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Sunday, 24 September 2017
Alert: Method specificity of box-and-whiskers plots

Non-parametric methods are of special value for small samples when the type of data distribution (normal, log-normal?) cannot be assessed with due certainty. Box-and-whiskers-plots (box-plots) are particularly useful in this regard since they provide an easily understandable descriptive data summary (central measure: median; measure of spread: box built by the 25% [Q25] and 75% [Q75] percentiles).

However, as pointed out by Dr. L. Turchanowa (ACPS) at the EACPT-meeting in Edinburg, box plots show relevant method-specificity, which demands due caution when using these formats.

An important part of this relates to the definition of the whiskers - Various approaches have been advocated:

  • ranging from minimum to maximum observed value

  • ranging from the lower to the upper outlier limits (Q25 - 1.5*IQR to Q75 + 1.5*IQR; in which IQR is the inter-quartile range = Q75-Q25)
  • ranging from the 10th (Q10) to the 90th (Q90) percentile

Similar issues affect the boxes. Indeed, with small datasets, Q10, Q25, Q50 (= median), Q75 and Q90 usually need to be approximated by interpolation. To this purpose, standard statistical and graphical packages (for instance MSO Excel, SAS, Sigmaplot, SPSS, PASW, Minitab, etc.) provide procedures that make it easier to make such interpolations. However, the results differ since they are procedure-specific.

Accordingly, there is reason for caution when using such measures without specifying the procedures used; furthermore, percentiles reported and tables and plotted in graphs may be discordant if different procedures (depending on the software used) were used within each of these applications.

 

Last Updated (Friday, 5 March 2010)

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