Reply to Parkinson

Abstract

Parkinson [1997] cited four criticisms of my reacknowledge the assistance of Parkinson [1995] in bringing this to light. cent paper [Davies, 1996] which I shall here deal with The final criticism concerns statistics. That in in turn. Firstly, I must draw attention to an error within some cases Parkinson arrives at probabilities at differmy paper which although it does not affect the validity ent sides of the P A 0.05 or P A 0.02 thresholds using of the results, may allay one of the criticisms of Parkina t-test rather than a Mann-Whitney test is immaterial son. In Tables 2 and 3 of Davies [1996] a Mann-Whitsince the data are either not normally distributed or not ney U value is indicated where the corresponding statishomoscedastic or both and thus cannot be subjected to tic presented in the Tables is a Mann-Whitney W value. parametric inferential statistics. In any case the probaW is the sum of the ranks of the treatment (E in Tables bility of committing a Type II error is greater with the 2 and 3) values. The probabilities associated with this Mann-Whitney test than with the t-test [e.g., Zar, 1984] statistic remain correct and indicate the probability (usand Parkinson’s adoption of a probability threshold of ing a non-parametric (ranked) test) that the two samples 0.02 is without explanation. The assertion of Parkinson under comparison were drawn from a common populathat parametric statistics are preferable to nonparamettion of values. ric statistics solely on the basis of sample size (in this Parkinson’s first criticism is that the experiment case of n A 13 0 16) is flawed and without reference. is ‘surprisingly’ noisy, although against what the magThat control means are larger than treatment means nitude of the noise is being judged is not clear. Indeed, has no biological relevance when the test statistics indiin two cases within RE1, RE2 and RE3 standard deviacate that the data derived from both treatment and contions are greater than their corresponding means, but trol are likely to be (at PA 0.05 or less) from a common in both cases differences between treatment and control pool. The setting of error rates must be a personal means are not significant. Such variation in biological choice, but I am following convention at 0.05 [e.g., data might be expected and large variances do not Zar, 1984]. disallow statistical comparison. Variance was exThus I contend that it is still clear that, at least pressed as standard error in Davies [1996] in order to on plant height and stem dry weight of radish, the standardise the variance measure to sample size. results presented by Davies [1996] do ‘‘concisely demThe second criticism is that there is large variaonstrate an EMF-effect.’’ tion between experiments. This was acknowledged in Davies [1996], and although temperature was one facREFERENCES tor that differed between the experiments, the origin of Davies MS (1996): Effects of 60 Hz electromagnetic fields on early the variation remains unascribed. It would be naive growth in three plant species and a replication of previous results. to think that all different parameters measured should Bioelectromagnetics 17:154–161. Parkinson WC (1997): Comment on ‘‘Effects of 60 Hz electromagnetic respond in the same way, i.e. all show an increase or fields on early growth in three plant species and a replication decrease, when an experiment is repeated at a different of previous results’’ by Mark S. Davies. Bioelectromagnetics time of year. Similarly it would be naive to equate 18:400. seasonality with temperature. Zar JH (1984): ‘‘Biostatistical Analysis.’’ Englewood Cliffs, New JerThe third criticism I have dealt with above and sey: Prentice-Hall.