BAYESIAN TESTS FOR GOODNESS OF FIT By R.R.P. van Nooijen(1) and A.G. Kolechkina(1,2) (1)Department of Water Management, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN, Delft, The Netherlands (firstname.lastname@example.org; email@example.com ) (2) Aronwis, Den Hoorn, The Netherlands
? They can at least prevent the two main erroneous interpretations of NHST which consists, on the one hand in confusing statistical significance with substantive significance (one of the most often denounced error: e.g. Selvin, 1957; Kish, 1959; Bolles, 1962; Bakan, 1966; etc.), and on the other hand in interpreting a non significant result as proof of the null hypothesis (an error which can be found in many experimental publications, even in prestigious journals, as noted by Harcum, 1990). ?
[mine] A statistically significance result means exactly and simply that it?s not conformable with the Null Hypothesis: the p-value is sufficiently short (at the set significance level alpha) to lead to reject H0, and is exclusively a mathematical matter. Surprisingly one scarcely do find results dealing with the probability that at least a given difference was found. Explicitly: if we observe theta´ and we wish to know if the probability that theta´- theta be at least equal to a positive d we should find the p-value concerning theta´- (theta + d), as simple as this . . . On contrary a substantive difference means that the difference is economically worthy (or by other reasons). For example, a new pill that enlarges, say, 5 minutes the sleeping time is not sufficient to lead industry to produce it, in view the modifications they compel and money to expense. The safety (counter - indications) could be a sufficient reason not to start the procedure. They are reasons to take into account but that are completely apart Statistical Decisions. One shouldn?t ask Statistics to answer questions to which it wasn?t invented to do.