Literature on one-sided tests
Here you can see a list of scientific papers, books and other literature arguing for and against the usage of one-sided tests of significance, one-sided confidence intervals, and other statistical tests. Most of these works are cited in articles published on OneSided.org.
For one-sided statistical tests
A non-exhaustive list of scientific publications which argue for using one-sided tests explicitly or implicitly. These are listed in chronological order. We offer an overview with short commentary on these in "Fisher, Neyman & Pearson - advocates for one-sided tests and confidence intervals" and "Proponents of one-sided statistical tests".
- Fisher R.A. (1925) "Statistical methods for research workers". Oliver & Boyd, Edinburg
- Fisher R.A. (1935) "The design of experiments", Oliver & Boyd, Edinburgh
- Neyman J., Pearson E.S. (1933) "On the Problem of the Most Efficient Tests of Statistical Hypotheses", Philosophical Transactions of the Royal Society of London Series A 231:289-337; https://doi.org/10.1098/rsta.1933.0009
- Neyman J., Pearson E.S. (1933) "On the problem of the most efficient tests of statistical hypotheses", Philosophical Transactions of the Royal Society of London Series A 231:289-337; https://doi.org/10.1098/rsta.1933.0009
- Neyman J. (1937) "Outline of a theory of statistical estimation based on the classical theory of probability", Philosophical Transactions of the Royal Society of London, Series A 236:333-380; https://doi.org/10.1098/rsta.1937.0005
- Kaiser H.F. (1960) "Directional statistical decisions", Psychological Review 67:160-170
- Boissel J.P. (1988) "Some thoughts on two-tailed tests (and two-sided designs)", Controlled Clinical Trials 9(4):385-386
- Peace K.E. (1988) "Some thoughts on one-tailed tests", Biometrics 44(3):911-912
- Peace K.E. (1989) "The alternative hypothesis: one-sided or two-sided", Journal of Clinical Epidemiology 42(5):473-476
- Overall J.E. (1990) "Tests of one-sided versus two-sided hypotheses in placebo-controlled clinical trials", Neuropsychopharmacology 3(4):233-235.
- Peace K.E. (1991) "One-sided or two-sided ρ values: which most appropriately address the question of drug efficacy", Journal of Biopharmaceutical Statistics 1(1):133-138
- Wolterbeek R. (1994) "One and two sided tests of significance", British Medical Journal (Clinical Research Edition) 309(6958):873-874
- Enkin M.W. (1994) "One sided tests should be used more often", British Medical Journal (Clinical Research Edition) 309(6958):873-874
- Mayo D.G., Spanos A. (2006) "Severe testing as a basic concept in a Neyman–Pearson philosophy of induction", The British Journal for the Philosophy of Science, Volume 57(2):323–357; https://doi.org/10.1093/bjps/axl003
- Freedman L.S. (2008) "An analysis of the controversy over classical one-sided tests", Clinical Trials (London, England) 5(6):635-640; https://doi.org/10.1177/1740774508098590
- Mayo D.G., Spanos A. (2010) "Error statistics", in P. S. Bandyopadhyay & M. R. Forster (Eds.), Philosophy of Statistics, (7, 152–198). Handbook of the Philosophy of Science. The Netherlands: Elsevier; ISBN: 9780444518620
- Cho H.C., Abe S. (2013) "Is two-tailed testing for directional research hypotheses tests legitimate?", Journal of Business Research 66:1261-1266; https://doi.org/10.1016/j.jbusres.2012.02.023
- Greenland S. et al. (2016) "Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations", European Journal of Epidemiology 31:337–350; https://doi.org/10.1007/s10654-016-0149-3
- Murphy R. (2018) "On the use of one‐sided statistical tests in biomedical research", Clinical and experimental pharmacology & physiology 45(1):109-114; https://doi.org/10.1111/1440-1681.12754
- Rubin M. (2020) "That's not a two-sided test! It's two one-sided tests!" Significance 17:38-41; https://doi.org/10.1111/1740-9713.01405
To the above I'd add Daniel Lakens's (Lakens D., 2016) "One-sided tests: Efficient and Underused" [online] and my own (Georgiev G.Z. 2017) "One-tailed vs two-tailed tests of significance in A/B testing" [online]. There are also the EPA's "Data quality assessment: statistical methods for practitioners" which advocate for using one-sided tests where appropriate.
Against one-sided statistical tests
A non-exhaustive list of scientific publications which argue against using one-sided tests or for significant restrictions and precautions in their use. Brief commentary on their content is available in "Examples of negative portrayals of one-sided significance tests".
- Hick W.E. (1952) "A note on one-tailed and two-tailed tests", Psychological Review 59(4):316-318; http://dx.doi.org/10.1037/h0056061
- Burke C. J. (1953) "A brief note on one-tailed tests" Psychological Bulletin, 50(5):384-387; http://dx.doi.org/10.1037/h0059627
- Kimmel H.D. (1957) "Three criteria for the use of one-tailed tests", Psychological Bulletin, 54(4):351-353; http://dx.doi.org/10.1037/h0046737
- Fisher L.D. (1991) "The use of one-sided tests in drug trials: an FDA advisory committee member's perspective.", Journal of Biopharmaceutical Statistics 1(1):151-156; https://doi.org/10.1080/10543409108835012
- Bland J.M., Altman D.G. (1994) "Statistics Notes: One and two sided tests of significance", British Medical Journal (Clinical Trials Edition) 309-6949:248; https://doi.org/10.1136/bmj.309.6949.248
- Goodman S. (1988) "One-sided or two-sided p values?", Controlled Clinical Trials 9(4):387-388
- Moyé M.D.; Tita A.T (2002) "Defending the Rationale for the Two-Tailed Test in Clinical Research", Circulation 105(25):3062-5; http://dx.doi.org/10.1161/01.CIR.0000018283.15527.97
- Lombardi C.M., Hurlbert S.H. (2009) "Misrepresentation and misuse of one-tailed tests", Austral Ecology 34(4):447-468; https://doi.org/10.1111/j.1442-9993.2009.01946.x
- Ruxton G.D., Neuhäuser M. (2010) "When should we use one‐tailed hypothesis testing?", Methods in Ecology and Evolution 1(2):114-117; http://dx.doi.org/10.1111/j.2041-210X.2010.00014.x
Regulatory guidelines in which one-sided tests are treated differently than two-sided tests (more restrictions, need to "justify", etc.). If you have more such examples from another agency, contact us and let us know.
- US Food and Drug Administration (FDA): "Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests", drafted in 2003, issued on March 13, 2007.
- European Medicines Agency (EMA): "Statistical Principles for Clinical Trials", drafted 1997, issued Mar 1998.
Books with misinformation about one-sided tests (feel free to send more examples as we have limited ability to purchase and go through books).
- Baguley T. (2012) "Serious Stats: A guide to advanced statistics for the behavioral sciences" published by Macmillan International Higher Education
- Gabay M. (2015) "The clinical practice of drug information" published by Jones & Bartlett Learning.
Negative portrayal, misconseptions and confusion are also spread through online resources like Wikipedia, Investopedia, university online courses, statistical software vendor sites, sites/blogs of various statistical consultants, etc., some of which I review in "Examples of negative portrayal of one-sided significance tests" as well.