This Article Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Handelsman, D. J. Search for Related Content PubMed PubMed Citation Articles by Handelsman, D. J.

Optimal Power Transformations for Analysis of Sperm Concentration and Other Semen Variables

From the ANZAC Research Institute and Department of Andrology, Concord Hospital, University of Sydney, Sydney, Australia.

Correspondence to: Prof David J. Handelsman, ANZAC Research Institute, Sydney NSW 2139, Australia (e-mail: djh{at}anzac.edu.au).

The nongaussian (or nonnormal) distribution of sperm concentration, and variables deriving from it, is a common practical problem in the statistical evaluation of semen data. Yet it has been little studied, and its importance to data analysis, as well as to practical remedies, is not widely appreciated. Inappropriate use of the raw scale of measurement produces inflated estimates of mean and variance, leading to false-negative (underpowered) statistical comparisons and excessive sample size estimates. This study employs the Box-Cox family of power transforms to illustrate by a simple graphical method how to identify optimal power transforms for semen data variables. Using robust statistical methods, it is shown that the nongaussian distribution is due to right skewing rather than multimodality or influential outliers. The optimal power transform, typically in the region of 0.15 to 0.35 (most easily implemented as a cube-root transformation), usually performs better than the logarithmic transformation in normalizing the data. In addition, the power transformation has an important practical advantage over the logarithmic transformation in the appropriate handling of zeros (azoospermia), a regular and important features of such data sets in practice.

     Key words: Statistics, data transformation, male fertility

This article has been cited by other articles:

				R.P. Amann Evaluating testis function non-invasively: how epidemiologist-andrologist teams might better approach this task Hum. Reprod., January 1, 2010; 25(1): 22 - 28. [Abstract] [Full Text] [PDF]

				T. G. Cooper, E. Noonan, S. von Eckardstein, J. Auger, H.W. G. Baker, H. M. Behre, T. B. Haugen, T. Kruger, C. Wang, M. T. Mbizvo, et al. World Health Organization reference values for human semen characteristics Hum. Reprod. Update, December 4, 2009; (2009) dmp048v2. [Abstract] [Full Text] [PDF]

				R. P. Amann and P. L. Chapman Total Sperm per Ejaculate of Men: Obtaining a Meaningful Value or a Mean Value With Appropriate Precision J Androl, November 1, 2009; 30(6): 642 - 649. [Abstract] [Full Text] [PDF]

				L. P. Ly, P. Y. Liu, and D. J. Handelsman Rates of suppression and recovery of human sperm output in testosterone-based hormonal contraceptive regimens Hum. Reprod., June 1, 2005; 20(6): 1733 - 1740. [Abstract] [Full Text] [PDF]

				P. Christensen, D. Boelling, K. M. Pedersen, I. R. Korsgaard, and J. Jensen Relationship Between Sperm Viability as Determined by Flow Cytometry and Nonreturn Rate of Dairy Bulls J Androl, January 1, 2005; 26(1): 98 - 106. [Abstract] [Full Text] [PDF]