In the article “Response of tree phenology to climate change across Europe” (F.-M- Chmielewski and T. Rötzer, 2001, Agricultural and Forest Meteorology 108, 101-112), the problem of multiplicity in statistics (see my old questions which I asked in January and February 2014) arises again. Their table 4 is a list of 78 correlation coefficients between different temperatures and the beginning of growing season (B). Each of them is assumed to be significant at p
I would strongly recommend to use Bayesian inference http://en.wikipedia.org/wiki/Bayesian_inference instead of Fisherian (frequentist) statistics. Reasons are best explained in the Jaynes' book http://www-biba.inrialpes.fr/Jaynes/prob.html
There is a huge literature on p-values and why to avoid them.
Good books are:
http://www.amazon.com/Introduction-Bayesian-Statistics-2nd-Edition/dp/0470141158/
http://www.amazon.com/Doing-Bayesian-Data-Analysis-Tutorial/dp/0123814855/
http://www.amazon.com/Bayesian-Analysis-Edition-Chapman-Statistical/dp/1439840954/
HTH, Peter.
P is not a measure of evidence. And P=0.2 even tells us that the data we have observed would not be very unexpected if H0 was true.
Essentially all your critiques seem to be correct (to my knowledge and understanding).
Irnoring multiplicity is one problem. It refers to INDEPENDENT tests, but the regressions are unlikely to be independent. If they are (or can be considered as) independent, then the authors should have controlled at least the false-discovery rate (if not the family-wise error rate). If they are not, a common model should have been used, accounting for spatial effects. This would have been anyway better, to my opinion.
Finally, I find scientific arguing based on p-values wrong (and quite stupid). The data should be taken as is and interpreted as is. What are the observed effects? How precise are these estimates? Does the model give any reasonable (e.g. geophysical) explanation? Does it point to new insights beyond the data?
For the trend data You might consider a sign test: Under the null both signs are equally probably to occur, and independent by the way. Say 10 / 12 negative correlations is quite far from a global null.
I think it is time to get totally rid of this way of thinking: It has created more puzzles and gray zones than the convenience that it initially brought in statistics as a scientific branch. I cannot see why should we get trapped in such a class of questions: OK, I give an answer, positive or negative. And then what?
Dear Klaus, you have to see the policies under the paper: Which policy does that paper 'promote'?
I invite you at this discussion:
https://www.researchgate.net/post/What_is_really_happening_with_the_time_evolution_of_atmospheric_temperature
which is close to the core of the subject.
Anyway, if you want my opinion: of course p=0.2 is not acceptable, but keep in mind that 'climate science' is a big business today...
Not me, but Peter Cejchan recommended "Jaynes". But I will have a look at it!
By the way: One of the two authors of the article in question, Mr. Chmielewski, canceled his RG- Membership in the meantime without any reply to any of my comments and questions.
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