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Letter

Statistical errors and asymmetry indices

Peter Coles
  1. School of Physics and Astronomy, Cardiff University, Queen's Buildings, 5 The Parade, Cardiff CF24 3AA, United Kingdom

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PNAS November 11, 2008 105 (45) E82; https://doi.org/10.1073/pnas.0806646105
Peter Coles
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  • For correspondence: peter.coles@astro.cf.ac.uk
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Savic and Lindström (1) claim to have discovered significant differences in cerebral asymmetry and functional connectivity between homo- and heterosexual subjects. Unfortunately, the statistical analysis they present is strongly undermined by an inappropriate choice of variables. For example, in their analysis of cerebral asymmetry, the authors measure right and left cerebral volumes (R and L, respectively) and use these to construct an “asymmetry index” for each subject defined by V = (R − L)/(R + L) ≡ X/Y; they call this index AI. No details about the distribution of R and L are given in ref. 1, but if we assume that they are (correlated) bivariate normal variables then X = R − L and Y = R + L are in fact uncorrelated normal variables for which the exact ratio distribution is known (2) to have very long “tails.” This is a general problem with ratio distributions. Standard statistical methods, which assume normal distributions with rapidly decreasing tails, are not generally appropriate for this type of variable. Unfortunately, Savic and Lindström (1) seem unaware of this difficulty and proceed to use a standard t test and ANOVA: the P values emerging from this analysis are meaningless if the variables involved are ill conditioned.

One way to work around this problem is to use a different variable, such as U = (μx − μyV)/(σx2 + σy2V2)1/2, which is normally distributed (2) if X and Y are independent normal variables with means μx and μy and variances σx2 and σy2. Standard methods applied to U would give much more conclusive results than those obtained by using V. An alternative is to use the median instead of the mean (3).

Either way, a much more convincing statistical analysis is needed to establish whether the differences reported in ref. 1 are indeed significant.

Footnotes

  • 1To whom correspondence should be addressed. E-mail: peter.coles{at}astro.cf.ac.uk
  • Author contributions: P.C. wrote the paper.

  • The author declares no conflict of interest.

  • © 2008 by The National Academy of Sciences of the USA

References

  1. ↵
    1. Savic I,
    2. Lindström P
    (2008) PET and MRI show differences in cerebral asymmetry and functional connectivity between homo- and heterosexual subjects. Proc Natl Acad Sci USA 105:9403–9408.
    OpenUrlAbstract/FREE Full Text
  2. ↵
    1. Geary RC
    (1930) The frequency distribution of the quotient of two normal variates. J R Stat Soc 93:442–446.
    OpenUrlCrossRef
  3. ↵
    1. Brody JP,
    2. Williams BA,
    3. Wold BJ,
    4. Quake SR
    (2002) Significance and statistical errors in the analysis of DNA microarray data. Proc Natl Acad Sci USA 99:12975–12978.
    OpenUrlAbstract/FREE Full Text
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Statistical errors and asymmetry indices
Peter Coles
Proceedings of the National Academy of Sciences Nov 2008, 105 (45) E82; DOI: 10.1073/pnas.0806646105

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Statistical errors and asymmetry indices
Peter Coles
Proceedings of the National Academy of Sciences Nov 2008, 105 (45) E82; DOI: 10.1073/pnas.0806646105
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