Community Ecology

, Volume 19, Issue 1, pp 77–83 | Cite as

Cautionary note on calculating standardized effect size (SES) in randomization test

  • Z. Botta-DukátEmail author
Open Access


In community ecology, randomization tests with problem specific test statistics (e.g., nestedness, functional diversity, etc.) are often applied. Researchers in such studies may want not only to detect the significant departure from randomness, but also to measure the effect size (i.e., the magnitude of this departure). Measuring the effect size is necessary, for instance, when the roles of different assembly forces (e.g., environmental filtering, competition) are compared among sites. The standard method is to calculate standardized effect size (SES), i.e., to compute the departure from the mean of random communities divided by their standard deviations. Standardized effect size is a useful measure if the test statistic (e.g., nestedness index, phylogenetic or functional diversity) in the random communities follows a symmetric distribution. In this paper, I would like to call attention to the fact that SES may give us misleading information if the distribution is asymmetric (skewed). For symmetric distribution median and mean values are equal (i.e., SES = 0 indicates p = 0.5). However, this condition does not hold for skewed distributions. For symmetric distributions departure from the mean shows the extremity of the value, regardless of the sign of departure, while in asymmetric distributions the same deviation can be highly probable and extremely improbable, depending on its sign. To avoid these problems, I recommend checking symmetry of null-distribution before calculating the SES value. If the distribution is skewed, I recommend either log-transformation of the test statistic, or using probit-transformed p-value as effect size measure.


Functional diversity Randomization test Standardized effect size Statistics 



Cumulative Distribution Function


Leaf Dry Matter Content


Rao’s Quadratic entropy


Standardized Effect Size


Specific Leaf Area



Thanks to M. Scotti, B. Lhotsky and two anonymous reviewers for their comments that helped to improve the manuscript.

Supplementary material

42974_2018_19010077_MOESM1_ESM.pdf (175 kb)
Cautionary note on calculating standardized effect size (SES) in randomization test


  1. Astor, T., J. Strengbom, M.P. Berg, L. Lenoir, B. Marteinsdóttir and J. Bengtsson. 2014. Underdispersion and overdispersion of traits in terrestrial snail communities on islands. Ecol. Evol. 4:2090–2102.PubMedPubMedCentralGoogle Scholar
  2. de Bello, F. 2012. The quest for trait convergence and divergence in community assembly: are null-models the magic wand? Global Ecol. Biogeogr. 21:312–317.CrossRefGoogle Scholar
  3. Bennett, J. R. and B. Gilbert. 2016. Contrasting beta diversity among regions: how do classical and multivariate approaches compare? Global Ecol. Biogeogr. 25:368–377.CrossRefGoogle Scholar
  4. Bernard-Verdier, M., M.-L. Navas, M. Vellend, C. Violle, A. Fayolle and E. Garnier. 2012. Community assembly along a soil depth gradient: contrasting patterns of plant trait convergence and divergence in a Mediterranean rangeland. J. Ecol. 100:1422–1433.CrossRefGoogle Scholar
  5. Botta-Dukát, Z. 2005. Rao’s quadratic entropy as a measure of functional diversity based on multiple traits. J. Veg. Sci. 16:533–540.CrossRefGoogle Scholar
  6. Botta-Dukát, Z. 2018. The generalized replication principle and the partitioning of functional diversity into independent alpha and beta components. Ecography 41:40–50.CrossRefGoogle Scholar
  7. Botta-Dukát, Z. and B. Czúcz. 2016. Testing the ability of functional diversity indices to detect trait convergence and divergence using individual-based simulation. Methods Ecol. Evol. 7:114–126.CrossRefGoogle Scholar
  8. Briscoe Runquist, R., D. Grossenbacher, S. Porter, K. Kay and J. Smith. 2016. Pollinator-mediated assemblage processes in California wildflowers. J. Evol. Biol. 29:1045–1058.CrossRefGoogle Scholar
  9. Gotelli, N.J. and G.R. Graves. 1996. Null Models in Ecology. Smithsonian Institution Press, Washington, D.C.Google Scholar
  10. Gotelli, N.J. and D.J. McCabe. 2002. Species co-occurrence: a me-ta-analysis of J. M. Diamond’s assembly rules model. Ecology 83:2091–2096.Google Scholar
  11. Götzenberger, L., F. de Bello, K.A. Bråthen, J. Davison, A. Dubuis, A. Guisan, J. Lepš, R. Lindborg, M. Moora, M. Pärtel, L. Pellissier, J. Pottier, P. Vittoz, K. Zobel and M. Zobel. 2012. Ecological assembly rules in plant communities—approaches, patterns and prospects. Biol. Rev. 87:111–127.CrossRefGoogle Scholar
  12. Harrison, F. 2011. Getting started with meta-analysis. Methods Ecol. Evol. 2: 1–10.CrossRefGoogle Scholar
  13. Heino, J., J. Soininen, J. Alahuhta, J. Lappalainen and R. Virtanen. 2015. A comparative analysis of metacommunity types in the freshwater realm. Ecol. Evol. 5:1525–1537.CrossRefGoogle Scholar
  14. Joanes, D.N. and C.A. Gill. 1998. Comparing measures of sample skewness and kurtosis. J. Roy. Stat. Soc. D 47:183–189.CrossRefGoogle Scholar
  15. Knijnenburg, T.A., L.F.A. Wessels, M.J.T. Reinders and I. Shmu levich. 2009. Fewer permutations, more accurate P-values. Bioinformatics 25:i161–i168.CrossRefGoogle Scholar
  16. Koricheva, J., J. Gurevitch and K. Mengersen (eds.) 2013. Handbook of Meta-analysis in Ecology and Evolution. Princeton University Press, Princeton.CrossRefGoogle Scholar
  17. Kraft, N.J.B., L.S. Comita, J.M. Chase, N.J. Sanders, N.G. Swenson, T.O. Crist, J.C. Stegen, M. Vellend, B. Boyle, M.J. Anderson, H.V. Cornell, K.F. Davies, A.L. Freestone, B.D. Inouye, S.P. Harrison and J.A. Myers. 2011. Disentangling the drivers of β diversity along latitudinal and elevational gradients. Science 333:1755–1758.CrossRefGoogle Scholar
  18. Leinster, T. and C.A. Cobbold. 2011. Measuring diversity: the importance of species similarity. Ecology 93:477–489.CrossRefGoogle Scholar
  19. Lhotsky, B., B. Kovács, G. Ónodi, A. Csecserits, T. Rédei, A. Lengyel, M. Kertész and Z. Botta-Dukát. 2016. Changes in assembly rules along a stress gradient from open dry grasslands to wetlands. J. Ecol. 104:507–517.CrossRefGoogle Scholar
  20. MacArthur, R. and R. Levins. 1967. The limiting similarity, convergence, and divergence of coexisting species. Amer.Nat. 101:377–385.CrossRefGoogle Scholar
  21. Manly, B.F.J. 1997. Randomization, Bootstrap and Monte Carlo Methods in Biology. Second Edition. Chapman & Hall, London.Google Scholar
  22. Mason, N.W.H., S.J. Richardson, D.A. Peltzer, F. de Bello, D.A. Wardle and R.B. Allen. 2012. Changes in coexistence mechanisms along a long-term soil chronosequence revealed by functional trait diversity. J. Ecol. 100:678–689.CrossRefGoogle Scholar
  23. Nakagawa, S. and I.C. Cuthill. 2007. Effect size, confidence interval and statistical significance: a practical guide for biologists. Biol. Rev. 82:591–605.CrossRefGoogle Scholar
  24. Pásztor, E., Z. Botta-Dukát, T. Czárán, G. Magyar and G. Meszéna. 2016. Theory Based Ecology. The Darwinian Approach. Oxford Uninersity Press, Oxford, UK.CrossRefGoogle Scholar
  25. R Core Team. 2013. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL:
  26. Rothstein, H., M. Borenstein, L.V. Hedges and J.P.T. Higgins. 2013. Introduction to Meta-analysis. Wiley, Hoboken, N.J.Google Scholar
  27. Sanders, N.J., N.J. Gotelli, N.E. Heller and D.M. Gordon. 2003. Community disassembly by an invasive species. PNAS 100:2474–2477.CrossRefGoogle Scholar
  28. Schamp, B.S. and L. W. Aarssen. 2009. The assembly of forest communities according to maximum species height along resource and disturbance gradients. Oikos 118:564–572.CrossRefGoogle Scholar
  29. Signorell, A. 2015. DescTools: Tools for descriptive statistics.Google Scholar
  30. Stoll, S., P. Breyer, J.D. Tonkin, D. Früh and P. Haase. 2016. Scale-dependent effects of river habitat quality on benthic invertebrate communities — Implications for stream restoration practice. Sci. Total Env. 553:495–503.CrossRefGoogle Scholar
  31. Stubbs, W.J. and J.B. Wilson. 2004. Evidence for limiting similarity in a sand dune community. J. Ecol. 92:557–567.CrossRefGoogle Scholar
  32. Ulrich, W. and N.J. Gotelli. 2007. Null model analysis of species nestedness patterns. Ecology 88:1824–1831.CrossRefGoogle Scholar
  33. Ulrich, W. and N.J. Gotelli. 2010. Null model analysis of species associations using abundance data. Ecology 91:3384–3397.CrossRefGoogle Scholar
  34. Veech, J. A. 2012. Significance testing in ecological null models. Theor. Ecol. 5:611–616.CrossRefGoogle Scholar
  35. Webb, C.O., D.D. Ackerly, M.A. McPeek and M.J. Donoghue. 2002. Phylogenies and community ecology. Annu. Rev. Ecol. Syst. 33:475–505.CrossRefGoogle Scholar

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© Akadémiai Kiadó, Budapest 2018

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited, you give a link to the Creative Commons License, and indicate if changes were made.

Authors and Affiliations

  1. 1.Centre for Ecological ResearchInstitute of Ecology and BotanyVácrátótHungary

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