Null hypothesis (English Wikipedia)

Neyman, J; Pearson, E. S. (1 January 1933). "On the Problem of the most Efficient Tests of Statistical Hypotheses". Philosophical Transactions of the Royal Society A. 231 (694–706): 289–337. Bibcode:1933RSPTA.231..289N. doi:10.1098/rsta.1933.0009.
Zhao, Guolong (18 April 2015). "A Test of Non Null Hypothesis for Linear Trends in Proportions". Communications in Statistics – Theory and Methods. 44 (8): 1621–1639. doi:10.1080/03610926.2013.776687. ISSN 0361-0926. S2CID 120030713.
Cox, DR (1982). "Statistical Significance Tests". Br. J. Clin. Pharmacol. 14 (3): 325–331. doi:10.1111/j.1365-2125.1982.tb01987.x. PMC 1427620. PMID 6751362.
Jones, B; P Jarvis; J A Lewis; A F Ebbutt (6 July 1996). "Trials to assess equivalence: the importance of rigorous methods". BMJ. 313 (7048): 36–39. doi:10.1136/bmj.313.7048.36. PMC 2351444. PMID 8664772. It is suggested that the default position (the null hypothesis) should be that the treatments are not equivalent. Conclusions should be made on the basis of confidence intervals rather than significance.
Lombardi, Celia M.; Hurlbert, Stuart H. (2009). "Misprescription and misuse of one-tailed tests". Austral Ecology. 34 (4): 447–468. Bibcode:2009AusEc..34..447L. doi:10.1111/j.1442-9993.2009.01946.x. Discusses the merits and historical usage of one-tailed tests in biology at length.
Bland, J Martin; Altman, Douglas G (23 July 1994). "One and two sided tests of significance". BMJ. 309 (6949): 248. doi:10.1136/bmj.309.6949.248. PMC 2540725. PMID 8069143. With respect to medical statistics: "In general a one sided test is appropriate when a large difference in one direction would lead to the same action as no difference at all. Expectation of a difference in a particular direction is not adequate justification." "Two sided tests should be used unless there is a very good reason for doing otherwise. If one sided tests are to be used the direction of the test must be specified in advance. One sided tests should never be used simply as a device to make a conventionally non-significant difference significant."
Jones, Lyle V.; Tukey, John W. (2000). "A Sensible Formulation of the Significance Test". Psychological Methods. 5 (4): 411–414. doi:10.1037/1082-989X.5.4.411. PMID 11194204. S2CID 14553341. Test results are signed: significant positive effect, significant negative effect or insignificant effect of unknown sign. This is a more nuanced conclusion than that of the two-tailed test. It has the advantages of one-tailed tests without the disadvantages.
Hurlbert, S. H.; Lombardi, C. M. (2009). "Final collapse of the Neyman-Pearson decision theoretic framework and rise of the neoFisherian". Ann. Zool. Fennici. 46 (5): 311–349. doi:10.5735/086.046.0501. ISSN 1797-2450. S2CID 9688067.
Lehmann, E. L. (December 1993). "The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?". Journal of the American Statistical Association. 88 (424): 1242–1249. Bibcode:1993JASA...88.1242L. doi:10.1080/01621459.1993.10476404.

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Neyman, J; Pearson, E. S. (1 January 1933). "On the Problem of the most Efficient Tests of Statistical Hypotheses". Philosophical Transactions of the Royal Society A. 231 (694–706): 289–337. Bibcode:1933RSPTA.231..289N. doi:10.1098/rsta.1933.0009.
Lombardi, Celia M.; Hurlbert, Stuart H. (2009). "Misprescription and misuse of one-tailed tests". Austral Ecology. 34 (4): 447–468. Bibcode:2009AusEc..34..447L. doi:10.1111/j.1442-9993.2009.01946.x. Discusses the merits and historical usage of one-tailed tests in biology at length.
Lehmann, E. L. (December 1993). "The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?". Journal of the American Statistical Association. 88 (424): 1242–1249. Bibcode:1993JASA...88.1242L. doi:10.1080/01621459.1993.10476404.

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Hayes, Adam. "Null Hypothesis Definition". Investopedia. Retrieved 10 December 2019.

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Aldrich, John. "Earliest Known Uses of Some of the Words of Probability & Statistics". Retrieved 30 June 2014. Last update 12 March 2003. From Jeff Miller.

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Cox, DR (1982). "Statistical Significance Tests". Br. J. Clin. Pharmacol. 14 (3): 325–331. doi:10.1111/j.1365-2125.1982.tb01987.x. PMC 1427620. PMID 6751362.
Jones, B; P Jarvis; J A Lewis; A F Ebbutt (6 July 1996). "Trials to assess equivalence: the importance of rigorous methods". BMJ. 313 (7048): 36–39. doi:10.1136/bmj.313.7048.36. PMC 2351444. PMID 8664772. It is suggested that the default position (the null hypothesis) should be that the treatments are not equivalent. Conclusions should be made on the basis of confidence intervals rather than significance.
Bland, J Martin; Altman, Douglas G (23 July 1994). "One and two sided tests of significance". BMJ. 309 (6949): 248. doi:10.1136/bmj.309.6949.248. PMC 2540725. PMID 8069143. With respect to medical statistics: "In general a one sided test is appropriate when a large difference in one direction would lead to the same action as no difference at all. Expectation of a difference in a particular direction is not adequate justification." "Two sided tests should be used unless there is a very good reason for doing otherwise. If one sided tests are to be used the direction of the test must be specified in advance. One sided tests should never be used simply as a device to make a conventionally non-significant difference significant."
Jones, Lyle V.; Tukey, John W. (2000). "A Sensible Formulation of the Significance Test". Psychological Methods. 5 (4): 411–414. doi:10.1037/1082-989X.5.4.411. PMID 11194204. S2CID 14553341. Test results are signed: significant positive effect, significant negative effect or insignificant effect of unknown sign. This is a more nuanced conclusion than that of the two-tailed test. It has the advantages of one-tailed tests without the disadvantages.

ncbi.nlm.nih.gov

Cox, DR (1982). "Statistical Significance Tests". Br. J. Clin. Pharmacol. 14 (3): 325–331. doi:10.1111/j.1365-2125.1982.tb01987.x. PMC 1427620. PMID 6751362.
Jones, B; P Jarvis; J A Lewis; A F Ebbutt (6 July 1996). "Trials to assess equivalence: the importance of rigorous methods". BMJ. 313 (7048): 36–39. doi:10.1136/bmj.313.7048.36. PMC 2351444. PMID 8664772. It is suggested that the default position (the null hypothesis) should be that the treatments are not equivalent. Conclusions should be made on the basis of confidence intervals rather than significance.
Bland, J Martin; Altman, Douglas G (23 July 1994). "One and two sided tests of significance". BMJ. 309 (6949): 248. doi:10.1136/bmj.309.6949.248. PMC 2540725. PMID 8069143. With respect to medical statistics: "In general a one sided test is appropriate when a large difference in one direction would lead to the same action as no difference at all. Expectation of a difference in a particular direction is not adequate justification." "Two sided tests should be used unless there is a very good reason for doing otherwise. If one sided tests are to be used the direction of the test must be specified in advance. One sided tests should never be used simply as a device to make a conventionally non-significant difference significant."

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"OECD Glossary of Statistical Terms – Non-null hypothesis Definition". stats.oecd.org. Retrieved 5 December 2020.

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Chiang, I. -Chant A.; Jhangiani, Rajiv S.; Price, Paul C. (13 October 2015). "Understanding Null Hypothesis Testing – Research Methods in Psychology". opentextbc.ca. Retrieved 10 December 2019.

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Zhao, Guolong (18 April 2015). "A Test of Non Null Hypothesis for Linear Trends in Proportions". Communications in Statistics – Theory and Methods. 44 (8): 1621–1639. doi:10.1080/03610926.2013.776687. ISSN 0361-0926. S2CID 120030713.
Jones, Lyle V.; Tukey, John W. (2000). "A Sensible Formulation of the Significance Test". Psychological Methods. 5 (4): 411–414. doi:10.1037/1082-989X.5.4.411. PMID 11194204. S2CID 14553341. Test results are signed: significant positive effect, significant negative effect or insignificant effect of unknown sign. This is a more nuanced conclusion than that of the two-tailed test. It has the advantages of one-tailed tests without the disadvantages.
Hurlbert, S. H.; Lombardi, C. M. (2009). "Final collapse of the Neyman-Pearson decision theoretic framework and rise of the neoFisherian". Ann. Zool. Fennici. 46 (5): 311–349. doi:10.5735/086.046.0501. ISSN 1797-2450. S2CID 9688067.

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Helmenstine, Anne Marie. "What Is the Null Hypothesis? Definition and Examples". ThoughtCo. Retrieved 10 December 2019.
Helmenstine, Anne Marie. "What Is the Null Hypothesis? Definition and Examples". ThoughtCo. Retrieved 10 April 2025.

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Zhao, Guolong (18 April 2015). "A Test of Non Null Hypothesis for Linear Trends in Proportions". Communications in Statistics – Theory and Methods. 44 (8): 1621–1639. doi:10.1080/03610926.2013.776687. ISSN 0361-0926. S2CID 120030713.
Hurlbert, S. H.; Lombardi, C. M. (2009). "Final collapse of the Neyman-Pearson decision theoretic framework and rise of the neoFisherian". Ann. Zool. Fennici. 46 (5): 311–349. doi:10.5735/086.046.0501. ISSN 1797-2450. S2CID 9688067.

Null hypothesis (English Wikipedia)

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