Testing Precise Hypotheses
Open accessAbstract
Testing of precise (point or small interval) hypotheses is reviewed, with special emphasis placed on exploring the dramatic conflict between conditional measures (Bayes factors and posterior probabilities) and the classical P-value (or observed significance level). This conflict is highlighted by finding lower bounds on the conditional measures over wide classes of priors, in normal and binomial situations, lower bounds, which are much larger than the P-value; this leads to the recommendation of several alternatives to P-values. Results are also given concerning the validity of approximating an interval null by a point null. The overall discussion features critical examination of issues such as the probability of objective testing and the possibility of testing from confidence sets.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The posterior probability of 'no effect' can be viewed as an approximation to the posterior probability of the effect being 'small' (|β| < ε), provided ε is at most about one half of a standard error.
“The posterior probability of 'no effect' can be viewed as an approximation to the posterior probability of the effect being 'small,' namely, P lparenOSCASB vertSHT β vertSHT < ε rparenOSCASB , provided that ε is at most about onehalf of a standard error (Berger and Delampady, 1987).”
From Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors (1999) · cites this paper as Berger and Delampady, 1987
P-values arguably overstate the evidence for an effect even when there is no model uncertainty.
“In fact, p -values arguably overstate the evidence for an effect even when there is no model uncertainty (Edwards, Lindman and Savage, 1963; Berger and Delampady, 1987; Berger and Sellke, 1987).”
From Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors (1999) · cites this paper as Berger and Delampady, 1987
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Statistical Decision Theory and Bayesian Analysis
Berger, J. O. (1985) · Springer Series in Statistics · doi:10.1007/978-1-4757-4286-2 · Cited by 7,722 · see citing works
Self-citationApplied Statistical Decision Theory
Lindley, D. V., Raiffa, H., & Schlaifer, R. (1962) · Econometrica · doi:10.2307/1909900 · Cited by 2,186 · see citing works
An Introduction to Bayesian Inference in Econometrics.
Sargan, J. D., & Zellner, A. (1974) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2344559 · Cited by 1,937 · see citing works
Bayesian statistical inference for psychological research.
Edwards, W., Lindman, H., & Savage, L. J. (1963) · Psychological Review · doi:10.1037/h0044139 · Cited by 1,734 · see citing works
Specification Searches: Ad Hoc Inference with Non-Experimental Data.
Richard, J., & Leamer, E. E. (1981) · Economica · doi:10.2307/2553491 · Cited by 1,129 · see citing works
Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence
Berger, J. O., & Sellke, T. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478397 · Cited by 971 · see citing works
Self-citationLindley, D. V. (1957) · Biometrika · doi:10.1093/biomet/44.1-2.187 · Cited by 946 · see citing works
Probability and the Weighing of Evidence.
M., P. A., & Good, I. J. (1950) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2981046 · Cited by 753 · see citing works
Berger, J. O., & Wolpert, R. L. (1988) · doi:10.1214/lnms/1215466210 · Cited by 616 · see citing works
Self-citationThe Estimation of Probabilities: An Essay on Modern Bayesian Methods
Sparks, J. N., & Good, I. J. (1967) · American Educational Research Journal · doi:10.2307/1162122 · Cited by 533 · see citing works
Posterior odds ratios for selected regression hypotheses
Zellner, A., & Siow, A. (1980) · Trabajos de Estadistica y de Investigacion Operativa · doi:10.1007/bf02888369 · Cited by 490 · see citing works
The Weighted Likelihood Ratio, Linear Hypotheses on Normal Location Parameters
Dickey, J. (1971) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177693507 · Cited by 485 · see citing works
Reconciling Bayesian and Frequentist Evidence in the One-Sided Testing Problem
Casella, G., & Berger, R. L. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478396 · Cited by 417 · see citing works
Good Thinking: The Foundations of Probability and Its Applications.
Berger, J. O., & Good, I. J. (1985) · Journal of the American Statistical Association · doi:10.2307/2288079 · Cited by 390 · see citing works
Self-citationBayes Factors and Choice Criteria for Linear Models
Smith, A. F. M., & Spiegelhalter, D. J. (1980) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1980.tb01122.x · Cited by 339 · see citing works
Lindley, D. V. (1977) · Biometrika · doi:10.1093/biomet/64.2.207 · Cited by 257 · see citing works
Shafer, G. R. (1982) · Journal of the American Statistical Association · doi:10.1080/01621459.1982.10477809 · Cited by 195 · see citing works
Clinical Trials and Statistical Verdicts: Probable Grounds for Appeal
Diamond, G. A., & FORRESTER, J. S. (1983) · Annals of Internal Medicine · doi:10.7326/0003-4819-98-3-385 · Cited by 137 · see citing works
The Use of Prior Probability Distributions in Statistical Inference and Decisions
Lindley, D. V. (1961) · Project Euclid (Cornell University) · Cited by 129 · see citing works
Significance Tests in Parallel and in Series
Good, I. J. (1958) · Journal of the American Statistical Association · doi:10.1080/01621459.1958.10501480 · Cited by 124 · see citing works
Testing the Approximate Validity of Statistical Hypotheses
Hodges, J. L., & Lehmann, E. L. (2011) · Springer eBooks · doi:10.1007/978-1-4614-1412-4_15 · Cited by 117 · see citing works
Posterior Probabilities of Alternative Linear Models.
Gaver, K. M., & Lempers, F. B. (1973) · Journal of the American Statistical Association · doi:10.2307/2284117 · Cited by 104 · see citing works
DeGroot, M. H. (1973) · Journal of the American Statistical Association · doi:10.1080/01621459.1973.10481456 · Cited by 99 · see citing works
The Relevance of Stopping Rules in Statistical Inference
Berger, J. O., & Berry, D. A. (1988) · Springer eBooks · doi:10.1007/978-1-4613-8768-8_5 · Cited by 85 · see citing works
Self-citationPersonal Probability and Statistical Analysis
Smith, C. A. B. (1965) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343466 · Cited by 76 · see citing works
Bayesian Statisticians and Remote Clients
Hildreth, C. (1963) · Econometrica · doi:10.2307/1909982 · Cited by 75 · see citing works
A Bayesian analysis of classical hypothesis testing
Bernardo, J. M. (1980) · Trabajos de Estadistica y de Investigacion Operativa · doi:10.1007/bf02888370 · Cited by 73 · see citing works
Approximate Posterior Distributions
Dickey, J. (1976) · Journal of the American Statistical Association · doi:10.1080/01621459.1976.10481547 · Cited by 65 · see citing works
Scientific Reporting and Personal Probabilities: Student's Hypothesis
Dickey, J. (1973) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1973.tb00959.x · Cited by 65 · see citing works
Is the Tail Area Useful as an Approximate Bayes Factor?
Dickey, J. (1977) · Journal of the American Statistical Association · doi:10.1080/01621459.1977.10479922 · Cited by 54 · see citing works
Posterior odds ratios for regression hypotheses
Zellner, A. (1981) · Journal of Econometrics · doi:10.1016/0304-4076(81)90082-8 · Cited by 52 · see citing works
POSTERIOR PROBABILITIES OF ALTERNATIVE LINEAR MODELSPreprint
Kloek, T., & Lempers, F. B. (1970) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.272033 · Cited by 24 · see citing works
Hill, B. M. (1982) · Journal of the American Statistical Association · doi:10.2307/2287249 · Cited by 13 · see citing works
C272. A flexible bayesian model for comparing two treatments
Good, I. J. (1986) · Journal of Statistical Computation and Simulation · doi:10.1080/00949658608810971 · Cited by 5 · see citing works
Rubin, H. (1971) · Elsevier eBooks · doi:10.1016/b978-0-12-307550-5.50009-5 · Cited by 4 · see citing works
Flagged first, then by citations
Research works printed but not linked: 8
- BERGER, J. (1986). Are P-values reasonable measures of accuracy. In Pacific Statistical Congress (I. S. Francis et al., eds.). NorthHolland, Amsterdam.
- DEMPSTER, A. P. (1971). Model searching and estimation in the logic of inference. In Foundations of Statistical Inference (V. P. Godambe and D. A. Sprott, eds.). Holt, Rinehart, and Winston, Toronto.
- DEMPSTER, A. P. (1973). The direct use of likelihood for significance testing. In Proc. of the Conference on Foundational Questions in Statistical Inference (O. Barndorff-Nielsen et al., eds.) 335–352. Dept. Theoretical Statistics, Univ. Aarhus.
- DICKEY, J. M. (1974). Bayesian alternatives to the F test and least squares estimate in the linear model. In Studies in Bayesian Econometrics and Statistics (S. E. Fienberg and A. Zellner, eds.) 515–554. North-Holland, Amsterdam.
- DIcKEY, J. M. (1980). Approximate coherence for regression model inference— with a new analysis of Fisher's Broadback Wheatfield example. In Bayesian Analysis in Econometrics and Statistics: Essays in Honor of Harold Jeffreys (A. Zellner, ed.) 333-354. North-Holland, Amsterdam.
- GooD, I. J. (1985). Weight of evidence: A brief survey. In Bayesian Statistics 2 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 249–270. North-Holland, Amsterdam.
- JEFFREYs, H. (1957). Scientific Inference. Cambridge Univ. Press, Cambridge.
- JEFFREYs, H. (1961). Theory of Probability, 3rd ed. Oxford Univ. Press, London.
Cited by
Sorted by citations
Kass, R. E., & Raftery, A. E. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476572 · Cited by 12,558 · see citing works
Bayesian model selection in social research
Raftery, A. E. (1995) · Sociological Methodology · doi:10.2307/271063 · Cited by 6,823 · see citing works
The ASA Statement on <i>p</i> -Values: Context, Process, and Purpose
Wasserstein, R. L., & Lazar, N. A. (2016) · The American Statistician · doi:10.1080/00031305.2016.1154108 · Cited by 6,306 · see citing works
Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999) · Statistical Science · doi:10.1214/ss/1009212519 · Cited by 4,118 · see citing works
A practical solution to the pervasive problems ofp values
Wagenmakers, E.-J. (2007) · Psychonomic Bulletin & Review · doi:10.3758/bf03194105 · Cited by 2,490 · see citing works
Using Bayes to get the most out of non-significant results
Dienes, Z. (2014) · Frontiers in Psychology · doi:10.3389/fpsyg.2014.00781 · Cited by 1,998 · see citing works
POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES
Gelman, A., Meng, X., & Stern, H. S. (1996) · Cited by 1,982 · see citing works
Bayesian inference for psychology. Part II: Example applications with JASP
Wagenmakers, E., Love, J., Marsman, M., Jamil, T., Ly, A., Verhagen, J., Selker, R., Gronau, Q. F., Dropmann, D., boutin, B., et al. (2017) · Psychonomic Bulletin & Review · doi:10.3758/s13423-017-1323-7 · Cited by 1,705 · see citing works
Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications
Wagenmakers, E., Marsman, M., Jamil, T., Ly, A., Verhagen, J., Love, J., Selker, R., Gronau, Q. F., Šmíra, M., Epskamp, S., et al. (2017) · Psychonomic Bulletin & Review · doi:10.3758/s13423-017-1343-3 · Cited by 1,652 · see citing works
The horseshoe estimator for sparse signals
Carvalho, C. M., Polson, N., & Scott, J. G. (2010) · Biometrika · doi:10.1093/biomet/asq017 · Cited by 1,397 · see citing works
(2013) · Cited by 1,351 · see citing works
Handbook of Economic Forecasting
(2013) · Handbook of economic forecasting · doi:10.1016/b978-0-444-53683-9.00023-2 · Cited by 1,290 · see citing works
Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window
Madigan, D., & Raftery, A. E. (1994) · Journal of the American Statistical Association · doi:10.1080/01621459.1994.10476894 · Cited by 1,205 · see citing works
The Insignificance of Statistical Significance Testing
Johnson, D. H. (1999) · Journal of Wildlife Management · doi:10.2307/3802789 · Cited by 1,104 · see citing works
The Intrinsic Bayes Factor for Model Selection and Prediction
Berger, J. O., & Pericchi, L. R. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476668 · Cited by 1,008 · see citing works
Self-citationStatistical Evidence in Experimental Psychology: An Empirical Comparison Using 855 <i>t</i> Tests
Wetzels, R., Matzke, D., Lee, M. D., Rouder, J. N., Iverson, G. J., & Wagenmakers, E.-J. (2011) · Perspectives on Psychological Science · doi:10.1177/1745691611406923 · Cited by 945 · see citing works
Bayesian Model Selection and Model Averaging
Wasserman, L. (2000) · Journal of Mathematical Psychology · doi:10.1006/jmps.1999.1278 · Cited by 989 · see citing works
Wagenmakers, E.-J., Wetzels, R., Borsboom, D., & van der Maas, H. L. J. (2011) · Journal of Personality and Social Psychology · doi:10.1037/a0022790 · Cited by 977 · see citing works
Calibration of ρ Values for Testing Precise Null Hypotheses
Sellke, T., Bayarri, M. J., & Berger, J. O. (2001) · The American Statistician · doi:10.1198/000313001300339950 · Cited by 856 · see citing works
Self-citationRevised standards for statistical evidence
Johnson, V. E. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1313476110 · Cited by 808 · see citing works
A tutorial on a practical Bayesian alternative to null-hypothesis significance testing
Masson, M. E. J. (2011) · Behavior Research Methods · doi:10.3758/s13428-010-0049-5 · Cited by 752 · see citing works
Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method
Wagenmakers, E.-J., Lodewyckx, T., Kuriyal, H., & Grasman, R. (2010) · Cognitive Psychology · doi:10.1016/j.cogpsych.2009.12.001 · Cited by 740 · see citing works
Fractional Bayes Factors for Model Comparison
O’Hagan, A. (1995) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1995.tb02017.x · Cited by 673 · see citing works
Approximate Bayes factors and accounting for model uncertainty in generalised linear models
Raftery, A. E. (1996) · Biometrika · doi:10.1093/biomet/83.2.251 · Cited by 634 · see citing works
An overview of robust Bayesian analysis
Berger, J. O., Moreno, E., Pericchi, L. R., Bayarri, M. J., Bernardo, J. M., Cano, J. A., de la Horra, J., Martín, J., Insua, D. R., Betrò, B., et al. (1994) · Test · doi:10.1007/bf02562676 · Cited by 591 · see citing works
Self-citationBayes factor approaches for testing interval null hypotheses.
Morey, R. D., & Rouder, J. N. (2011) · Psychological Methods · doi:10.1037/a0024377 · Cited by 584 · see citing works
Bayes’ Theorem and Naive Bayes Classifier
Berrar, D. (2018) · Elsevier eBooks · doi:10.1016/b978-0-12-809633-8.20473-1 · Cited by 442 · see citing works
Type S error rates for classical and Bayesian single and multiple comparison procedures
Gelman, A., & Tuerlinckx, F. (2000) · Computational Statistics · doi:10.1007/s001800000040 · Cited by 380 · see citing works
Bayesian Estimation and Inference
Zyphur, M. J., & Oswald, F. L. (2013) · Journal of Management · doi:10.1177/0149206313501200 · Cited by 392 · see citing works
Robust Bayesian analysis: sensitivity to the prior
Berger, J. O. (1990) · Journal of Statistical Planning and Inference · doi:10.1016/0378-3758(90)90079-a · Cited by 373 · see citing works
Self-citationBayesian Model Selection in Structural Equation Models
Raftery, A. E. (1992) · Cited by 364 · see citing works
Objective Bayesian Methods for Model Selection: Introduction and Comparison
Berger, J. O., & Pericchi, L. R. (2001) · Lecture notes-monograph series · doi:10.1214/lnms/1215540968 · Cited by 359 · see citing works
Self-citationLow P-Values or Narrow Confidence Intervals: Which Are More Durable?
Poole, C. (2001) · Epidemiology · doi:10.1097/00001648-200105000-00005 · Cited by 363 · see citing works
Could Fisher, Jeffreys and Neyman Have Agreed on Testing?
Berger, J. O. (2003) · Statistical Science · doi:10.1214/ss/1056397485 · Cited by 348 · see citing works
Self-citationAn Introduction to Bayesian Hypothesis Testing for Management Research
Andraszewicz, S., Scheibehenne, B., Rieskamp, J., Grasman, R. P. P. P., Verhagen, J., & Wagenmakers, E. (2014) · Journal of Management · doi:10.1177/0149206314560412 · Cited by 344 · see citing works
P Values for Composite Null Models
Bayarri, M. J., & Berger, J. O. (2000) · Journal of the American Statistical Association · doi:10.1080/01621459.2000.10474309 · Cited by 335 · see citing works
Self-citationA Bayesian Perspective on the Reproducibility Project: Psychology
Etz, A., & Vandekerckhove, J. (2016) · PLOS ONE · doi:10.1371/journal.pone.0149794 · Cited by 295 · see citing works
“Decades of reliance on orthodox statistical inference—which is known to overstate the evidence against a null hypothesis (Berger & Delampady, 1987; Berger & Sellke, 1987; Edwards, Lindman, & Savage, 1963; Goodman, 2008)—have obfuscated the widespread problem of small samples in psychological…”
Publication Bias (The "File-Drawer Problem") in Scientific Inference
Scargle, J. D. (1999) · arXiv · doi:10.48550/arxiv.physics/9909033 · Cited by 313 · see citing works
Final Collapse of the Neyman-Pearson Decision Theoretic Framework and Rise of the neoFisherian
Hurlbert, S. H., & Lombardi, C. M. (2009) · Annales Zoologici Fennici · doi:10.5735/086.046.0501 · Cited by 277 · see citing works
When Null Hypothesis Significance Testing Is Unsuitable for Research: A Reassessment
Szucs, D., & Ioannidis, J. P. A. (2017) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2017.00390 · Cited by 298 · see citing works
Nonlinear Wavelet Shrinkage with Bayes Rules and Bayes Factors
Vidaković, B. (1998) · Journal of the American Statistical Association · doi:10.1080/01621459.1998.10474099 · Cited by 291 · see citing works
Confusion Over Measures of Evidence (p's) Versus Errors (α's) in Classical Statistical Testing
Hubbard, R., & Bayarri, M. J. (2003) · The American Statistician · doi:10.1198/0003130031856 · Cited by 288 · see citing works
Variable selection and Bayesian model averaging in case‐control studies
Viallefont, V., Raftery, A. E., & Richardson, S. T. (2001) · Statistics in Medicine · doi:10.1002/sim.976 · Cited by 263 · see citing works
The reproducibility of research and the misinterpretation of p -values
Colquhoun, D. (2017) · Royal Society Open Science · doi:10.1098/rsos.171085 · Cited by 258 · see citing works
A tutorial on testing hypotheses using the Bayes factor.
Hoijtink, H. J. A., Mulder, J., Lissa, C. J. V., & Gu, X. (2019) · Psychological Methods · doi:10.1037/met0000201 · Cited by 237 · see citing works
Bayesian Model Averaging in Proportional Hazard Models: Assessing the Risk of a Stroke
Volinsky, C. T., Madigan, D., Raftery, A. E., & Kronmal, R. A. (1997) · Journal of the Royal Statistical Society Series C: Applied Statistics · doi:10.1111/1467-9876.00082 · Cited by 226 · see citing works
A Critique of the Bayesian Information Criterion for Model Selection
WEAKLIEM, D. L. (1999) · Sociological Methods & Research · doi:10.1177/0049124199027003002 · Cited by 349 · see citing works
Why P Values Are Not a Useful Measure of Evidence in Statistical Significance Testing
Hubbard, R., & Lindsay, R. (2008) · Theory & Psychology · doi:10.1177/0959354307086923 · Cited by 244 · see citing works
Inequality Constrained Analysis of Variance: A Bayesian Approach.
Klugkist, I. G., Laudy, O., & Hoijtink, H. J. A. (2005) · Psychological Methods · doi:10.1037/1082-989x.10.4.477 · Cited by 205 · see citing works
Validation of reliability computational models using Bayes networks
Mahadevan, S., & Rebba, R. (2004) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2004.05.001 · Cited by 201 · see citing works
Unified frequentist and Bayesian testing of a precise hypothesis
Berger, J. O., Boukai, B., & Wang, Y.-J. (1997) · Statistical Science · doi:10.1214/ss/1030037904 · Cited by 190 · see citing works
Self-citationA Bayesian analysis of the unit root in real exchange rates
Schotman, P. C., & van Dijk, H. K. (1991) · Journal of Econometrics · doi:10.1016/0304-4076(91)90014-5 · Cited by 178 · see citing works
Relaxing Measurement Invariance in Cross-National Consumer Research Using a Hierarchical IRT Model
de Jong, M. G., Steenkamp, J. E. M., & Fox, J. (2007) · Journal of Consumer Research · doi:10.1086/518532 · Cited by 175 · see citing works
On Bayesian routes to unit roots
Schotman, P. C., & van Dijk, H. K. (1991) · Journal of Applied Econometrics · doi:10.1002/jae.3950060407 · Cited by 169 · see citing works
Kass, R. E., & Vaidyanathan, S. K. (1992) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1992.tb01868.x · Cited by 168 · see citing works
There’s more than one way to conduct a replication study: Beyond statistical significance.
Anderson, S. F., & Maxwell, S. E. (2016) · Psychological Methods · doi:10.1037/met0000051 · Cited by 167 · see citing works
A Multivariate Multilevel Approach to the Modeling of Accuracy and Speed of Test Takers
Entink, R. H. K., Fox, J., & van der Linden, W. J. (2008) · Psychometrika · doi:10.1007/s11336-008-9075-y · Cited by 164 · see citing works
On the Reproducibility of Psychological Science
Johnson, V. E., Payne, R. D., Wang, T., Asher, A., & Mandal, S. (2016) · Journal of the American Statistical Association · doi:10.1080/01621459.2016.1240079 · Cited by 150 · see citing works
Feeney, S. M., Mortlock, D. J., & Dalmasso, N. (2018) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/sty418 · Cited by 150 · see citing works
Dette, H. (1999) · The Annals of Statistics · doi:10.1214/aos/1018031266 · Cited by 142 · see citing works
Full Bayesian Inference for GARCH and EGARCH Models
Vrontos, I. D., Δελλαπόρτας, Π., & Politis, D. N. (2000) · Journal of Business and Economic Statistics · doi:10.1080/07350015.2000.10524861 · Cited by 141 · see citing works
The Bayes factor for inequality and about equality constrained models
Klugkist, I. G., & Hoijtink, H. J. A. (2007) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2007.01.024 · Cited by 141 · see citing works
Bayesian Hypothesis Testing: A Reference Approach
Bernardo, J. M., & Rueda, R. (2002) · International Statistical Review · doi:10.1111/j.1751-5823.2002.tb00175.x · Cited by 135 · see citing works
An Intrinsic Limiting Procedure for Model Selection and Hypotheses Testing
Moreno, E., Bertolino, F., & Racugno, W. (1998) · Journal of the American Statistical Association · doi:10.1080/01621459.1998.10473805 · Cited by 137 · see citing works
Computational methods for model reliability assessment
Rebba, R., & Mahadevan, S. (2007) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2007.08.001 · Cited by 136 · see citing works
The False Positive Risk: A Proposal Concerning What to Do About p -Values
Colquhoun, D. (2019) · The American Statistician · doi:10.1080/00031305.2018.1529622 · Cited by 134 · see citing works
Ranges of Posterior Measures for Priors with Unimodal Contaminations
Sivaganesan, S., & Berger, J. O. (1989) · The Annals of Statistics · doi:10.1214/aos/1176347148 · Cited by 132 · see citing works
Self-citationDefault “Gunel and Dickey” Bayes factors for contingency tables
Jamil, T., Ly, A., Morey, R. D., Love, J., Marsman, M., & Wagenmakers, E. (2016) · Behavior Research Methods · doi:10.3758/s13428-016-0739-8 · Cited by 131 · see citing works
Bayes Factors Based on Test Statistics
Johnson, V. E. (2005) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2005.00521.x · Cited by 127 · see citing works
Nonparametric analysis of covariance
Dette, H., & Neumeyer, N. (2001) · The Annals of Statistics · doi:10.1214/aos/1013203458 · Cited by 127 · see citing works
Taheri, S. M. (2016) · Austrian Journal of Statistics · doi:10.17713/ajs.v32i3.459 · Cited by 123 · see citing works
Chapter 1 Bayesian Forecasting
Geweke, J. F., & Whiteman, C. H. (2006) · Handbook of economic forecasting · doi:10.1016/s1574-0706(05)01001-3 · Cited by 122 · see citing works
A Default Bayesian Hypothesis Test for ANOVA Designs
Wetzels, R., Grasman, R. P. P. P., & Wagenmakers, E. (2012) · The American Statistician · doi:10.1080/00031305.2012.695956 · Cited by 123 · see citing works
The Need for Bayesian Hypothesis Testing in Psychological Science
Wagenmakers, E., Verhagen, J., Ly, A., Matzke, D., Steingroever, H., Rouder, J. N., & Morey, R. D. (2017) · Wiley eBooks · doi:10.1002/9781119095910.ch8 · Cited by 122 · see citing works
The 1988 Wald Memorial Lectures: The Present Position in Bayesian Statistics
Lindley, D. V. (1990) · Statistical Science · doi:10.1214/ss/1177012253 · Cited by 119 · see citing works
Greenland, S., & Poole, C. (2012) · Epidemiology · doi:10.1097/ede.0b013e3182785741 · Cited by 115 · see citing works
How Bayesian statistics are needed to determine whether mental states are unconscious
Dienes, Z. P. (2015) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199688890.003.0012 · Cited by 115 · see citing works
Default Bayes Factors for Nonnested Hypothesis Testing
Berger, J. O., & Mortera, J. (1999) · Journal of the American Statistical Association · doi:10.1080/01621459.1999.10474149 · Cited by 115 · see citing works
Self-citationHubbard (2004) · doi:10.1177/0959354304043638 · Cited by 114 · see citing works
The effect of horizontal eye movements on free recall: A preregistered adversarial collaboration.
Matzke, D., Nieuwenhuis, S., van Rijn, H., Slagter, H. A., van der Molen, M. W., & Wagenmakers, E. (2015) · Journal of Experimental Psychology General · doi:10.1037/xge0000038 · Cited by 114 · see citing works
A Logic of Probability, with Application to the Foundations of Statistics
Vovk, V. (1993) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1993.tb01904.x · Cited by 113 · see citing works
How to become a Bayesian in eight easy steps: An annotated reading list
Etz, A. J., Gronau, Q. F., Dablander, F., Edelsbrunner, P. A., & Baribault, B. (2017) · Psychonomic Bulletin & Review · doi:10.3758/s13423-017-1317-5 · Cited by 112 · see citing works
Local Shrinkage Rules, Lévy Processes and Regularized Regression
Polson, N. G., & Scott, J. G. (2012) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2011.01015.x · Cited by 110 · see citing works
Causality and Causal Modelling in the Social Sciences
Federica Russo, B. (2008) · Springer eBooks · doi:10.1007/978-1-4020-8817-9 · Cited by 111 · see citing works
Bartos̆, F., Maier, M., Quintana, D. S., & Wagenmakers, E. (2022) · Advances in Methods and Practices in Psychological Science · doi:10.1177/25152459221109259 · Cited by 115 · see citing works
Nonparametric Validation of Similar Distributions and Assessment of Goodness of Fit
Munk, A., & Czado, C. (1998) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00121 · Cited by 108 · see citing works
Bayesian Inference in Non‐Replicated Ecological Studies
Reckhow, K. H. (1990) · Ecology · doi:10.2307/1938619 · Cited by 104 · see citing works
Is There a Free Lunch in Inference?
Rouder, J. N., Morey, R. D., Verhagen, J., Province, J. M., & Wagenmakers, E. (2016) · Topics in Cognitive Science · doi:10.1111/tops.12214 · Cited by 104 · see citing works
Three Insights from a Bayesian Interpretation of the One-Sided P Value
Marsman, M., & Wagenmakers, E. (2016) · Educational and Psychological Measurement · doi:10.1177/0013164416669201 · Cited by 103 · see citing works
Bayesian risk-based decision method for model validation under uncertainty
Jiang, X., & Mahadevan, S. (2006) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2006.03.006 · Cited by 101 · see citing works
A review of issues about null hypothesis Bayesian testing.
Tendeiro, J. N., & Kiers, H. A. L. (2019) · Psychological Methods · doi:10.1037/met0000221 · Cited by 105 · see citing works
Senn, S. J. (2001) · Journal of Epidemiology and Biostatistics · doi:10.1080/135952201753172953 · Cited by 98 · see citing works
Cognitive model decomposition of the BART: Assessment and application
van Ravenzwaaij, D., Dutilh, G., & Wagenmakers, E. (2010) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2010.08.010 · Cited by 98 · see citing works
Mulder, J., & Wagenmakers, E. (2016) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2016.01.002 · Cited by 99 · see citing works
Accounting for input-model and input-parameter uncertainties in simulation
Zouaoui, F., & Wilson, J. R. (2004) · IIE Transactions · doi:10.1080/07408170490500708 · Cited by 97 · see citing works
The Analysis of Gene Expression Data: An Overview of Methods and Software
Parmigiani, G., Garrett, E. S., Irizarry, R. A., & Zeger, S. L. (2003) · Statistics for biology and health · doi:10.1007/0-387-21679-0_1 · Cited by 96 · see citing works
Model choice in generalised linear models: a Bayesian approach via Kullback-Leibler projections
Goutis, C. (1998) · Biometrika · doi:10.1093/biomet/85.1.29 · Cited by 94 · see citing works
Bayesian routes and unit roots: De rebus prioribus semper est disputandum
Phillips, P. C. B. (1991) · Journal of Applied Econometrics · doi:10.1002/jae.3950060411 · Cited by 92 · see citing works
Bayesian Inference and Portfolio Efficiency
Kandel, S., McCulloch, R., & Stambaugh, R. F. (1995) · Review of Financial Studies · doi:10.1093/rfs/8.1.1 · Cited by 92 · see citing works
On the bayesianity of pereira-stern tests
Madruga, M. R., Esteves, L. G., & Wechsler, S. (2001) · Test · doi:10.1007/bf02595698 · Cited by 87 · see citing works
- Authors
- Berger, J. O., & Delampady, M.
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 1987-08-01
- Volume
- 2
- Issue
- 3
- Pages
- 317-335
- ISSN
- 0883-4237 (ISSN-L)
- 2168-8745
- OpenAlex
- W2128585330
- Cited by
- 664
- References
- 35
- Citations by year
- 2025: 6 · 2024: 11 · 2023: 14 · 2022: 20 · 2021: 29 · 2020: 24 · 2019: 29 · 2018: 26 · 2017: 22 · 2016: 32 · 2015: 23 · 2014: 21 · 2013: 23 · 2012: 22
- FWCI
- 10.67
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Science (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- point null hypothesis, p-values, Bayes factor, posterior probability, normal distribution, binomial distribution, objective testing, confidence regions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
