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Numbats and aardwolves—how low is low? A re-affirmation of the need for statistical rigour in evaluating regression predictions

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Abstract

Many comparative physiological studies aim to determine if a particular species differs from a prediction based on a linear allometric regression for other species. However, the judgment as to whether the species in question conforms to this allometric relationship is often not based on any formal statistical analysis. An appropriate statistical method is to compare the new species’ value with the 95% confidence limits for predicting an additional datum from the relationship for the other species. We examine the basal metabolic rate (BMR) of the termitivorous numbat (Myrmecobius fasciatus) and aardwolf (Proteles cristatus) to demonstrate the use of the 95% prediction limits to determine statistically if they have a lower-than-expected BMR compared to related species. The numbat’s BMR was 83.6% of expected from mass, but fell inside the 95% prediction limits for a further datum; a BMR < 72.5% of predicted was required to fall below the one-tail 95% prediction limits. The aardwolf had a BMR that was only 74.2% of predicted from the allometric equation, but it also fell well within the 95% prediction limits; a BMR of only 41.8% of predicted was necessary to fall below the one-tail 95% prediction limits. We conclude that a formal statistical approach is essential, although it is difficult to demonstrate that a single species statistically differs from a regression relationship for other species.

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Abbreviations

BMR:

Basal metabolic rate

C:

Thermal conductance

EWL:

Evaporative water loss

FMR:

Field metabolic rate

MMR:

Maximum metabolic rate

RMR:

Resting metabolic rate

\(\bar{{X}}\) :

Mean X

\(\hat{{Y}}\) :

Predicted Y value

∑x 2 :

Corrected sum of squares for X

s Y·X :

Standard error of estimate for Y

\({s}_{\hat{Y}}\) :

Standard error of predicted Y

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Authors and Affiliations

  1. Department of Environmental Biology, Curtin University of Technology, P.O. Box U1987, Perth, WA, 6845, Australia

    C. E. Cooper

  2. Zoology, School of Animal Biology M092, University of Western Australia, Crawley, WA, 6009, Australia

    P. C. Withers

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  1. C. E. Cooper
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Correspondence to C. E. Cooper.

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Communicated by I.D. Hume

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Cooper, C.E., Withers, P.C. Numbats and aardwolves—how low is low? A re-affirmation of the need for statistical rigour in evaluating regression predictions. J Comp Physiol B 176, 623–629 (2006). https://doi.org/10.1007/s00360-006-0085-8

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