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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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“, factorial ANOVA F test) are not suitable for assessing a lack of relationship (e.g., Rogers, Howard, & Vessey, 1993; Wellek, 2010).”
BackgroundMethodTesting for a lack of relationship among categorical variables
Shishkina, T., Farmus, L., & Cribbie, R. A. (2018) · The Quantitative Methods for Psychology · doi:10.20982/tqmp.14.3.p167 · Cited by 12
“Following Wellek (2010),H0: D∗2 ≥ ε2 is rejected if the upper limit of the 1−α CI forD2 falls below ε2, where the upper limit forD2 is calculated as: D2 + z1−αseD2 , where seD2 = vn/ √ n and D2 = r∑ i=1 c∑ j=1 (πij − g (πij))2 = r∑ i=1 c∑ j=1 (πij − γi (π) ηj (π))2 where πij = (nij/N represents the observed probabilit…”
BackgroundMethodInfluentialWiegel, T., Albers, P., Bartkowiak, D., Bussar-Maatz, R., Härter, M. C., Kristiansen, G., Martus, P., Wellek, S., Schmidberger, H., Grozinger, K., et al. (2020) · Journal of Cancer Research and Clinical Oncology · doi:10.1007/s00432-020-03327-2 · Cited by 12
“Sample size planning (N = 7.600) was subject to the requirement that the one-sided log-rank test for noninferiority (Wellek 2010) at a multiplicity-corrected significance level of 1.67% should provide a power of 90% against the alternative that the probability of not dying from PCa within 13 years…”
MethodInfluentialSelf-citationClarke, P., Bibby-Jones, A.-M., & Hayward, M. (2021) · The Cognitive Behaviour Therapist · doi:10.1017/s1754470x21000143 · Cited by 12
“For our primary outcome only, if the between-group pre–post difference was non-significant (i.e. the interaction was p>0.05), then pre–post differences for the two groups were tested for statistical equivalence using the confidence interval approach (Wellek, 2010).”
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“Like these methods, equivalence testing (see, e.g., Wellek 2010; Walker and Nowacki 2011; Anderson-Cook and Borror 2016) also acknowledges the distinction between statistical and practical significance and also requires defining a ROPE.”
MethodMasharipov, R. S., Knyazeva, I., Nikolaev, Y., Korotkov, A. D., Didur, M., Cherednichenko, D. V., & Kireev, M. V. (2021) · Frontiers in Neuroinformatics · doi:10.3389/fninf.2021.738342 · Cited by 12
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“In statistics such an equivalence procedure (equivalence is assessed if several componentwise tests all decide in favor of equivalence) is called intersection–union test (21).”
MethodEfficient collection of training data for sub-pixel land cover classification using neural networks
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“, its probability of demonstrating equivalence where it exists), and demonstrating equivalence requires a larger sample size, generally, than showing a difference in a traditional test (5).”
BackgroundInfluentialJennen-Steinmetz, C. (2013) · Statistics in Medicine · doi:10.1002/sim.6024 · Cited by 11
“The latter scale should be favored, as it applies to the specification of indifference zones for equivalence testing of two proportions ([21] Chap.”
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“In this study, we evaluated the validity of the peer score by comparing the average weighted peer score and the R score using equivalence testing [39,40].”
MethodAllan, T. A., & Cribbie, R. A. (2013) · Canadian Journal of Behavioural Science/Revue canadienne des sciences du comportement · doi:10.1037/a0033357 · Cited by 10
“The significance testing for equivalence literature cites both examples of correctly and incorrectly applied procedures (Kline, 2004; Wellek, 2010).”
BackgroundMethodInfluentialNurmi, T., Jaatela, J., Vallinoja, J., et al. (2021) · NeuroImage Clinical · doi:10.1016/j.nicl.2021.102795 · Cited by 10
“254 Equivalence testing (R package: equivUMP, function: equiv.test; Wellek, 2010) where the null 255 hypothesis is reversed (i.e. null hypothesis: there is difference between index finger and ankle 256 stimulation) was used to see if head movement during finger stimulation was similar to head 257…”
MethodSteuer, T., Filighera, A., Tregel, T., & Miede, A. (2022) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2022.900304 · Cited by 10
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“Although the correction methods have been criticized (e.g. Cunningham & Baumeister, 2016), these null effects (or better, the effect sizes equivalent to zero; Wellek, 2010) were confirmed by a large multi-lab replication project (Hagger et al., 2016).”
MethodPharmacokinetics of Coencapsulated Antiretrovirals with Ingestible Sensors
Liu, H., Daar, E. S., Wang, Y., Siqueiros, L., Campbell, K. M., Shen, J., Guerrero, M., Ko, M.-W., Xiong, D., Dao, J., et al. (2019) · AIDS Research and Human Retroviruses · doi:10.1089/aid.2019.0202 · Cited by 10
“If coencapsulation did reduce or delay Cmax, this choice could bias (minimize) an effect on AUC.”
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“(Testing for equivalence could be used instead, see Wellek, 2010.)”
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“Questions about whether the effects produced by VCP are essentially the same or, at least, not meaningfully worse than IP are better answered by equivalence and noninferiority designs (Wellek, 2010).”
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“Согласно Wellek [6] функция T2EQ может применяться для оценки эквивалентности профилей СТКР ЛС.”
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“This procedure is called equivalence (Lakens, 2017; Wellek, 2010).”
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“…is to explicitly quantify the evidence for the absence of an effect, more appropriate methods designed for this task, such as equivalence testing ( Wellek, 2010 ; Lakens, 2017 ; Senn, 2021 ) or Bayes factors ( Kass and Raftery, 1995 ; Goodman, 1999 ; Goodman, 2005 ; Dienes, 2014 ; Keysers et al.,…”
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“The third equivalence test is the Wellek’s test 40,41 that determines whether if the probability of the difference of two random variables lies within a (small) threshold around 50%.”
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“To this end, equivalence between the two multinomial distributions was tested using the goodness-of-fit χ(2)-test (31), with a significance level of 5% and an equivalence margin of 0.”
MethodEquivalence hypothesis testing in experimental software engineering
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“The underlying idea in this procedure is to compute a (1 - 2 a )100 % statistical confidence interval around the sample mean differences, (cid:2) l T (cid”
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“The null hypothesis of dissimilarity is rejected if the region of equivalence does not contain these confidence intervals entirely (Wellek, 2010).”
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“In the context of equivalence testing, Giani and Finner (1991), Wellek (2010), and Shieh (2016) examined the analysis of variance (ANOVA) F-test based on the variance of the standardized means and the studentized range test for the range of the standardized means.”
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“Traditional statistics, ANOVAs, were performed first and followed up with confidence interval equivalency tests to determine whether the performance of the novices and intermediates was statistically equivalent to the experts (Snow, Reising, Barry, & Hartstock, 1999; Wellek, 2010).”
MethodStevens, N. T., Lu, L., Anderson‐Cook, C. M., & Rigdon, S. E. (2020) · Quality Engineering · doi:10.1080/08982112.2020.1741619 · Cited by 8
“…of agreement (BPA) approach builds on the fundamental assumption of equivalence testing (Anderson-Cook and Borror (2016); Szarka III (2014); Wellek (2010); Richter and Richter (2002)), which is that the populations are more safely assumed to be different until there is evidence to support…”
BackgroundStern, M. B., Follett, K. A., & Weaver, F. M. (2013) · PubMed · Cited by 8
What to make of non-inferiority and equivalence testing with a post-specified margin?Preprint
Campbell, H., & Gustafson, P. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1807.03413 · Cited by 8
“Instead, to correctly conclude the absence of an effect under the frequentist paradigm, the recommended tool is the equivalence test (also known as a “non-inferiority test” for one-sided testing [44]), which tests whether an effect is at most constrained within a given equivalence margin.”
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“, [16]), to reject the null hypothesis in (7) if the one-sided 1− α confidence interval [0, du] defined in (6) is completely inside the parametric region of H1 (i.”
BackgroundEquivalence Testing Based Fit Index: Standardized Root Mean Squared Residual
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A unified approach to permutation testing for equivalence
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“…IU-NPC permutation approach is it possible to express margins in terms of the same physical measurement units of variable X. Rank solutions as discussed in Wellek (2010) and Janssen and Wellek (2010) express margins in terms of rank transformations so as to mimic solutions based on normal settings.”
BackgroundMethodInfluentialAn Equivalence Testing Approach for Evaluating Substantial Mediation
Beribisky, N., Mara, C. A., & Cribbie, R. A. (2020) · The Quantitative Methods for Psychology · doi:10.20982/tqmp.16.4.p424 · Cited by 7
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“Further to the above, Wellek (2010) provided a definition about this testing: “equiva-lence means here equality except for practically irrelevant deviations” (p. 1): i.e., the difference between two populations’ means ( (cid:22) 1 – (cid:22) 2 ) is within two limits: i.e., Lower Equivalence bound (…”
InfluentialBrown, S., Song, M., Cook, T. D., & Garet, M. S. (2022) · American Educational Research Journal · doi:10.3102/00028312221136565 · Cited by 6
“…causal signs or statistical significance patterns, (b) the RCT and NECGD estimates having similar theoretical or policy implications, (c) researcher consensus about a particular ROPE criterion, or (d) results from equivalence and nonequivalence statistical tests (Rogers et al., 1993; Wellek, 2010).”
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“Statistical equivalence tests [12] were performed based on 95% two-sided Tukey confidence intervals (CIs) of differences of the mean LRs observed from the theoretical LR using an equivalency margin 0.5 log 10 .”
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“Wellek (2010, Table 1.1) defines a strict margin to be d S = 0 .”
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“Our results can be seen as a generalization of the confidence interval inclusion principle in one-dimensional equivalence testing, cf. chapter 3.1 in Wellek (2010): If a (1 − 2𝛼)-confidence interval 𝐶 for 𝜃 ∈ R is given, then for any bounded interval𝑅 the rule to reject𝐻0 ∶ 𝜃 ∉ 𝑅 if 𝐶 ⊆ 𝑅…”
InfluentialBio-equivalence tests in functional data by maximum deviation
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“1 of [10] defines equivalence between multinomial distributions of common dimension k in terms of the Euclidean distance between the corresponding parameter vectors π and π ̊, where π refers to the unknown distribution underlying the data and π ̊ to the model to be fitted.”
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“Other ROPE-based approaches are also appealing for equivalence testing such as using the proportion of the posterior mass inside the ROPE rather than just the overlapwith the 95%HDI (Wellek, 2010).”
MethodInvestigating non-inferiority or equivalence in time-to-event data under non-proportional hazards
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“Bayesian probability of agreement between system and component reliabilities An alternative to the standard hypothesis test proposed is the equivalence test (Wellek, 2010).”
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“…hypothesis H 1 ,j : γ j (cid:54) = 0 holds) or in formula Then a simultaneous test for H 0 can be conducted by applying Hotelling’s T 2 test statistic (Wellek, 2010, pp. 235–264) as follows: Under For example, to perform a simultaneous test of no DIF in m items we can use the global test…”
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“A more informative element in conventional statistical inference is the p-value, which is the area beyond the observed statistic under the probability-density curve of ðFT jH0Þ: The concept of p-value in ET is defined similarly (Wellek, 2010).”
BackgroundProcedure to categorize wheelchair cushion performance using compliant buttock models
Sprigle, S. H., & Deshpande, Y. (2022) · Frontiers in Bioengineering and Biotechnology · doi:10.3389/fbioe.2022.1006767 · Cited by 5
“Its analysis is often more appropriate than inferring a lack of a difference when assessed by traditional statistical means (Wellek, 2010).”
BackgroundA novel embedded kernel CNN-PCFF algorithm for breast cancer pathological image classification
Liu, W., Liang, S., & Qin, X. (2024) · Scientific Reports · doi:10.1038/s41598-024-74025-z · Cited by 5
Zhang, L., Pan, Z., Zheng, X., Wang, Q., Tang, P., Zhou, F., Liu, F., Yu, B., Leung, F. K. L., Wu, A., et al. (2023) · European Journal of Trauma and Emergency Surgery · doi:10.1007/s00068-023-02231-x · Cited by 6
Effect sizes for equivalence testing: Incorporating the equivalence interval
Gutierrez, N. M., & Cribbie, R. A. (2023) · Methods in Psychology · doi:10.1016/j.metip.2023.100127 · Cited by 5
“Generally, it is advised that the EI be specified a priori to data collection (Lakens et al., 2018; Wellek, 2010).”
BackgroundMethodPredictors of Parkinson's disease—not quite sound
Montgomery, E. B. (2013) · Movement Disorders · doi:10.1002/mds.25432 · Cited by 5
“The appropriate analytic method involves determining, before conducting the study, the magnitude and direction (greater, lesser, or the same) of a meaningful difference.(5) Neither correct nor incorrect, the conclusions reached by Behnke and colleagues simply cannot be interpreted.”
MethodEvaluation of estimation models using the Minimum Interval of Equivalence
Dolado, J. J., Rodríguez, D., Harman, M., Langdon, W. B., & Sarro, F. (2016) · Applied Soft Computing · doi:10.1016/j.asoc.2016.03.026 · Cited by 5
Morgan, B., Chen, S. Y., Christopher, D., et al. (2018) · AAPS PharmSciTech · doi:10.1208/s12249-017-0941-8 · Cited by 5
Traditional and bayesian approaches for testing mean equivalence and a lack of association
Hoyda, J. J., Counsell, A., & Cribbie, R. A. (2019) · The Quantitative Methods for Psychology · doi:10.20982/tqmp.15.1.p012 · Cited by 5
“Over the past few decades, the field of equivalence testing has provided a variety of alternative hypothesis testing methods to assess whether groups of subjects do not differ significantly on an outcome variable (e.g., Anderson & Hauck, 1983; Wellek, 2010; Westlake, 1976).”
BackgroundMisinformation Effect in Aging: A New Light with Equivalence Testing
Tessoulin, M., Galharret, J., Gilet, A.-L., & Colombel, F. (2019) · The Journals of Gerontology Series B · doi:10.1093/geronb/gbz057 · Cited by 5
Guo, J., & Luh, W. (2019) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12172 · Cited by 5
The Impact of Major Events on Ongoing Noninferiority Trials, With Application to COVID-19
Wiens, B. L., & Lipkovich, I. A. (2020) · Statistics in Biopharmaceutical Research · doi:10.1080/19466315.2020.1788983 · Cited by 5
“More comprehensive discussions can be found in, for example, Wellek (2010) or Rothmann, Wiens, and Chan (2012).”
BackgroundMath approach training changes implicit identification with math: A close preregistered replication
Batailler, C., Dominique Muller, B., Nurra, C., Rougier, M., & Trouilloud, D. O. (2020) · Journal of Experimental Social Psychology · doi:10.1016/j.jesp.2020.104059 · Cited by 5
With Bayesian estimation one can get all that Bayes factors offer, and more
Kiers, H. A. L., & Kiers, H. A. L. (2022) · Psychonomic Bulletin & Review · doi:10.3758/s13423-022-02164-3 · Cited by 10
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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