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 as 10% (ε = 0.36).
“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.”
The sample size was established a priori based on a power analysis for non-inferiority trials.
“The sample size was established a priori based on a power analysis for non-inferiority trials [53,54].”
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Lakens, D. (2017) · Social Psychological and Personality Science · doi:10.1177/1948550617697177 · Cited by 2,161 · see citing works
“When researchers want to argue for the absence of an effect that is large enough to be worthwhile to examine, they can test for equivalence (Wellek, 2010).”
Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P.-C. (2021) · Bayesian Analysis · doi:10.1214/20-ba1221 · Cited by 1,810 · see citing works
“In addition, small probability intervals can be used in practical equivalence testing (see, e.g., Wellek, 2010).”
MethodKruschke, J. K., & Liddell, T. M. (2018) · Psychonomic Bulletin & Review · doi:10.3758/s13423-016-1221-4 · Cited by 1,288 · see citing works
“A different Bayesian decision rule for equivalence examines only the posterior probability mass inside the ROPE, without regard to the HDI (e.g., Wellek, 2010) but we prefer to treat the probability density as a meaningful quantity that better handles skewed distributions (Kruschke, 2015, Section…”
Cronbach's alpha reliability: Interval estimation, hypothesis testing, and sample size planning
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Brenner, P. S., & DeLamater, J. (2016) · Social Psychology Quarterly · doi:10.1177/0190272516628298 · Cited by 457 · see citing works
Bayesian Analysis Reporting Guidelines
Kruschke, J. K. (2021) · Nature Human Behaviour · doi:10.1038/s41562-021-01177-7 · Cited by 462 · see citing works
Amrhein, V., Trafimow, D., & Greenland, S. (2019) · The American Statistician · doi:10.1080/00031305.2018.1543137 · Cited by 432 · see citing works
On the Proper Use of the Crossover Design in Clinical Trials
Wellek, S., & Blettner, M. (2012) · Deutsches Ärzteblatt international · doi:10.3238/arztebl.2012.0276 · Cited by 424 · see citing works
Self-citationStatistical Inference as Severe Testing: How to Get Beyond the Statistics Wars
Mayo, D. G. (2018) · doi:10.1017/9781107286184 · Cited by 376 · see citing works
A Review of Android Malware Detection Approaches Based on Machine Learning
Liu, K., Xu, S., Xu, G., Zhang, M., Sun, D., & Liu, H. (2020) · IEEE Access · doi:10.1109/access.2020.3006143 · Cited by 396 · see citing works
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“According to [14], a commonly used strict relative margin is 10%.”
MethodGreenland, S. (2019) · The American Statistician · doi:10.1080/00031305.2018.1529625 · Cited by 313 · see citing works
“…may even make more sense contextually to reverse the role of the test and alternative hypothesis, so that the tested H becomes |β −b| ≥ c, as in equivalence testing (Berger and Hsu 1996; Senn 2008; Wellek 2010).8 Other examples of role reversal include risklimiting audits (Lindeman and Stark 2012).”
ResultWhen 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
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Rainey, C. (2014) · American Journal of Political Science · doi:10.1111/ajps.12102 · Cited by 242 · see citing works
Assessing Structural Equation Models by Equivalence Testing With Adjusted Fit Indexes
Yuan, K., Chan, W., Marcoulides, G. A., & Bentler, P. M. (2015) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2015.1065414 · Cited by 226 · see citing works
“In contrast to NHT, equivalence testing allows us to control the size of misspecification at a prespecified value so that we can claim how good the model is with a desired level of confidence (Wellek, 2010).”
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An Equivalence Approach to Balance and Placebo Tests
Hartman, E., & Hidalgo, F. D. (2018) · American Journal of Political Science · doi:10.1111/ajps.12387 · Cited by 189 · see citing works
Equivalence Tests: A Practical Primer for t-Tests, Correlations, and Meta-AnalysesPreprint
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“Here we use the term noninferiority to denote absence of a relevant difference in spike detection sensitivity and false positive rate between the skilled human readers and a spike detection algorithm (see Wellek for discussion of noninferiority (Wellek, 2010)).”
MethodHartman, E., Grieve, R., Ramsahai, R. R., & Sekhon, J. S. (2015) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/rssa.12094 · Cited by 145 · see citing works
“We follow the recommendations of Hartman and Hidalgo (2011) and define equivalence as a mean difference between the reweighted sample treated and the true population treated of no more than 0.2 standardized differences and use the t-test for equivalence that is defined in Wellek (2010).”
MethodInfluentialMarcoulides, K. M., & Yuan, K. (2016) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705511.2016.1225260 · Cited by 151 · see citing works
“For a general treatment of the topic in statistical hypothesis testing, readers are referred to Wellek (2010).”
BackgroundComparative evaluation of heart rate-based monitors: Apple Watch vs Fitbit Charge HR
Bai, Y., Hibbing, P. R., Mantis, K., & Welk, G. J. (2017) · Journal of Sports Sciences · doi:10.1080/02640414.2017.1412235 · Cited by 147 · see citing works
“The methodology to test the equivalence null hypothesis has been previously described (Wellek, 2010) and a methodology paper written by our research group is available to provide specific examples (Dixon et al., 2017).”
MethodLeddy, J. J., Baker, J. G., Merchant, A., et al. (2014) · Clinical Journal of Sport Medicine · doi:10.1097/jsm.0000000000000128 · Cited by 144 · see citing works
“Tests of equivalence were conducted using the two one-sided test approach with an epsilon value set equal to the estimated standard error.(19) With 22 individual variables tested and using a P value of 0.”
MethodLiu, L., Wang, Y., & Xu, Y. (2020) · SSRN Electronic Journal · doi:10.2139/ssrn.3555463 · Cited by 142 · see citing works
Peugh, J., & Feldon, D. F. (2020) · CBE—Life Sciences Education · doi:10.1187/cbe.20-01-0016 · Cited by 150 · see citing works
“For SEM fit equivalence testing, the meaningful effect of interest is ε0, which quantifies a minimal acceptable value for SEM misfit (Wellek, 2010).”
BackgroundYuan, Z., Chen, H., Xie, P., Zhang, P., Liu, J., & Li, T. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107353 · Cited by 141 · see citing works
Testing Equivalence in Communication Research: Theory and Application
Weber, R., & Popova, L. (2012) · Communication Methods and Measures · doi:10.1080/19312458.2012.703834 · Cited by 135 · see citing works
“…confidence intervals is provided by standard nullhypothesis effect tests (Levine, Weber, Park et al., 2008) that are supplemented by the use of non-central sampling distributions and the determination of a “minimum substantial effect ” for the test of statistical equivalence (Wellek, 2003, 2010).”
MethodMatusiewicz, A. K., Carter, A. E., Landes, R. D., & Yi, R. (2013) · Behavioural Processes · doi:10.1016/j.beproc.2013.07.019 · Cited by 125 · see citing works
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Beninger, P., Boldina, I., & Katsanevakis, S. (2012) · Journal of Experimental Marine Biology and Ecology · doi:10.1016/j.jembe.2012.05.020 · Cited by 85 · see citing works
“These may be relatively straightforward, such as confidence interval construction (Garrett, 1997; http:// www.graphpad.com), or very sophisticated (Wellek, 2010).”
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Wellek, S. (2017) · Biometrical Journal · doi:10.1002/bimj.201700001 · Cited by 82 · see citing works
“…the construction of an optimal solution to some testing problem leads to a critical region that does not admit of a representation in terms of a p-value (noticeable examples are optimal tests for two-sided equivalence problems with nonsymmetrically specified equivalence margins—see Wellek, 2010).”
BackgroundInfluentialSelf-citationKarnani, F. (2012) · The Journal of Technology Transfer · doi:10.1007/s10961-012-9251-1 · Cited by 82 · see citing works
“The overall sample size was too small and the mean variances differed too much (cf. Wellek 2010).”
BackgroundTomaszewska, M., Nguyen, L. H., & Henebry, G. M. (2020) · Remote Sensing of Environment · doi:10.1016/j.rse.2020.111675 · Cited by 80 · see citing works
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Aliper, A. M., Csoka, A. B., Buzdin, A. A., Jetka, T., Roumiantsev, S. A., Moskalev, A., & Zhavoronkov, A. A. (2015) · Aging · doi:10.18632/aging.100717 · Cited by 77 · see citing works
“Equivalence intervals were chosen according to referenced values from [61], so that all tests are comparable (0.”
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Dennis, B., Ponciano, J. M., Taper, M. L., & Lele, S. R. (2019) · Frontiers in Ecology and Evolution · doi:10.3389/fevo.2019.00372 · Cited by 74 · see citing works
“Equivalence testing and noninferiority testing (e.g., Wellek, 2010) are statistical methods designed to address the problem that “absence of a significant effect” is not the same as “an effect is significantly absent.””
MethodKapitány, R., Kavanagh, C. M., Buhrmester, M. D., Newson, M., & Whitehouse, H. (2019) · Self and Identity · doi:10.1080/15298868.2019.1578686 · Cited by 77 · see citing works
“…of p = .0018 (accounting for 28 comparisons).3 Additionally, as it is inferentially weak to predict null findings, we conducted equivalence testing (Wellek, 2010) on fusion scores at T1 and T2 (where we did not expect any difference) using the Two One-Sided Tests (TOST) procedure (Lakens, 2017).”
MethodBadde, S., Navarro, K. T., & Landy, M. S. (2020) · Cognition · doi:10.1016/j.cognition.2019.104170 · Cited by 72 · see citing works
“Therefore, non-significant comparisons were further followed-up by a t-test for equivalence (Wellek, 2010), which enabled us to formulate the absence of a difference as an alternative hypothesis and consequently rendered it testable within the null-hypothesis significance-testing framework.”
MethodDarling, S. R., Leddy, J. J., Baker, J. G., et al. (2013) · Clinical Journal of Sport Medicine · doi:10.1097/jsm.0000000000000026 · Cited by 74 · see citing works
“Specifically, two 1-sided tests were performed with a bound of 2 for the ANAM variables and a bound of 30 for the ImPACT variables with the (unadjusted) P values given in Table 2.(29) Significance for the ImPACT equivalence tests was assessed using a Bonferroni corrected alpha level that required a P value less than 0.”
Methodvan der Meer, T., Hakhverdian, A., & Aaldering, L. (2015) · International Journal of Public Opinion Research · doi:10.1093/ijpor/edu041 · Cited by 73 · see citing works
Savard, J., Ivers, H., Savard, M., Morin, C. M., Caplette‐Gingras, A., Bouchard, S., & Lacroix, G. (2021) · SLEEP · doi:10.1093/sleep/zsab166 · Cited by 74 · see citing works
“The noninferiority of a treatment can be established: (1) by computing a direct p-value to accept or reject the null hypothesis of inferiority at a 5% alpha level or (2) by verifying whether the estimated difference and the lower bound of its 95% confidence interval falls within the pre-established noninferiority marg…”
BackgroundMicroelectrode targeting of the subthalamic nucleus for deep brain stimulation surgery
Montgomery, E. B. (2012) · Movement Disorders · doi:10.1002/mds.25000 · Cited by 71 · see citing works
Sent, U., Gössl, R., Elliott, J., et al. (2015) · Journal of Veterinary Internal Medicine · doi:10.1111/jvim.13639 · Cited by 62 · see citing works
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Müller, C., Stahl, M., Alder, M., & Müller, M. (2019) · European Journal of Open Distance and E-Learning · doi:10.2478/eurodl-2018-0006 · Cited by 60 · see citing works
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Turkstra, L. S., Quinn-Padron, M., Johnson, J., Workinger, M. S., & Antoniotti, N. M. (2011) · Journal of Head Trauma Rehabilitation · doi:10.1097/htr.0b013e31823346fc · Cited by 60 · see citing works
“Although between-conditions differences were very small, the small sample size was clearly a limitation and the study must be replicated in a larger sample so that formal tests of equivalence can be completed (see [43] for further discussion of equivalence testing).”
BackgroundRedirected Touching: Training and adaptation in warped virtual spaces
Kohli, L., Whitton, M. C., & Brooks, F. P. (2013) · IEEE Symposium on 3D User Interfaces (3DUI) · doi:10.1109/3dui.2013.6550201 · Cited by 58 · see citing works
“We would like to show that task performance in Vd is no worse than in Vo and R, which we test for by using a non-inferiority test, a form of equivalence testing [30].”
MethodBonett, D. G. (2019) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12189 · Cited by 58 · see citing works
“A 100(1 – a)% confidence interval for qi can be used to conduct a non-inferiority test (Wellek, 2010).”
BackgroundMethodInfluentialKruschke, J. K., & Liddell, T. M. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2606016 · Cited by 57 · see citing works
Performing Inferential Statistics Prior to Data Collection
Trafimow, D., & MacDonald, J. A. (2016) · Educational and Psychological Measurement · doi:10.1177/0013164416659745 · Cited by 56 · see citing works
“…idea is to control the size of misspecification at a prespecified value so as to assess the goodness of the model at a desired level of confidence (Wellek, 2010).2 Equivalence testing has been advocated, for example, when the goal is to show that a treatment is equivalent to some other…”
BackgroundTests for multivariate normality—a critical review with emphasis on weighted $$L^2$$-statistics
Ebner, B., & Henze, N. (2020) · Test · doi:10.1007/s11749-020-00740-0 · Cited by 1 · see citing works
“Notice that this test is in the spirit of bioequivalence testing (see, e.g., Czado et al. (2007), Dette and Munk (2003) or Wellek (2010)), since it aims at validating a certain neighborhood of a hypothesized model.”
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Nelli, D., Rossi, G., Wang, Z., et al. (2020) · Nanoscale · doi:10.1039/c9nr10163b · Cited by 56 · see citing works
McGarvey, D. J., Menon, M., Woods, T. E., et al. (2017) · Ecography · doi:10.1111/ecog.03134 · Cited by 55 · see citing works
“Hypotheses regarding the overall differences between CPC and IPC models were then tested with the ‘two one-sided tests of equivalence’ (TOST; Wellek 2010) procedure.”
MethodEvaluating Equivalence Testing Methods for Measurement Invariance
Counsell, A., Cribbie, R. A., & Flora, D. B. (2019) · Multivariate Behavioral Research · doi:10.1080/00273171.2019.1633617 · Cited by 54 · see citing works
“Many univariate equivalence tests (EQs) have been developed for evaluating means (e.g., Anderson & Hauck, 1983; Koh & Cribbie, 2013; Mara & Cribbie, 2012; Schuirmann, 1987; Wellek, 2010; Westlake, 1972) and correlations (e.g., Counsell & Cribbie, 2015; Goertzen & Cribbie, 2010).”
BackgroundLv, Z., Wang, W., Xu, Z., Zhang, K., Fan, Y., & Song, Y. S. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107891 · Cited by 53 · see citing works
Developing a Bi-objective Mathematical Model to Design the Fish Closed-loop Supply Chain
Fasihi, M., Tavakkoli-Moghaddam, R. R., Najafi, E., et al. (2021) · International Journal of Engineering · doi:10.5829/ije.2021.34.05b.19 · Cited by 53 · see citing works
“Testing the hypothesis of equality of means is appropriate for comparing the results of two samples [39].”
ResultBouchard, S., Allard, M., Robillard, G., Dumoulin, S., Guitard, T., Loranger, C., Green-Demers, I., Marchand, A., Renaud, P., Cournoyer, L.-G., et al. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.02164 · Cited by 52 · see citing works
“Repeated measures ANOVAs were performed to document treatment efficacy, and non-inferiority was tested using Wellek (2010) procedures and tables using a strict margin of tolerance for non-inferiority of 0.20 at the significance level of 0.05.”
MethodInfluentialKremsner, P. G., Adégnika, A. A., Hounkpatin, A. B., Zinsou, J. F., Taylor, T. E., Chimalizeni, Y. F., Liomba, A., Kombila, M., Bouyou-Akotet, M. K., Mboumba, D. P. M., et al. (2016) · PLoS Medicine · doi:10.1371/journal.pmed.1001938 · Cited by 51 · see citing works
“Fisher’s exact test for one-sided equivalence [22] was used to assess treatment group differences in parasite clearance for the per-protocol (PP) and intention-to-treat (ITT) populations, and Artesunate and Severe Malaria in Children”
MethodGodfroid, A., & Spino, L. A. (2015) · Language Learning · doi:10.1111/lang.12136 · Cited by 50 · see citing works
Mechler, J., Lindqvist, K., Carlbring, P., Topooco, N., Falkenström, F., Lilliengren, P., Andersson, G., Johansson, R., Midgley, N., Edbrooke-Childs, J. H., et al. (2022) · The Lancet Digital Health · doi:10.1016/s2589-7500(22)00095-4 · Cited by 48 · see citing works
“20,31 Cohen’s d was calculated following recommendations by Feingold, 32 using change over time from estimated fixed effects from the final model and the observed pretreatment sample SD.”
Functional data analysis in the Banach space of continuous functions
Dette, H., Kokot, K., & Aue, A. (2020) · The Annals of Statistics · doi:10.1214/19-aos1842 · Cited by 48 · see citing works
“Observe also that tests for relevant differences between two finite-dimensional parameters corresponding to different populations have been considered mainly in the biostatistical literature, for example in Wellek [44].”
BackgroundInfluentialP > .05: The incorrect interpretation of “not significant” results is a significant problem
Smith, R. J. (2020) · American Journal of Physical Anthropology · doi:10.1002/ajpa.24092 · Cited by 47 · see citing works
Lackner, J. M., Keefer, L., Jaccard, J. J., Firth, R. S., Brenner, D. M., Bratten, J. R., Dunlap, L. J., Ma, C., & Byroads, M. (2012) · Contemporary Clinical Trials · doi:10.1016/j.cct.2012.07.013 · Cited by 47 · see citing works
“If the upper limit of the interval is less than +TV and the lower limit of the interval is greater than−TV, then functional equivalence is declared [95].”
BackgroundBaringhaus, L., Ebner, B., & Henze, N. (2016) · Annals of the Institute of Statistical Mathematics · doi:10.1007/s10463-016-0567-8 · Cited by 47 · see citing works
“Notice that this test is in the spirit of bioequivalence testing [see, e.g., Czado et al. (2007) or Wellek (2010)], since it aims at validating a certain neighborhood of a hypothesizedmodel.”
MethodTesting Relevant Hypotheses in Functional Time Series via Self-Normalization
Dette, H., Kokot, K., & Stanislav Volgushev, A. (2020) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12370 · Cited by 48 · see citing works
“(1.2) and (1.3) are called precise hypotheses or relevant hypotheses in the literature [see Berger and Delampady (1987)] and are frequently used in biostatistics. We refer to Chow and Liu (1992) and Wellek (2010) for more details and applications. In this paper we discuss the problem of testing relevant hypotheses in…”
BackgroundInfluentialMichaelsen, P., Johansson, L., & Hedesström, M. (2021) · Behavioural Public Policy · doi:10.1017/bpp.2021.5 · Cited by 46 · see citing works
A step-by-step guide on preregistration and effective data sharing for psychopathology research.
Krypotos, A., Klugkist, I. G., Mertens, G., & Engelhard, I. M. (2019) · Journal of Abnormal Psychology · doi:10.1037/abn0000424 · Cited by 40 · see citing works
Lamanna, C. A., Hachhethu, K., Chesterman, S., Singhal, G., Mwongela, B., Ngendo, M., Passeri, S., Farhikhtah, A., Kadiyala, S., Bauer, J.-M., et al. (2019) · PLoS ONE · doi:10.1371/journal.pone.0210050 · Cited by 44 · see citing works
“Equivalence Tests [49] against varying levels of difference assessed if differences by mode were clinically significant (large enough in magnitude to alter a nutritionist’s interpretation of the resultant data).”
BackgroundExact Power and Sample Size Calculations for the Two One-Sided Tests of Equivalence
Shieh, G. (2016) · PLoS ONE · doi:10.1371/journal.pone.0162093 · Cited by 42 · see citing works
Expanding Statistical Frontiers in Sexual Science: Taxometric, Invariance, and Equivalence Testing
Sakaluk, J. K. (2019) · The Journal of Sex Research · doi:10.1080/00224499.2019.1568377 · Cited by 39 · see citing works
“Key TOST references (e.g., Schuirmann, 1987; Wellek, 2010), for example, have not yet been cited in any articles published in JSR or ASB.”
Should Rape Kit Testing Be Prioritized by Victim–Offender Relationship?
Campbell, R., Pierce, S. J., Sharma, D. B., Feeney, H., & Fehler‐Cabral, G. (2016) · Criminology & Public Policy · doi:10.1111/1745-9133.12205 · Cited by 40 · see citing works
Equivalence of Regression Curves
Dette, H., Möllenhoff, K., Stanislav Volgushev, A., & Bretz, F. (2017) · Journal of the American Statistical Association · doi:10.1080/01621459.2017.1281813 · Cited by 39 · see citing works
“If the null hypothesis is rejected, one can then claim at a prespecified significance level α that, in the previous example, the two treatments have an equivalent effect (see Wellek 2010).”
BackgroundHarris, A. H. S., Fernandes‐Taylor, S., & Giori, N. J. (2012) · Journal of Bone and Joint Surgery · doi:10.2106/jbjs.k.00568 · Cited by 39 · see citing works
Conditional equivalence testing: An alternative remedy for publication bias
Campbell, H., & Gustafson, P. (2018) · PLoS ONE · doi:10.1371/journal.pone.0195145 · Cited by 40 · see citing works
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Baringhaus, L., & Henze, N. (2017) · Journal of nonparametric statistics · doi:10.1080/10485252.2017.1285029 · Cited by 35 · see citing works
Union–intersection permutation solution for two-sample equivalence testing
Pesarin, F., Salmaso, L., Carrozzo, E., et al. (2015) · Statistics and Computing · doi:10.1007/s11222-015-9552-y · Cited by 35 · see citing works
“…perspectives, we do not consider here any comparison with the so-called Intersection–Union approach to the general equivalence and non inferiority problems as used in some questions linked to clinical trials and pharmacostatistics (Berger 1982; Hung and Wang 2009; Romano 2005; Wellek 2010).”
MethodJiang, G., Mai, Y., & Yuan, K. (2017) · Frontiers in Psychology · doi:10.3389/fpsyg.2017.01823 · Cited by 35 · see citing works
“ET can also be used for parameter testing, especially when a particular value of the parameter is of special interest (Wellek, 2010).”
MethodEstablishing Equivalence or Non-Inferiority in Clinical Trials
Wellek, S., & Blettner, M. (2012) · Deutsches Ärzteblatt international · doi:10.3238/arztebl.2012.0674 · Cited by 36 · see citing works
“The statistical literature contains a number of optimal tests for equivalence and non-inferiority hypotheses that cover a large range of situations differing with respect to study design and the nature of the outcome variable (4).”
BackgroundSelf-citationDesign and Analysis of Replication Studies
Bonett, D. G. (2020) · Organizational Research Methods · doi:10.1177/1094428120911088 · Cited by 34 · see citing works
“If the response variable is dichotomous in a two-group design, Wellek (2010) recommended specifying the ROPE in terms of a log-odds ratio rather than a difference in proportions.”
BackgroundMethodSanz, G., Martínez-Aranda, L. M., Tesch, P. A., Fernandez‐Gonzalo, R., & Lundberg, T. R. (2019) · Journal of Applied Physiology · doi:10.1152/japplphysiol.00257.2019 · Cited by 32 · see citing works
Using Noninferiority Tests to Evaluate Telemedicine and E-Health Services: Systematic Review
Kummervold, P. E., Johnsen, J.-A. K., Skrøvseth, S. O., & Wynn, R. (2012) · Journal of Medical Internet Research · doi:10.2196/jmir.2169 · Cited by 34 · see citing works
Mullins, F. (2017) · Human Resource Management · doi:10.1002/hrm.21828 · Cited by 33 · see citing works
Basic statistical considerations for physiology: The journal Temperature toolbox
Caldwell, A. R., & Cheuvront, S. N. (2019) · Temperature · doi:10.1080/23328940.2019.1624131 · Cited by 35 · see citing works
“Instead, we encourage researchers to use wellestablished and valid tests of equivalence, superiority, or non-inferiority which have known error rates that do not change with sample size [53].”
MethodTroesch, B., Demmelmair, J., Gimpfl, M., Hecht, C., Lakovic, G., Roehle, R., Sipka, L., Trisic, B., Vusurovic, M., Schoop, R., et al. (2019) · PLoS ONE · doi:10.1371/journal.pone.0216790 · Cited by 33 · see citing works
“For the primary analysis following Schuirman [26] and Wellek [27], both groups were considered equivalent if the 95% CI for the difference of the mean daily weight gain was within the pre-specified equivalence margin of ±3.”
MethodInfluentialSuarez‐Sharp, S., Abend, A. M., Hoffelder, T., LeBlond, D. J., Delvadia, P. R., Kovács, E. T., & Diaz, D. A. (2020) · The AAPS Journal · doi:10.1208/s12248-020-00458-9 · Cited by 33 · see citing works
Puhlmann, L. M. C., Linz, R., Valk, S. L., Vrtička, P., de Wael, R. V., Bernasconi, A., Bernasconi, N., Caldairou, B., Papassotiriou, I., Chrousos, G. P., et al. (2021) · NeuroImage · doi:10.1016/j.neuroimage.2021.118011 · Cited by 34 · see citing works
“non-significant p-values in null hypothesis tests), we employed equivalence tests (Wellek, 2010).”
Nearby outdoor recreation modelling: An agent-based approach
Мorelle, К., Buchecker, M., Kienast, F., & Tobias, S. (2018) · Urban forestry & urban greening · doi:10.1016/j.ufug.2018.07.007 · Cited by 32 · see citing works
“We performed a two one-sided t-test (TOST) (Wellek 2010).”
MethodShieh, G. (2019) · Statistics in Biopharmaceutical Research · doi:10.1080/19466315.2019.1677495 · Cited by 32 · see citing works
“The related extensions of ANOVA F-test and the studentized range test for assessing equivalence between several groups have been addressed in Giani and Finner (1991), Shieh (2016b), and Wellek (2010).”
MethodHüls, A., Krämer, U., Stolz, S., et al. (2016) · PLoS ONE · doi:10.1371/journal.pone.0157569 · Cited by 32 · see citing works
“We first tested our data for a healthy survivor bias by comparing baseline lung function indices and baseline covariates of the HNSW lost to follow-up to baseline characteristics of the HNSW available at follow-up (two-sample t-test [13] and Fisher's exact test [14] at the 5% significance level).”
Method
- 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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