Researches on Population Ecology

, Volume 41, Issue 3, pp 229–234

Transformation using (x + 0.5) to stabilize the variance of populations

  • Kohji Yamamura

DOI: 10.1007/s101440050026

Cite this article as:
Yamamura, K. Res Popul Ecol (1999) 41: 229. doi:10.1007/s101440050026


Transformation is required to achieve homo-scedasticity when we perform ANOVA to test the effect of factors on population abundance. The effectiveness of transformations decreases when the data contain zeros. Especially, the logarithmic transformation or the Box–Cox transformation is not applicable in such a case. For the logarithmic transformation, 1 is traditionally added to avoid such problems. However, there is no concrete foundation as to why 1 is added rather than other constants, such as 0.5 or 2, although the result of ANOVA is much influenced by the added constant. In this paper, I suggest that 0.5 is preferable to 1 as an added constant, because a discrete distribution defined in {0, 1, 2, . . .} is approximately described by a corresponding continuous distribution defined in (0, ≧) if we add 0.5. Numerical investigation confirms this prediction.

Key words ANOVABox–Cox transformationHeteroscedasticityIwao's m*−m regressionTaylor's power law

Copyright information

© The Society of Population Ecology and Springer-Verlag Tokyo 1999

Authors and Affiliations

  • Kohji Yamamura
    • 1
  1. 1.Laboratory of Population Ecology, National Institute of Agro-Environmental Sciences, 3-1-1 Kannondai, Tsukuba 305-8604, Japan Tel. +81-298-38-8313; Fax +81-298-38-8199 e-mail: yamamura@niaes.affrc.go.jpJP