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Raised conditional level of significance for the 2 × 2‐table when testing the equality of two probabilities

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  • R. D. Boschloo

Abstract

In this paper it is to be shown that Fisher's non‐randomizing exact test for 2 × 2‐tables, which is a conditional test, can by simple means be changed into an unconditional test using raised levels of significance; not seldom, especially for not too large samples, the level of significance can be doubled. This leads in many cases to a considerable increase of power of the test. A table with raised levels has been prepared up to sample sizes of 50 and a rule of thumb, which can be used if this table is not available, has been developEd.

Suggested Citation

  • R. D. Boschloo, 1970. "Raised conditional level of significance for the 2 × 2‐table when testing the equality of two probabilities," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 24(1), pages 1-9, March.
    • Handle: RePEc:bla:stanee:v:24:y:1970:i:1:p:1-9
    DOI: 10.1111/j.1467-9574.1970.tb00104.x
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    Cited by:

    1. Mariana Blanco & Dirk Engelmann & Alexander Koch & Hans-Theo Normann, 2010. "Belief elicitation in experiments: is there a hedging problem?," Experimental Economics, Springer;Economic Science Association, vol. 13(4), pages 412-438, December.
    2. Shan, Guogen, 2013. "More efficient unconditional tests for exchangeable binary data with equal cluster sizes," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 644-649.
    3. Blanco, Mariana & Engelmann, Dirk & Koch, Alexander K. & Normann, Hans-Theo, 2014. "Preferences and beliefs in a sequential social dilemma: a within-subjects analysis," Games and Economic Behavior, Elsevier, vol. 87(C), pages 122-135.
    4. Skipka, G. & Munk, A. & Freitag, G., 2004. "Unconditional exact tests for the difference of binomial probabilities--contrasted and compared," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 757-773, November.
    5. Stefan Wellek, 2015. "Nearly exact sample size calculation for powerful non-randomized tests for differences between binomial proportions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 358-373, November.
    6. Munk, A. & Skipka, G. & Stratmann, B., 2005. "Testing general hypotheses under binomial sampling: the two sample case--asymptotic theory and exact procedures," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 723-739, June.
    7. Bartke, Simon & Friedl, Andreas & Gelhaar, Felix & Reh, Laura, 2017. "Social comparison nudges—Guessing the norm increases charitable giving," Economics Letters, Elsevier, vol. 152(C), pages 73-75.
    8. Nour Hawila & Arthur Berg, 2023. "Exact‐corrected confidence interval for risk difference in noninferiority binomial trials," Biometrics, The International Biometric Society, vol. 79(2), pages 1133-1144, June.
    9. Antonia Moreno Cano & Rafael Romón Sagredo & Rocío García-Carrión & Begonya Garcia-Zapirain, 2020. "Social Impact Assessment of HealthyAIR Tool for Real-Time Detection of Pollution Risk," Sustainability, MDPI, vol. 12(23), pages 1-21, November.
    10. Martin Andres, A. & Sanchez Quevedo, M. J. & Silva Mato, A., 1998. "Fisher's Mid-P-value arrangement in 2x2 Comparative trials," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 107-115, November.
    11. Fabian Bopp & Wendelin Schnedler, 2023. "Does room for reflection reduce ignorance and increase pro-social behavior? An experimental study," Working Papers Dissertations 109, Paderborn University, Faculty of Business Administration and Economics.
    12. Phipps, Mary C. & Byron, Peter M., 2007. "A filter for "confidence interval P-values"," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6435-6446, August.
    13. Martin Andres, A. & Mato, A. Silva & Garcia, J. M. Tapia & Quevedo, M. J. Sanchez, 2004. "Comparing the asymptotic power of exact tests in 2x2 tables," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 745-756, November.

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