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Testing Statistical Hypotheses of Equivalence and Noninferiority
Abstract
While continuing to focus on methods of testing for two-sided equivalence, Testing Statistical Hypotheses of Equivalence and Noninferiority, Second Edition gives much more attention to noninferiority testing. It covers a spectrum of equivalence testing problems of both types, ranging from a one-sample problem with normally distributed observations
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“The non-inferiority margin was defined a priori (in the grant application) by a strict and small margin of tolerance for non-inferiority of 10%, or a ε of 0.36 [53], p.16 which, for example, represents a difference in change between the two conditions of no more than 10% on the primary outcome measure.”
In the citing paper
“The sample size was established a priori based on a power analysis for non-inferiority trials [53,54].”
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“Further details on this test, as well as sample code, may be found in the book by Wellek.”
Thou Shalt Not Bear False Witness Against Null Hypothesis Significance Testing
García-Pérez, M. Á. (2016) · Educational and Psychological Measurement · doi:10.1177/0013164416668232 · Cited by 30
“…da Silva, Logan, & Klein, 2009), and they are well covered in a number of reference sources some of which include computer code (e.g., Ng, 2014; Pardo, 2014; Rothmann, Wiens, & Chan, 2011; Wellek, 2010), although they have not yet made it into classical software packages for statistical analyses.”
BackgroundComparison of Volunteer and Paid EMS Professionals in the United States
Cash, R. E., Rivard, M. K., Chrzan, K., et al. (2020) · Prehospital Emergency Care · doi:10.1080/10903127.2020.1752867 · Cited by 30
“001 Administrator/supervisor 313 (5) 5,074 (12) 7% <0.”
MethodLuke, T. J., & Alceste, F. (2020) · Law and Human Behavior · doi:10.1037/lhb0000410 · Cited by 28
Brain‐wide inferiority and equivalence tests in fMRI group analyses: Selected applications
Gerchen, M. F., Kirsch, P., & Feld, G. B. (2021) · Human Brain Mapping · doi:10.1002/hbm.25664 · Cited by 34
Political Deepfakes Are As Credible As Other Fake Media And (Sometimes) Real Media
Barari, S., Lucas, C., & Munger, K. (2021) · doi:10.31219/osf.io/cdfh3 · Cited by 51
Testing for Equivalence of Pre-Trends in Difference-in-Differences Estimation
Dette, H., & Schumann, M. (2024) · Journal of Business & Economic Statistics · doi:10.1080/07350015.2024.2308121 · Cited by 30
“In bio-statistics, the popularity of equivalence tests has led to a consensus on sensible choices for U , and regulators frequently specify the equivalence thresholds that should be employed (see Wellek 2010 for a recent review).”
Gabrielli, M., Turolla, A., & Antonelli, M. (2021) · Journal of Environmental Management · doi:10.1016/j.jenvman.2021.112151 · Cited by 28
McNeish, D. (2023) · Multivariate Behavioral Research · doi:10.1080/00273171.2022.2163477 · Cited by 36
“EQT allows researchers to test a prespecified magnitude of misspecification (Wellek, 2010).”
BackgroundKruschke, J. K., & Liddell, T. M. (2016) · doi:10.31219/osf.io/ksfyr · Cited by 29
Equivalence analyses of dissolution profiles with the Mahalanobis distance
Hoffelder, T. (2018) · Biometrical Journal · doi:10.1002/bimj.201700257 · Cited by 27
“The Mahalanobis distance can be interpreted as a multivariate generalization of the distance measure (𝜇𝑇𝐸𝑆𝑇 − 𝜇𝑅𝐸𝐹 )∕𝜎 for which Wellek (2010) derived its two-sample t-test for equivalence for normally distributed data.”
BackgroundMethodInfluentialWidespread cryptic variation in genetic architecture between the sexes
van der Bijl, W., & Mank, J. E. (2021) · Evolution Letters · doi:10.1002/evl3.245 · Cited by 28
Valentin, O., Viallet, G., Delnavaz, A., et al. (2021) · Sensors · doi:10.3390/s21092953 · Cited by 26
“This observation is supported by a two-sample t-test for noninferiority [38] computed using R 3.”
MethodAn Exact Procedure for the Evaluation of Reference-Scaled Average Bioequivalence
Tóthfalusi, L., & Endrényi, L. (2016) · The AAPS Journal · doi:10.1208/s12248-016-9873-6 · Cited by 24
Liao, J., Midya, V., & Berg, A. S. (2019) · The American Statistician · doi:10.1080/00031305.2019.1701550 · Cited by 25
Campbell, H., & Lakens, D. (2020) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12201 · Cited by 26
“, to confirm the lack of an association), the recommended frequentist tool, the equivalence test, is well-suited [43].”
MethodMultivariate Equivalence Tests for Use in Pharmaceutical Development
Hoffelder, T., Gössl, R., & Wellek, S. (2014) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2014.920344 · Cited by 25
“Nevertheless, it is known from Wellek (2010) that the T2-test for equivalence can be conservative for nonnormally distributed data and also for heteroskedastic data.”
BackgroundMethodInfluentialSelf-citationLalonde, R. N., Cila, J., Lou, E., & Cribbie, R. A. (2015) · Peace and Conflict Journal of Peace Psychology · doi:10.1037/pac0000134 · Cited by 26
“To demonstrate that these groups are statistically equivalent on this measure, we used a robust version of the method outlined by Wellek (2010) and Koh and Cribbie (2013) for evaluating the equivalence of two or more independent groups, even when population variances are unequal.”
MethodAnalysing the ocular biometry of new‐born infants
Rozema, J., Herscovici, Z., Snir, M., et al. (2017) · Ophthalmic and Physiological Optics · doi:10.1111/opo.12433 · Cited by 24
“55 In order to demonstrate that the synthetic data from the statistical eye model and their derived parameters are statistically indistinguishable from the original data, the non-Figure parametric Mann-Whitney equivalence test 56 was used, assuming uniform limits of tolerance and e = 0.10 .”
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Eichberg, D. G., Di, L., Shah, A. H., Luther, E., Richardson, A. M., Sarkiss, C. A., Ivan, M. E., & Komotar, R. J. (2019) · World Neurosurgery · doi:10.1016/j.wneu.2019.08.219 · Cited by 24
Multiple peer effects in the diffusion of innovations on social networks: a simulation study
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“Under such paradigm, the increase in the number of simulations will increase the precision and reduce the p values but will not produce artificially significant small-effect sizes (Wellek 2010).”
BackgroundKelter, R. (2021) · BMC Medical Research Methodology · doi:10.1186/s12874-021-01341-7 · Cited by 25
“For extensions and modifications of the TOST procedure see Anderson & Hauck [94], Berger & Hsu [97], Schuirmann [70, 93], Meyners [98], Chow & Liu [99], and Wellek [100].”
MethodInfluentialPolitical Deepfakes Are as Credible as Other Fake Media and (Sometimes) Real Media
Barari, S., Lucas, C., & Munger, K. (2024) · The Journal of Politics · doi:10.1086/732990 · Cited by 71
Stephens, A. R., Tyser, A. R., Presson, A. P., et al. (2020) · Journal of Hand Surgery Global Online · doi:10.1016/j.jhsg.2020.10.009 · Cited by 23
Rauch, G., & Beyersmann, J. (2013) · Statistics in Medicine · doi:10.1002/sim.5798 · Cited by 22
Kolková, Z., Arakelyan, A., Casslén, B. G., et al. (2013) · Journal of Ovarian Research · doi:10.1186/1757-2215-6-60 · Cited by 23
“The Equivalence test [7-9] and statistical applets BestKeeper [10], geNorm [11], and NormFinder [12] were used for analysis of genes expression stability.”
MethodBatterham, M. J., Loo, C. V., Charlton, K. E., Cliff, D. P., & Okely, A. D. (2016) · British Journal Of Nutrition · doi:10.1017/s0007114516000040 · Cited by 23
Is Automated Topic Model Evaluation Broken?: The Incoherence of CoherencePreprint
Hoyle, A., Goel, P., Peskov, D., Hian-Cheong, A., Boyd-Graber, J. L., & Resnik, P. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.02173 · Cited by 93
“Since human effects in the opposite direction of automated metrics also imply a false discovery, we conduct a test of non-inferiority; this is the same as using a large negative lower bound in the two-one-sided tests procedure for equivalence (Schuirmann, 1987; Wellek, 2010).”
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“Using a two one-sided test (TOST) procedure we test whether the means of the two cohorts are equivalent when allowing for a small margin of acceptable difference (see, e.g., Wellek 2010).”
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Dürig, T., White, J. D. L., Zimanowski, B., Büttner, R., Murch, A., & Carey, R. (2020) · Bulletin of Volcanology · doi:10.1007/s00445-020-01408-1 · Cited by 21
“It determines the maximum “acceptable” difference from the mean of the compared shape parameter (Rasch and Guiard 2004; Wellek 2010).”
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“If the one-tailed t test results lead to a rejection of both null hypotheses, relationship (8) is valid and statistical equivalence is verified (Rasch and Guiard 2004; Wellek 2010; Dürig et al. 2012a).”
BackgroundMethodInfluentialFreise, K. J., Lin, T., Fan, T. M., et al. (2013) · Journal of Veterinary Internal Medicine · doi:10.1111/jvim.12211 · Cited by 22
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Janssen, L., Steenbergen, B., & Carson, R. G. (2013) · Cerebral Cortex · doi:10.1093/cercor/bht220 · Cited by 22
“In addition, an inferential test of equivalence (Wellek and Michaelis 1991), specifically the paired t-test for equivalence (Wellek 2010), was calculated for each comparison.”
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Brañas‐Garza, P., Jorrat, D., Espín, A. M., & Sánchez, A. (2022) · Experimental Economics · doi:10.1007/s10683-022-09776-5 · Cited by 31
“This technique is called equivalence testing (ET; Lakens, 2017; Wellek, 2010) and is based on testing whether the observed effect falls within or outside an equivalence interval, defined by two predetermined bounds: the lower (-γL) and the upper bound (γU).”
MethodBouchard, S., Dugas, M. J., Belleville, G., Langlois, F., Gosselin, P., Robillard, G., Corno, G., & Marchand, A. (2022) · Journal of Clinical Medicine · doi:10.3390/jcm11195924 · Cited by 21
“The sample size was established a priori based on a power analysis for non-inferiority trials [53,54].”
InfluentialTodeschini, P., Salviato, E., Romani, C., Raimondi, V., Ciccarese, F., Ferrari, F. G., Tognon, G., Marchini, S., D’Incalci, M., Zanotti, L., et al. (2021) · Cancers · doi:10.3390/cancers13133358 · Cited by 21
“To ensure adequate power of the test, the equivalence range (±ε) was chosen depending on data variability following Wellek criteria [28].”
MethodRelevant change points in high dimensional time series
Dette, H., & Gösmann, J. (2018) · Electronic Journal of Statistics · doi:10.1214/18-ejs1464 · Cited by 21
“nsidered as non-relevant. The problem of testing for a relevant dierence between (one dimensional) means of two samples has been discussed by numerous authors mainly in the eld of biostatistics (see Wellek (2010) for a recent review). In particular testing relevant hypotheses avoids the consistency problem as mentione…”
BackgroundBuchan, D. S., Boddy, L. M., & McLellan, G. (2020) · Measurement in Physical Education and Exercise Science · doi:10.1080/1091367x.2020.1801441 · Cited by 23
Equivalence Testing for Regression Discontinuity Designs
Hartman, E. (2020) · Political Analysis · doi:10.1017/pan.2020.43 · Cited by 20
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“For HUmean scores, means for CNN and FBP were tested for equivalence using two onesided paired t tests, and 90% confidence intervals for the true differences were calculated (19).”
MethodThe wild bootstrap for multivariate Nelson–Aalen estimators
Bluhmki, T., Dobler, D., Beyersmann, J., & Pauly, M. (2018) · Lifetime Data Analysis · doi:10.1007/s10985-018-9423-x · Cited by 20
“Adapting the principle of confidence interval inclusion as discussed in Wellek (2010), Section 3.1, to time-simultaneous confidence bands, hypothesis tests for equivalence of cumulative hazard functions become readily available.”
BackgroundMethodInfluentialThiese, M. S., Walker, S. D., & Lindsey, J. (2017) · Journal of Thoracic Disease · doi:10.21037/jtd.2017.09.24 · Cited by 20
“These tests are not stating that two groups are simply not statistically different (37).”
BackgroundSimulation Accuracy, Uncertainty, and Predictive Capability: A Physical Sciences Perspective
Oberkampf, W. L. (2019) · Simulation foundations, methods and applications · doi:10.1007/978-3-319-70766-2_3 · Cited by 21
Macpherson, M. C., Fay, N., & Miles, L. K. (2020) · Acta Psychologica · doi:10.1016/j.actpsy.2020.103140 · Cited by 20
Shi, D., Song, H., DiStefano, C., Maydeu-Olivares, A., McDaniel, H. L., & Jiang, Z. (2019) · Multivariate Behavioral Research · doi:10.1080/00273171.2018.1514484 · Cited by 19
“Since the tests are conducted within the framework of equivalence testing (see Dunnett & Gent, 1977; Marcoulides & Yuan, 2017; Wellek, 2010; Yuan et al., 2016), rejecting the null hypothesis could provide statistical evidence 2That is, the difficulty parameter (b) decreased by .1 in Group 2.”
MethodEvaluating Equivalence and Confirming the Null in the Organizational Sciences
Stanton, J. M. (2020) · Organizational Research Methods · doi:10.1177/1094428120921934 · Cited by 19
“Rules of thumb for equivalence (e.g., Frick, 1995; Wellek, 2010) lack the contextual information on effect sizes provided by the literature and should not serve as the basis for choosing equivalence boundaries.”
BackgroundMethodPéris-Baquero, Ó., & Osma, J. (2023) · Depression and Anxiety · doi:10.1155/2023/1981377 · Cited by 21
“The noninferiority margin was defined a priori by a strict and small margin of tolerance for noninferiority of 10%, in accordance with recommendations [57, 58], applied to the lower bound when the UP showed smaller improvements in comparison to active control condition or to the upper bound of equivalence of the TOST…”
Tests for equivalence of two survival functions: Alternative to the tests under proportional hazards
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Comparing the Reliability of Related Populations With the Probability of Agreement
Stevens, N. T., & Anderson‐Cook, C. M. (2016) · Technometrics · doi:10.1080/00401706.2016.1214180 · Cited by 18
“A more appropriate class of methods relates to equivalence testing (see Wellek 2010; Szarka 2014 for more details), where methods allow for user calibration of what types of differences are important and begin with the assumption that populations should be treated as different until there is…”
MethodValidation of automatic passenger counting: introducing the t-test-induced equivalence test
Siebert, M., & Ellenberger, D. (2019) · Transportation · doi:10.1007/s11116-019-09991-9 · Cited by 21
Weighted p-norm distance t kernel SVM classification algorithm based on improved polarization
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Model Selection and Evaluation
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“For all 5 methods, proportions of grammatical, sensible, and specific messages are found to be statistically equivalent (Wellek, 2010) to the original ( ϵ = 0 .”
MethodMachine learning and hypothesis driven optimization of bull semen cryopreservation media
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Statistical Analysis in the Safety Evaluation of Genetically‐Modified Crops: Equivalence Tests
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“Section 10.2.2 of Wellek (2010) offers some insightful reasoning to this concern.”
BackgroundMethodInfluentialSome Elementary Theory of Permutation Tests
Pesarin, F. (2015) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2013.802350 · Cited by 17
“In some forthcoming papers, we will refer to theory, related methods, and applications on at least three important problems: (i) testing for two-sample survival curves under informative right-censoring; (ii) testing for two-sample survival curves in a competing risk setting; (iii) testing for the so-called equivalence…”
MethodComparison of Dissolution Profiles: A Statistician’s Perspective
Hoffelder, T. (2017) · Therapeutic Innovation & Regulatory Science · doi:10.1177/2168479017749230 · Cited by 17
Detecting structural breaks in eigensystems of functional time series
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“…hypotheses have been considered in statistics to different degrees since the mid 20th century (see Hodges and Lehmann (1954)), and have been investigated intensively in biostatistics, where tests for “bioequivalence” of certain drugs have nowadays become standard (see for example Wellek (2010)).”
BackgroundInfluentialEfficient model-based bioequivalence testing
Möllenhoff, K., Loingeville, F., Bertrand, J., Nguyen, T. T., Sharan, S., Zhao, L., Fang, L., Sun, G., Grosser, S. C., Mentré, F., et al. (2020) · Biostatistics · doi:10.1093/biostatistics/kxaa026 · Cited by 17
“We develop a methodology which mimics the uniformly most powerful test for normally distributed data with known variance, which can be found in many text books on mathematical statistics (see for example, Lehmann and Romano (2006), or Wellek (2010)).”
BackgroundMethodInfluentialvan der Asdonk, S., de Haan, W. D., van Berkel, S. R., van IJzendoorn, M. H., Rippe, R. C. A., Schuengel, C., Kuiper, C. H. Z., Lindauer, R., Overbeek, M. M. M., & Alink, L. R. A. (2020) · Infant Mental Health Journal · doi:10.1002/imhj.21874 · Cited by 17
Confidence Intervals for Ratios of Means and Medians
Bonett, D. G., & Price, R. M. (2020) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998620934125 · Cited by 17
“Confidence intervals for ratios can be used to perform an equivalence test, a noninferiority test, and a superiority test (Wellek, 2010).”
MethodComparing Kaplan‐Meier curves with the probability of agreement
Stevens, N. T., & Lu, L. (2020) · Statistics in Medicine · doi:10.1002/sim.8744 · Cited by 17
Kelter, R. (2022) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12267 · Cited by 21
Zelken, J. A., Hayes, A. G., Parks, B. G., et al. (2015) · The Journal Of Hand Surgery · doi:10.1016/j.jhsa.2015.02.012 · Cited by 17
“5 mm) to compare their potential clinical adequacy.(17) We also performed a power analysis with 90% power to account for type II error where the outcomes were statistically significant.”
Osborne, D., Yan, S., Stuckey, A. C., Pryer, L., Richey, T., & Wall, J. S. (2012) · PLoS ONE · doi:10.1371/journal.pone.0049936 · Cited by 17
“To assess the baseline similarities between groups, a series of Two One-Sided t-test (TOST) equivalency procedures were conducted [17].”
MethodThe difference between “equivalent” and “not different”
Anderson‐Cook, C. M., & Borror, C. M. (2015) · Quality Engineering · doi:10.1080/08982112.2015.1079918 · Cited by 17
“The appropriate test for this scenario is an equivalence test (see Berger 1982; Berger and Hsu 1996; Wellek 2010).”
BackgroundMethodInfluentialHow to Choose between Different Bayesian Posterior Indices for Hypothesis Testing in Practice
Kelter, R. (2021) · Multivariate Behavioral Research · doi:10.1080/00273171.2021.1967716 · Cited by 19
Munson, M. R., Raghavan, R., Shimizu, R., Rodwin, A. H., & Jaccard, J. J. (2022) · Psychiatric Services · doi:10.1176/appi.ps.202100202 · Cited by 16
Are deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimators
Bücher, A., Dette, H., & Heinrichs, F. (2021) · The Annals of Statistics · doi:10.1214/21-aos2098 · Cited by 16
“…and develop methodology to decide whether possible smooth changes in the mean deviate in some sense “substantially” from a given benchmark (see also Wellek, 2010, who considers hypotheses that finite dimensional parameters from different groups do not differ substantially in the field of…”
Establishment of an Equivalence Acceptance Criterion for Accelerated Stability Studies
Burdick, R. K., & Sidor, L. (2013) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2013.789891 · Cited by 16
“Wellek (2010) argues that a sensible measure of dissimilarity in the context of an independent twosample t-test is the effect size (ES), where”
BackgroundDISSOLUTION PROFILE SIMILARITY ANALYSES—STATISTICAL PRINCIPLES, METHODS AND CONSIDERATIONS
Hoffelder, T., LeBlond, D. J., Alstine, L. V., Diaz, D. A., Suarez‐Sharp, S., Witkowski, K., Altan, S., Reynolds, J., Bergeron, Z., Lief, K., et al. (2022) · The AAPS Journal · doi:10.1208/s12248-022-00697-y · Cited by 16
“The statistical synonym for “similarity” is “equivalence” that in turn stands for “equality except for practically irrelevant deviations” [9].”
BackgroundMethodInfluentialYevtushenko, P., Goubergrits, L., Franke, B., Kühne, T., & Schafstedde, M. (2023) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2023.1136935 · Cited by 16
Fesenfeld, L., McGrath, L. F., Sun, Y., Wicki, M., & Bernauer, T. (2024) · PLOS Climate · doi:10.1371/journal.pclm.0000297 · Cited by 25
Effect of Rotational Therapy on Aspiration Risk of Enteral Feeds
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Evaluating published approaches for modelling diameter at breast height from stump dimensions
Pond, N. C., & Froese, R. E. (2014) · Forestry An International Journal of Forest Research · doi:10.1093/forestry/cpu029 · Cited by 15
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Stevens, N. T., Rigdon, S. E., & Anderson‐Cook, C. M. (2019) · Journal of Quality Technology · doi:10.1080/00224065.2019.1569961 · Cited by 15
“Equivalence testing (described by Anderson-Cook and Borror 2016; Szarka 2014; and Wellek 2010) uses a hypothesis-testing based approach to compare static populations in this way.”
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Chernev, A., Blair, S., Böckenholt, U., & Mishra, H. (2021) · Journal of Public Policy & Marketing · doi:10.1177/07439156241264286 · Cited by 22
“Even though it is statistically impossible to support the hypoth-esisthatatrueeffectsizeisexactly zero,itisneverthelesspossibleto statistically reject effects large enough to be deemed meaningful (Wellek 2010).”
Vahl, C. I., & Kang, Q. (2015) · The Journal of Agricultural Science · doi:10.1017/s0021859615000271 · Cited by 14
“When normality is in doubt or there are unexplainable outliers, nonparametric statistics may still serve as a last resort (a comprehensive review can be found in Chapters 5 and 6 of Wellek 2010; also see Freitag et al. 2007).”
BackgroundCIHR Candrive Cohort Comparison with Canadian Household Population Holding Valid Driver’s Licenses
Gagnon, S., Marshall, S., Kadulina, Y., et al. (2016) · Canadian Journal on Aging / La Revue canadienne du vieillissement · doi:10.1017/s0714980816000052 · Cited by 14
Validation of CT‐MRI fusion for intraoperative assessment of stereotactic accuracy in DBS surgery
Montgomery, E. B. (2015) · Movement Disorders · doi:10.1002/mds.26178 · Cited by 14
How to Host An Effective Data Competition: Statistical Advice for Competition Design and Analysis
Anderson‐Cook, C. M., Myers, K., Lu, L., Fugate, M., Quinlan, K., & Pawley, N. H. (2019) · Statistical Analysis and Data Mining The ASA Data Science Journal · doi:10.1002/sam.11404 · Cited by 15
“Equivalence testing [4, 25, 26] has been developed for evaluating the practical equivalence between groups.”
MethodInterval-Based Hypothesis Testing and Its Applications to Economics and Finance
Kim, J. H., & Robinson, A. P. (2019) · Econometrics · doi:10.3390/econometrics7020021 · Cited by 14
Fernández, M. V. A., López, F. J. A., & Jiménez-Gamero, M. D. (2021) · Remote Sensing · doi:10.3390/rs13112069 · Cited by 13
“When the interest is centred in proving that P = P0, the hypotheses in (1) must be adequately switched, and an equivalence test should be applied, see [19].”
BackgroundReplication of null results: Absence of evidence or evidence of absence?
Pawel, S., Heyard, R., Micheloud, C., & Held, L. (2024) · eLife · doi:10.7554/elife.92311.3 · Cited by 13
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Fernández–Prades, C., Vilà‐Valls, J., Arribas, J., & Ramos, A. (2018) · IEEE Access · doi:10.1109/access.2018.2822835 · Cited by 12
Testing for Equivalence: An Intersection-Union Permutation Solution
Arboretti, R., Carrozzo, E., Pesarin, F., & Salmaso, L. (2018) · Statistics in Biopharmaceutical Research · doi:10.1080/19466315.2018.1447993 · Cited by 13
“…quite wide and to our goal of presenting a new permutation procedure, we quote only some few relevant papers: Berger (1982); Berger and Hsu (1996); Wellek (2010); Liu et al. (2002); Laster and Johnson (2003);Mehta, Patel, and Tsiatis (1984); Romano (2005); Zhong, Chen, and Jin (2012); D’Agostino,…”
BackgroundMethodInfluentialNurmi, T., Hakonen, M., Bourguignon, M., et al. (2023) · NeuroImage · doi:10.1016/j.neuroimage.2023.119937 · Cited by 13
“…(i.e. p > 0.05), one sample analog of Hotelling T 2 test with Mahalanobis distance of 1 (i.e. corresponding to 1 standard deviation) was used to determine if all of the ranges were equivalent (R software version 4.0.2; library ―cribbie/equivalencetests‖, function: ―eq.hotT2‖; Wellek, 2010).”
InfluentialBayesian probability of predictive agreement for comparing the outcome of two separate regressions
Stevens, N. T., Rigdon, S. E., & Anderson‐Cook, C. M. (2018) · Quality and Reliability Engineering International · doi:10.1002/qre.2284 · Cited by 13
TACKLING FALSE POSITIVES IN BUSINESS RESEARCH: A STATISTICAL TOOLBOX WITH APPLICATIONS
Kim, J. H. (2018) · Journal of Economic Surveys · doi:10.1111/joes.12303 · Cited by 14
Flores, P., & Ocaña, J. (2019) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2019.1649698 · Cited by 13
“It is based on the equivalence test for dispersion of two Gaussian distributions of Wellek (Wellek 2010, pp. 164).”
BackgroundMethodInfluentialMethods of Determining Sample Sizes
Ryan, T. P. (2013) · Wiley series in probability and statistics · doi:10.1002/9781118439241.ch2 · Cited by 13
Consistency-adjusted alpha allocation methods for a time-to-event analysis of composite endpoints
Rauch, G., Wirths, M., & Kieser, M. (2014) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2014.01.017 · Cited by 12
Mombelli, A., & Zekeridou, A. (2025) · Periodontology 2000 · doi:10.1111/prd.12630 · Cited by 15
Rukhin, A. L. (2013) · Metrologia · doi:10.1088/0026-1394/50/1/49 · Cited by 12
“See [6] for a further discussion and [17] for a review of available statistical techniques.”
BackgroundRahimi, A., & Wang, L. (2015) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2015.2395387 · Cited by 12
“5 [42], with 40 number of pairs, dθ resides in the rejection region at α level = 5%.”
What to make of equivalence testing with a post-specified margin?
Campbell, H., & Gustafson, P. (2021) · Meta-Psychology · doi:10.15626/mp.2020.2506 · Cited by 19
“is the equivalence test (also known as a “non-inferiority test” for one-sided testing (Wellek, 2010)).”
BackgroundMethodInfluentialThe Role of Prior Knowledge and Intelligence in Gaining from a Training on Proportional Reasoning
Thurn, C., Nussbaumer, D., Schumacher, R., & Stern, E. (2022) · Journal of Intelligence · doi:10.3390/jintelligence10020031 · Cited by 25
Metadata
- Authors
- Wellek, S.
- Corresponding author
- Wellek, Stefan
- ORCID
- Wellek, Stefan
- Venue
- Chapman & Hall/CRC eBooks
- Publisher
- Chapman and Hall/CRC
- Published
- 2010-06-24
- OpenAlex
- W2480935928
- Cited by
- 548
- References
- 0
- Citations by year
- 2026: 23 · 2025: 19 · 2024: 31 · 2023: 30 · 2022: 50 · 2021: 57 · 2020: 69 · 2019: 49 · 2018: 55 · 2017: 30 · 2016: 30 · 2015: 37 · 2014: 19 · 2013: 24 · 2012: 19
- FWCI
- 4.76
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Chapman & Hall/CRC eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- equivalence testing, non-inferiority testing, hypothesis testing, one-sample problem, clinical trials
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