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On the Statistical Significance of the Hutchinsonian Size‐Ratio Parameter
Author(s) -
MacNally Ralph Charles
Publication year - 1988
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.2307/1941175
Subject(s) - homoscedasticity , statistics , mathematics , sample size determination , series (stratigraphy) , geometric mean , confidence interval , goodness of fit , standard deviation , range (aeronautics) , constant (computer programming) , geometric series , heteroscedasticity , computer science , biology , mathematical analysis , paleontology , materials science , composite material , programming language , power series
A technique is presented for the analysis of sets of morphological data to test whether sympatric, closely related species form geometric series (or Hutchinsonian series, where the constant of proportionality, h, is 1.30 for linear characteristics). A basic two—parameter model is proposed. The logarithmically transformed version of the geometric model is used because of its simplicity, and the greater probability that variances will be homogeneous. The analysis provides methods for estimating the goodness of fit of a set of measurements to the model, a maximum likelihood estimate for h, h, and a 95% confidence interval for h. The mean, standard deviation, sample size, or, if possible, raw data for each species in the array are required. The present paper demonstrates the importance of using a method that intrinsically depends upon intraspecific variation. The assumptions of many existing analyses that are based only upon means or their ratios, such as homoscedasticity and negligible variances, generally are invalid. This result is damaging in more general terms because large variances often mean wide morphological overlap, even if means do differ. The method demonstrated that only a small fraction of collections of syntopic series conformed to the geometric model, and of these, few had confidence intervals for h in which 1.30 was included.