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Accounting Research as Bayesian Inference to the Best Explanation

  • Sanjay Kallapur ORCID logo EMAIL logo
Published/Copyright: October 20, 2023

Abstract

The problems with p-values have been extensively discussed recently, but there is little work about the broader aspects of scientific inference of which p-values are but one part. This article explains how scientific inference can be characterized as Bayesian inference to the best explanation, which involves developing and assessing theories based on their fit with background facts and their ability to explain the observed data better than competing theories can. These factors translate into prior odds and Bayes factor respectively, which determine posterior odds under Bayesian inference. I provide examples from accounting research to illustrate how attention to these points makes for better research designs and stronger justification for inferences.

JEL Classification: B41; M40

Corresponding author: Sanjay Kallapur, Indian School of Business, Gachibowli, Hyderabad 500111, India, E-mail:

This article is based on my monograph “Beyond p < 0.05: Scientific Inference in Accounting Research,” published by the American Accounting Association. A pre-print is available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4413565


References

Andersen, Hanne, and Brian Hepburn. 2020. “Scientific Method.” In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Winter 2020. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2020/entries/scientific-method/.Search in Google Scholar

Ball, Ray, and Philip Brown. 1968. “An Empirical Evaluation of Accounting Income Numbers.” Journal of Accounting Research 6 (2): 159–78. https://doi.org/10.2307/2490232.Search in Google Scholar

Basu, Sudipta. 2012. “How Can Accounting Researchers Become More Innovative?” Accounting Horizons 26 (4): 851–70. https://doi.org/10.2308/acch-10311.Search in Google Scholar

Beaver, William H. 1968. “The Information Content of Annual Earnings Announcements.” Journal of Accounting Research 6: 67–92. https://doi.org/10.2307/2490070.Search in Google Scholar

Berk, Jonathan B., Campbell R. Harvey, and David Hirshleifer. 2017. “How to Write an Effective Referee Report and Improve the Scientific Review Process.” The Journal of Economic Perspectives 31 (1): 231–44. https://doi.org/10.1257/jep.31.1.231.Search in Google Scholar

Bernard, Victor L., and Thomas L. Stober. 1989. “The Nature and Amount of Information in Cash Flows and Accruals.” The Accounting Review 64 (4): 624–52.Search in Google Scholar

Biondi, Yuri. 2025. “Limits of Empirical Studies in Accounting and Social Sciences: A Constructive Critique from Accounting, Economics and the Law.” Accounting, Economics, and Law: A Convivium 15 (1): 9–19. https://doi.org/10.1515/ael-2017-0026.Search in Google Scholar

Biondi, Yuri, and Imke J. Graeff. 2024. “Between Prudential Regulation and Shareholder Value: An Empirical Perspective on Bank Shareholder Equity (2001–2017).” Accounting, Economics, and Law: Convivium 14: 395–429. https://doi.org/10.1515/ael-2019-0083.Search in Google Scholar

Bloomfield, Robert J. 2002. “The ‘Incomplete Revelation Hypothesis’ and Financial Reporting.” Accounting Horizons 16 (3): 233–43. https://doi.org/10.2308/acch.2002.16.3.233.Search in Google Scholar

Bloomfield, Robert J. 2018. “Editor’s Comment.” Journal of Financial Reporting 3 (1): 45. https://doi.org/10.2308/jfir-10636.Search in Google Scholar

Bloomfield, Robert J., Mark W. Nelson, and Eugene Soltes. 2016. “Gathering Data for Archival, Field, Survey, and Experimental Accounting Research.” Journal of Accounting Research 54 (2): 341–95. https://doi.org/10.1111/1475-679x.12104.Search in Google Scholar

Breuer, Matthias. 2025. “Another Way Forward: Comments on Ohlson’s Critique of Empirical Accounting Research.” Accounting, Economics, and Law: Convivium 15: 123–39. https://doi.org/10.1515/ael-2022-0093.Search in Google Scholar

Breuer, Matthias, and Harm H. Schütt. 2023. “Accounting for Uncertainty: An Application of Bayesian Methods to Accruals Models.” Review of Accounting Studies 28 (2): 726–68. https://doi.org/10.1007/s11142-021-09654-0.Search in Google Scholar

Burgstahler, David, and Elizabeth Chuk. 2015. “Do Scaling and Selection Explain Earnings Discontinuities?” Journal of Accounting and Economics 60 (1): 168–86. https://doi.org/10.1016/j.jacceco.2014.08.002.Search in Google Scholar

Burgstahler, David, and Ilia D. Dichev. 1997. “Earnings Management to Avoid Earnings Decreases and Losses.” Journal of Accounting and Economics 24 (1): 99–126. https://doi.org/10.1016/s0165-4101(97)00017-7.Search in Google Scholar

Card, David. 1992. “Do Minimum Wages Reduce Employment? A Case Study of California, 1987-89.” Industrial and Labor Relations Review 46 (1): 38–54. https://doi.org/10.2307/2524737.Search in Google Scholar

Card, David. 2022. “Design-Based Research in Empirical Microeconomics.” The American Economic Review 112 (6): 1773–81. https://doi.org/10.1257/aer.112.6.1773.Search in Google Scholar

Card, David, and Stefano DellaVigna. 2013. “Nine Facts about Top Journals in Economics.” Journal of Economic Literature 51 (1): 144–61. https://doi.org/10.1257/jel.51.1.144.Search in Google Scholar

Card, David, and Alan B. Krueger. 1994. “Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania.” The American Economic Review 84 (4): 772–93.10.3386/w4509Search in Google Scholar

Carver, Ronald P. 1978. “The Case against Statistical Significance Testing.” Harvard Educational Review 48 (3): 378–99. https://doi.org/10.17763/haer.48.3.t490261645281841.Search in Google Scholar

Chintha, Bullipe, and Sanjay Kallapur. 2023. “Hierarchical Bayesian Models in Accounting Research.” Online Supplement to Kallapur, 2022, Beyond P<0.05: Scientific Inference in Accounting Research. https://doi.org/10.2139/ssrn.4444627.Search in Google Scholar

Christensen, Hans B. 2020. “Broad- versus Narrow-Sample Evidence in Disclosure Regulation Studies: A Discussion of “The Informational Effects of Tightening Oil and Gas Disclosure Rules.” Contemporary Accounting Research 37 (3): 1750–5. https://doi.org/10.1111/1911-3846.12572.Search in Google Scholar

DeAngelo, Linda E. 1981. “Auditor Independence, ‘Lowballing,’ and Disclosure Regulation.” Journal of Accounting and Economics 3: 113–27. https://doi.org/10.1016/0165-4101(81)90009-4.Search in Google Scholar

Dechow, Patricia M., Scott A. Richardson, and Tuna. Irem. 2003. “Why Are Earnings Kinky? an Examination of the Earnings Management Explanation.” Review of Accounting Studies 8 (2): 355–84. https://doi.org/10.1023/A:1024481916719.10.1023/A:1024481916719Search in Google Scholar

Deming, David. 2016. “Do Extraordinary Claims Require Extraordinary Evidence?” Philosophia 44 (4): 1319–31. https://doi.org/10.1007/s11406-016-9779-7.Search in Google Scholar

Durtschi, Cindy, and Peter Easton. 2005. “Earnings Management? the Shapes of the Frequency Distributions of Earnings Metrics Are Not Evidence Ipso Facto.” Journal of Accounting Research 43 (4): 557–92. https://doi.org/10.1111/j.1475-679X.2005.00182.x.Search in Google Scholar

Durtschi, Cindy, and Peter Easton. 2009. “Earnings Management? Erroneous Inferences Based on Earnings Frequency Distributions.” Journal of Accounting Research 47 (5): 1249–81. https://doi.org/10.1111/j.1475-679X.2009.00347.x.Search in Google Scholar

Erickson, Merle, Brian W. Mayhew, and William L. FelixJr. 2000. “Why Do Audits Fail? Evidence from Lincoln Savings and Loan.” Journal of Accounting Research 38 (1): 165–94. https://doi.org/10.2307/2672927.Search in Google Scholar

Fraassen, Bas C. van. 1989. Laws and Symmetry, 1st ed. Oxford: Oxford University Press.10.1093/0198248601.003.0001Search in Google Scholar

Frantz, Roger. 2003. “Herbert Simon. Artificial Intelligence as a Framework for Understanding Intuition.” Journal of Economic Psychology, The Economic Psychology of Herbert A. Simon 24 (2): 265–77. https://doi.org/10.1016/S0167-4870(02)00207-6.Search in Google Scholar

Gelman, Andrew. 2018. “The Failure of Null Hypothesis Significance Testing when Studying Incremental Changes, and what to Do about it.” Personality and Social Psychology Bulletin 44 (1): 16–23. https://doi.org/10.1177/0146167217729162.Search in Google Scholar

Gilliam, Thomas A., Heflin Frank, and Jeffrey S. Paterson. 2015. “Evidence that the Zero-Earnings Discontinuity Has Disappeared.” Journal of Accounting and Economics 60 (1): 117–32. https://doi.org/10.1016/j.jacceco.2014.07.001.Search in Google Scholar

Guo, Re-Jin, Baruch Lev, and Nan Zhou. 2004. “Competitive Costs of Disclosure by Biotech IPOs.” Journal of Accounting Research 42 (2): 319–55. https://doi.org/10.1111/j.1475-679X.2004.00140.x.Search in Google Scholar

Hand, John R. M. 1990. “A Test of the Extended Functional Fixation Hypothesis.” The Accounting Review 65 (4): 740–63.Search in Google Scholar

Harman, Gilbert H. 1965. “The Inference to the Best Explanation.” Philosophical Review 74 (1): 88–95. https://doi.org/10.2307/2183532.Search in Google Scholar

Harvey, Campbell R., and David A. Hirshleifer. 2020. “Up or Out: Resetting Norms for Peer Reviewed Publishing in the Social Sciences.” SSRN, December. https://doi.org/10.2139/ssrn.3744513.Search in Google Scholar

Healy, P. M. 1985. “The Effects of Bonus Schemes on Accounting Decisions.” Journal of Accounting and Economics 7 (1–3): 85–107. https://doi.org/10.1016/0165-4101(85)90029-1.Search in Google Scholar

Henderson, Leah. 2014. “Bayesianism and Inference to the Best Explanation.” The British Journal for the Philosophy of Science 65 (4): 687–715. https://doi.org/10.1093/bjps/axt020.Search in Google Scholar

Hubbard, Douglas W. 2014. How to Measure Anything: Finding the Value of Intangibles in Business, 3rd ed. Hoboken: Wiley.Search in Google Scholar

Hume, David. (1739) 2000. A Treatise of Human Nature. Oxford: Oxford University Press.10.1093/oseo/instance.00046221Search in Google Scholar

Johnstone, David. 2018. “Accounting Theory as a Bayesian Discipline.” Foundations and Trends® in Accounting 13 (1–2): 1–266. https://doi.org/10.1561/1400000056.Search in Google Scholar

Johnstone, David. 2021. “Accounting Research and the Significance Test Crisis.” Critical Perspectives on Accounting, March, 102296, https://doi.org/10.1016/j.cpa.2021.102296.Search in Google Scholar

Kallapur, Sanjay. 2022. Beyond P<0.05: Scientific Inference in Accounting Research. Studies in Accounting Research, Vol. 34. Sarasota: American Accounting Association.10.2139/ssrn.4413565Search in Google Scholar

Kaplan, Robert S. 2011. “Accounting Scholarship that Advances Professional Knowledge and Practice.” The Accounting Review 86 (2): 367–83. https://doi.org/10.2308/accr.00000031.Search in Google Scholar

Kaplan, Robert S., and Richard Roll. 1972. “Investor Evaluation of Accounting Information: Some Empirical Evidence.” Journal of Business 45 (2): 225–57. https://doi.org/10.1086/295446.Search in Google Scholar

Kerr, Norbert L. 1998. “HARKing: Hypothesizing after the Results Are Known.” Personality and Social Psychology Review 2 (3): 196–217. https://doi.org/10.1207/s15327957pspr0203_4.Search in Google Scholar

Klahr, David, and Herbert A. Simon. 1999. “Studies of Scientific Discovery: Complementary Approaches and Convergent Findings.” Psychological Bulletin 125 (5): 524–43. https://doi.org/10.1037/0033-2909.125.5.524.Search in Google Scholar

Kuhn, Thomas S. (1962) 1970. The Structure of Scientific Revolutions. University of Chicago Press.Search in Google Scholar

Leuz, Christian. 2022. “Towards a Design-Based Approach to Accounting Research.” Journal of Accounting and Economics 74 (2): 101550. https://doi.org/10.1016/j.jacceco.2022.101550.Search in Google Scholar

Lipton, Peter. 2004. Inference to the Best Explanation. New York: Routledge.10.4324/9780203470855Search in Google Scholar

Lo, Yafen, Ashley Sides, Rozelle Joseph, and Daniel Osherson. 2002. “Evidential Diversity and Premise Probability in Young Children’s Inductive Judgment.” Cognitive Science 26 (2): 181–206. https://doi.org/10.1207/s15516709cog2602_2.Search in Google Scholar

Lys, Thomas, and Linda Vincent. 1995. “An Analysis of Value Destruction in AT&T’s Acquisition of NCR.” Journal of Financial Economics 39 (2–3): 353–78. https://doi.org/10.1016/0304-405x(95)00831-x.Search in Google Scholar

Merton, R. K. 1957. “Priorities in Scientific Discovery: A Chapter in the Sociology of Science.” American Sociological Review 22 (6): 635–59. https://doi.org/10.2307/2089193.Search in Google Scholar

Ohlson, James A. 2021. “Researchers’ Data Analysis Choices: An Excess of False Positives?” Review of Accounting Studies. https://doi.org/10.1007/s11142-021-09620-w.Search in Google Scholar

Ohlson, James A. 2025. “Empirical Accounting Seminars: Elephants in the Room.” Accounting, Economics, and Law: Convivium 15: 1–8. https://doi.org/10.1515/ael-2021-0067.Search in Google Scholar

Pinker, Steven. 2003. How the Mind Works. London: Penguin Books.Search in Google Scholar

Profet, Margie. 1992. “Pregnancy Sickness as Adaptation: A Deterrent to Maternal Ingestion of Toxins.” In The Adapted Mind: Evolutionary Psychology and the Generation of Culture, , edited by Jerome Barkow, Leda Cosmides and John Tooby, 327–65. Oxford: Oxford University Press.10.1093/oso/9780195060232.003.0009Search in Google Scholar

Psillos, Stathis. 2000. “Abduction: Between Conceptual Richness and Computational Complexity.” In Abduction and Induction, edited by Peter A. Flach and Antonis C. Kakas, 59–74. Dordrecht: Springer.10.1007/978-94-017-0606-3_4Search in Google Scholar

Rosenbaum, Paul R. 1988. “Sensitivity Analysis for Matching with Multiple Controls.” Biometrika 75 (3): 577–81. https://doi.org/10.1093/biomet/75.3.577.Search in Google Scholar

Rosenbaum, Paul R. 2005. “Heterogeneity and Causality.” The American Statistician 59 (2): 147–52. https://doi.org/10.1198/000313005x42831.Search in Google Scholar

Rosenbaum, Paul R., and Donald B. Rubin. 1983. “The Central Role of the Propensity Score in Observational Studies for Causal Effects.” Biometrika 70 (1): 41–55. https://doi.org/10.1093/biomet/70.1.41.Search in Google Scholar

Russell, Bertrand. (1945) 1967. A History of Western Philosophy. New York: Simon & Schuster/Touchstone.Search in Google Scholar

Sagan, Carl. 1979. Broca’s Brain: Reflections on the Romance of Science. New York: Random House.Search in Google Scholar

Schatzberg, Jeffrey W. 1990. “A Laboratory Market Investigation of Low Balling in Audit Pricing.” The Accounting Review 65 (2): 337–62.Search in Google Scholar

Schrand, Catherine M. 2016. “Journal of Financial Reporting Inaugural Issue: Defining Our Content.” Journal of Financial Reporting 1 (1): 1–13. https://doi.org/10.2308/jfir-51406.Search in Google Scholar

Schrand, Catherine M. 2019. “Impediments to Relevant Research: The Journal Review and Publication Process.” Accounting Horizons 33 (2): 11–6. https://doi.org/10.2308/acch-10662.Search in Google Scholar

Schütt, Harm H. 2023. “What Can Bayesian Inference Do for Accounting Research?” Journal of Financial Reporting. August, 1–18. https://doi.org/10.2308/JFR-2021-002.Search in Google Scholar

Shipman, Jonathan E., Quinn T. Swanquist, and Robert L. Whited. 2016. “Propensity Score Matching in Accounting Research.” The Accounting Review 92 (1): 213–44. https://doi.org/10.2308/accr-51449.Search in Google Scholar

Simon, Herbert A. 1968. “On Judging the Plausibility of Theories.” In Logic, Methodology and Philosophy of Sciences III, edited by B. Van Roostelaar and J. F. Staal, 439–59. Amsterdam: North-Holland. http://link.springer.com/chapter/10.1007/978-94-010-9521-1_4.10.1016/S0049-237X(08)71211-4Search in Google Scholar

Skinner, Douglas J., and Suraj Srinivasan. 2012. “Audit Quality and Auditor Reputation: Evidence from Japan.” The Accounting Review 87 (5): 1737–65. https://doi.org/10.2308/accr-50198.Search in Google Scholar

Smith, C. Scott, and Douglas S. Paauw. 2000. “When You Hear Hoof Beats: Four Principles for Separating Zebras from Horses.” The Journal of the American Board of Family Medicine 13 (6): 424–9. https://doi.org/10.3122/15572625-13-6-424.Search in Google Scholar

Smith, Robin. 2020. “Aristotle’s Logic.” In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Fall 2020. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/fall2020/entries/aristotle-logic/.Search in Google Scholar

Sunder, Shyam. 1973. “Relationship between Accounting Changes and Stock Prices: Problems of Measurement and Some Empirical Evidence.” Journal of Accounting Research 11: 1–45. https://doi.org/10.2307/2490025.Search in Google Scholar

Teoh, Siew Hong, Tak J. Wong, and Gita R. Rao. 1998. “Are Accruals during Initial Public Offerings Opportunistic?” Review of Accounting Studies 3 (1): 175–208. https://doi.org/10.1023/a:1009688619882.10.1023/A:1009688619882Search in Google Scholar

Thagard, Paul R. 1978. “The Best Explanation: Criteria for Theory Choice.” The Journal of Philosophy 75 (2): 76–92. https://doi.org/10.2307/2025686.Search in Google Scholar

Tversky, Amos, and Daniel Kahneman. 1974. “Judgment under Uncertainty: Heuristics and Biases.” Science 185 (4157): 1124–31. https://doi.org/10.1126/science.185.4157.1124.Search in Google Scholar

Vogel, Rick, Fabian Hattke, and Jessica Petersen. 2017. “Journal Rankings in Management and Business Studies: What Rules Do We Play by?” Research Policy 46 (10): 1707–22. https://doi.org/10.1016/j.respol.2017.07.001.Search in Google Scholar

Wasserstein, Ronald L., Allen L. Schirm, and Nicole A. Lazar. 2019. “Moving to a World beyond ‘p < 0.05.” The American Statistician 73 (S1): 1–19. https://doi.org/10.1080/00031305.2019.1583913.Search in Google Scholar

Watts, Ross L., and Jerold L. Zimmerman. 1978. “Towards a Positive Theory of the Determination of Accounting Standards.” The Accounting Review 53 (1): 112–34.Search in Google Scholar

Wilson, G. Peter. 1987. “The Incremental Information Content of the Accrual and Funds Components of Earnings after Controlling for Earnings.” The Accounting Review 62 (2): 293–322.Search in Google Scholar

Received: 2021-09-14
Accepted: 2023-10-03
Published Online: 2023-10-20

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