Here are a few remarks on the article „Does climate influence the variation in traits of terrestrial orchids (Orchidaceae) symmetrically in various functional groups across European latitudes?“ (by I. Blinova and F.-M.-Chmieleski; J. Eur. Orc. 45 (2-4): 255 – 284. 2013)

The article itself is interesting (Intraspecific variation corresponds to a parabolic curve within species ranges with its maximum at the ecological optimum) but contains some severe errors and the statistical evaluation and the conclusions from these evaluations, respectively, are obscure.

The only equation on page 260 is wrong: The x-coordinate of the extreme value of a parabola is –b/(2a) whether or not it is a maximum or minimum (first derivative of y=ax**2+b*x+c must equal zero; ** means „to the square of“). (The authors claim that it is –b/(2a) for the maximum and b/(2a) for the minimum.) If it is a maximum or minimum is determined only by the sign of „a“ (the second derivative must be less or greater zero). See, e.g., http://de.wikipedia.org/wiki/Extrempunkt or remember the curve sketching at school.

Almost all references to the Tables are wrong (e.g. on page 261: „in Table 3“ would have to be „in Table 4“; „Table 4, 5 and 6“ on page 262 ought to be „Table 5,6 and 7“; „Tables 5 and 6“ on page 281 should be „Tables 5 and 7“; „Table 6“ in the legend of Figure 13 would have to be „Table 7“ and so on).

„R**2“ is called „Correlation“ (see legend of Table 5) but it is nowhere explained if R**2 is the coefficient of determination concerning „linear regression“ [in this case, the value of R**2= 0.99 (i.e. R=0.995) in Table 5 seems inappropriate high] or regarding „parabolic regression“ (in this last case the term „correlation“ would be wrong) or both (depending on the context).

The most serious problem is that the multiplicity is not taken into account (especially in Table 5 and Table 7). In Table 5 there are 280 simultaneous significance tests (8 meteorological parameters, 7 species, 5 traits), and even if there is no signal at all (i.e., the H0 is true and R**2=0, resp.), the probability to get one or more significant results is 1-(1-p)**280 = 99.9994% (assumed that the ‘tests’ are almost statistically independent; (1-p) is the selected significance level and p the p-value; p = 0.05 in the article. The probability that more than k tests are significant (without any signal) can be derived easily with the Binomial distribution). Performing such multiple tests, one should use adapted tests, or the p-value had to be reduced drastically (see „Holm’s Sequentially-Rejective Bonferroni Method“ or the „Simple Bonferroni Method“, e.g., in Shaffer, J. P. (1995): Multiple Hypothesis Testing. Annu. Rev. Psychol. Vol. 46, 561-584).

Because the specific p-values are not shown in Table 5 and 7, it is impossible to recalculate „adjusted significance levels“ and all significant (bold) R**2-values could be archieved by poor accident.

Hence all conclusions from these uncertain results are very doubtful.

Article Does climate influence the variation in traits of terrestria...