and problems with ratios. Taxon 32:535–544
Prairie YT, Bird DF (1989) Some misconceptions about the spurious correlation problem in the ecological literature. Oecologia 81:285–289
Sokal RR, Rohlf FJ (1981) Biometry. 2nd Ed. Freeman and Co., New York
Tanasichuk RW, Mackay WC (1989) Quantitative and qualitative characteristics of somatic and gonadal growth of yellow perch (Perca flavescens) from Lac Ste. Anne, Alberta. Can J Fish Aquat Sci 46:989–994
Willis DW (1989) Proposed standard length-weight equation for northern pike. N Am J Fish Manage 9:203–208
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Jackson, D.A., Somers, K.M. The spectre of ‘spurious’ correlations. Oecologia 86, 147–151 (1991). https://doi.org/10.1007/BF00317404
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DOI: https://doi.org/10.1007/BF00317404