2013 is right around the corner, and here are 13 well-known criticisms of statistical significance tests, and how they are addressed within the error statistical philosophy, as discussed in Mayo, D. G. and Spanos, A. (2011) “Error Statistics“.
- (#1) error statistical tools forbid using any background knowledge.
- (#2) All statistically signiﬁcant results are treated the same.
- (#3) The p-value does not tell us how large a discrepancy is found.
- (#4) With large enough sample size even a trivially small discrepancy from the null can be detected.
- (#5) Whether there is a statistically signiﬁcant diﬀerence from the null depends on which is the null and which is the alternative.
- (#6) Statistically insigniﬁcant results are taken as evidence that the null hypothesis is true.
- (#7) Error probabilities are misinterpreted as posterior probabilities.
- (#8) Error statistical tests are justiﬁed only in cases where there is a very long (if not inﬁnite) series of repetitions of the same experiment.
- (#9) Specifying statistical tests is too arbitrary.
- (#10) We should be doing conﬁdence interval estimation rather than signiﬁcance tests.
- (#11) Error statistical methods take into account the intentions of the scientists analyzing the data.
- (#12) All models are false anyway.
- (#13) Testing assumptions involves illicit data-mining.
You can read how we avoid them in the full paper here.
Mayo, D. G. and Spanos, A. (2011) “Error Statistics” in Philosophy of Statistics , Handbook of Philosophy of Science Volume 7 Philosophy of Statistics, (General editors: Dov M. Gabbay, Paul Thagard and John Woods; Volume eds. Prasanta S. Bandyopadhyay and Malcolm R. Forster.) Elsevier: 1-46.