Multiple Comparisons Using R
Abstract
Adopting a unifying theme based on maximum statistics, Multiple Comparisons Using R describes the common underlying theory of multiple comparison procedures through numerous examples. It also presents a detailed description of available software implementations in R. The R packages and source code for the analyses are available at https://CRAN.R-pro
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After Bonferroni correction, only the projections of areas 7A and DP to area 10 were inconsistent despite a statistically very low probability of being so.
“After applying the Bonferroni correction for evaluating multiple probabilities (Bretz et al. 2010), only the projections of areas 7A and DP to area 10 were inconsistent despite a statistically very low probability of being so.”
From A Weighted and Directed Interareal Connectivity Matrix for Macaque Cerebral Cortex (2014) · cites this paper as Bretz et al. 2010
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“ing multiple probabilities (Bretz et al. 2010), only the projections of areas 7A and DP to area 10 were inconsistent despite a statistically very low probability of being so.”
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“Then, we performed multiple comparisons “glht” among treatments by using the “Tukey” test and the function “sandwich” from the eponymous R package; this function provided a heteroscedasticity-consistent estimate of the covariance matrix (Zeileis, 2006; Bretz et al., 2011).”
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“The Holm procedure is slightly more powerful than the Bonferroni correction, without requiring additional assumptions (for other approaches, see Bretz et al., 2011).”
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“Significant findings between the groups were compared using the glht function in R (Bretz et al., 2010).”
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“62 Herein we focus on commonly encountered questions about the need for multiplicity corrections, using a tutorial style.”
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“Berger (1982) proposed this approach as an intersection–union test (Berger, 1982; Berger & Hsu, 1996; Bretz et al., 2011, p. 22).”
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“Each hypothesis was tested for each building, introducing the multiple comparison problem, which increases the probability of committing a Type I error (Bretz et al. 2010).”
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“For a comprehensive overview of parametric multiple contrast tests and SCI we refer the reader to Bretz, Hothorn, and Westfall (2010) and references therein.”
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“…was found to be significant at the P < 0.1 level following false discovery rate correction using the method of Benjamini & Hochberg (1995), a post hoc Tukey’s test was used to evaluate the significance of each pairwise comparison using the function ghlt of the multcomp package (Bretz et al. 2010).”
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“Post-hoc test were performed using glht function of the package multcomp [44].”
MethodElevated virulence of an emerging viral genotype as a driver of honeybee loss
McMahon, D. P., Natsopoulou, M. E., Doublet, V., Fürst, M. A., Weging, S., Brown, M. J. F., Gogol‐Döring, A., & Paxton, R. J. (2016) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2016.0811 · Cited by 244 · see citing works
“The R package ‘multcomp’ [46] was used for comparing significant differences between treatment means, using Bonferroni correction to account for multiple testing.”
MethodSonbul, S., & Schmitt, N. (2012) · Language Learning · doi:10.1111/j.1467-9922.2012.00730.x · Cited by 236 · see citing works
opm: an R package for analysing OmniLog® phenotype microarray data
Vaas, L. A. I., Sikorski, J., Hofner, B., Fiebig, A., Buddruhs, N., Klenk, H., & Göker, M. (2013) · Bioinformatics · doi:10.1093/bioinformatics/btt291 · Cited by 220 · see citing works
“Since most addressed experimental questions require to statistically compare not only single curves, but distinct groups of curves, the package provides adapted functionality for performing simultaneous multiple comparisons of group means (Bretz, Hothorn, and Westfall 2010).”
MethodVickerstaff, V., Omar, R., & Ambler, G. (2019) · BMC Medical Research Methodology · doi:10.1186/s12874-019-0754-4 · Cited by 212 · see citing works
“In the context of multiple outcomes, the power of the study can be defined in a number of ways depending on the clinical objective of the trial: i) ‘disjunctive power’, ii) ‘conjunctive power’ or iii) ‘marginal power’ [12].”
BackgroundInfluentialJakobsen, J. C., Gluud, C. N., Winkel, P., Lange, T., & Wetterslev, J. (2014) · BMC Medical Research Methodology · doi:10.1186/1471-2288-14-34 · Cited by 201 · see citing works
Rapid publication-ready MS-Word tables for one-way ANOVA
Assaad, H., Zhou, L. F., Carroll, R. J., & Wu, G. (2014) · SpringerPlus · doi:10.1186/2193-1801-3-474 · Cited by 203 · see citing works
“Increasing the power can be done by extending single-step testing procedures into stepwise procedures via a technique known as the closure principle (Bretz et al. 2010).”
MethodBlomster, T., Salojärvi, J., Sipari, N., Brosché, M., Ahlfors, R., Keinänen, M., Overmyer, K., & Kangasjärvi, J. (2011) · PLANT PHYSIOLOGY · doi:10.1104/pp.111.181883 · Cited by 188 · see citing works
“Contrasts were computed with the multcomp package (Bretz et al., 2010) with single-step P value correction.”
MethodDeep ploughing increases agricultural soil organic matter stocks
Alcántara, V., Don, A., Well, R., & Nieder, R. (2016) · Global Change Biology · doi:10.1111/gcb.13289 · Cited by 184 · see citing works
“The P-values were computed with Tukey’s ‘honest significant difference’ of means on 95% family-wise confidence level with Bonferroni correction (Bretz et al., 2010).”
MethodSeasonal priority effects: implications for invasion and restoration in a semi‐arid system
Wainwright, C. E., Wolkovich, E. M., & Cleland, E. E. (2011) · Journal of Applied Ecology · doi:10.1111/j.1365-2664.2011.02088.x · Cited by 170 · see citing works
Simulating ideal assistive devices to reduce the metabolic cost of walking with heavy loads
Dembia, C. L., Silder, A., Uchida, T. K., Hicks, J. L., & Delp, S. L. (2017) · PLoS ONE · doi:10.1371/journal.pone.0180320 · Cited by 170 · see citing works
Vaas, L. A. I., Sikorski, J., Michael, V., Göker, M., & Klenk, H. (2012) · PLoS ONE · doi:10.1371/journal.pone.0034846 · Cited by 165 · see citing works
“Second, as a somewhat more sophisticated approach, we provide a simultaneous multiple comparison procedure of means [70].”
MethodStatistical Analysis and Modeling of Mass Spectrometry-Based Metabolomics Data
Bowei Xi, C., Gu, H., Baniasadi, H. R., & Raftery, D. (2014) · Methods in molecular biology · doi:10.1007/978-1-4939-1258-2_22 · Cited by 164 · see citing works
“multiple comparison procedures such as the Bonferroni correction are too conservative and do not work well [10]; they set a cutoff value that is too close to 0 as the number of tests becomes large.”
Role of somatostatin-positive cortical interneurons in the generation of sleep slow waves
Funk, C. M., Peelman, K., Bellesi, M., Marshall, W., Cirelli, C., & Tononi, G. (2017) · The Journal of Neuroscience · doi:10.1523/jneurosci.1303-17.2017 · Cited by 145 · see citing works
“All post hoc comparisons in the LME models were z tests, performed using the glht() function of the multcomp package in R, with p values adjusted for multiple comparisons using the single-step method (Bretz et al., 2011).”
MethodRank-based multiple test procedures and simultaneous confidence intervals
Konietschke, F., Hothorn, L. A., & Brunner, E. (2012) · Electronic Journal of Statistics · doi:10.1214/12-ejs691 · Cited by 158 · see citing works
“For a comprehensive overview of existing parametric methods we refer to Bretz, Hothorn, and Westfall (2010) [4].”
MethodMichl, S. C., Ratten, J.-M., Beyer, M., Hasler, M., LaRoche, J., & Schulz, C. (2017) · PLoS ONE · doi:10.1371/journal.pone.0177735 · Cited by 158 · see citing works
Traditional multiplicity adjustment methods in clinical trials
Dmitrienko, A. A., & D’Agostino, R. B. (2013) · Statistics in Medicine · doi:10.1002/sim.5990 · Cited by 153 · see citing works
Destructive disinfection of infected brood prevents systemic disease spread in ant colonies
Pull, C. D., Ugelvig, L. V., Wiesenhofer, F. M., Grasse, A. V., Tragust, S., Schmitt, T., Brown, M. J. F., & Cremer, S. (2017) · eLife · doi:10.7554/elife.32073 · Cited by 147 · see citing works
Fischer, C., Roscher, C., Jensen, B., Eisenhauer, N., Baade, J., Attinger, S., Scheu, S., Weisser, W. W., Schumacher, J., & Hildebrandt, A. (2014) · PLoS ONE · doi:10.1371/journal.pone.0098987 · Cited by 140 · see citing works
“As the effects of the presence (or absence) of certain plant functional groups on the response variable were considered as post-hoc tests, the respective p-values were adjusted according to the Holm procedure to avoid inflation of Type I error rates [52].”
MethodMultiple testing in statistical analysis of systems-based information retrieval experiments
Carterette, B. (2012) · ACM Transactions on Information Systems · doi:10.1145/2094072.2094076 · Cited by 142 · see citing works
“A more powerful approach to adjusting p-values uses information about correlations between hypotheses [Hothorn et al. 2008; Bretz et al. 2010].”
MethodSimultaneous and selective inference: Current successes and future challenges
Benjamini, Y. (2010) · Biometrical Journal · doi:10.1002/bimj.200900299 · Cited by 169 · see citing works
“I was equally happy to learn that the book by Bretz et al. (2010) ‘‘Multiple Comparisons using R’’ has been just published, transferring into R realm the work and attitude of Westfall et al. (1999).”
MethodReward of labor coordination and hunting success in wild chimpanzees
Samuni, L., Preis, A., Deschner, T., Crockford, C., & Wittig, R. M. (2018) · Communications Biology · doi:10.1038/s42003-018-0142-3 · Cited by 135 · see citing works
Chadeau‐Hyam, M., Campanella, G., Jombart, T., Bottolo, L., Portengen, L., Vineis, P., Liquet, B., & Vermeulen, R. C. H. (2013) · Environmental and Molecular Mutagenesis · doi:10.1002/em.21797 · Cited by 133 · see citing works
“For instance, Holm’s procedure [Holm, 1979] is step-down and alternative step-up approaches starting from the largest p-value (e.g. Hochberg’s [Hochberg, 1988]) were shown to be more powerful [Bretz et al., 2011].”
MethodUse of acute and chronic ecotoxicity data in environmental risk assessment of pharmaceuticals
Vestel, J., Caldwell, D. J., Constantine, L. A., D’Aco, V. J., Davidson, T. L., Dolan, D. G., Millard, S. P., Murray‐Smith, R., Parke, N. J., Ryan, J. J., et al. (2015) · Environmental Toxicology and Chemistry · doi:10.1002/etc.3260 · Cited by 130 · see citing works
Cerin, E., Conway, T. L., Adams, M. A., Barnett, A. H., Cain, K. L., Owen, N. G., Christiansen, L. B., Dyck, D. V., Mitáš, J., Sarmiento, O. L., et al. (2018) · Social Science & Medicine · doi:10.1016/j.socscimed.2018.06.034 · Cited by 127 · see citing works
“All analyses were conducted in R (R Core Team, 2015) using the packages ‘mgcv’ (Wood, 2006) and ‘multcomp’ (Bretz et al., 2010).”
Regulation of cortical activity and arousal by the matrix cells of the ventromedial thalamic nucleus
Honjoh, S., Sasai, S., Schiereck, S. S., Nagai, H., Tononi, G., & Cirelli, C. (2018) · Nature Communications · doi:10.1038/s41467-018-04497-x · Cited by 118 · see citing works
Schuppli, C., Meulman, E. J. M., Forss, S., Aprilinayati, F., van Noordwijk, M. A., & van Schaik, C. P. (2016) · Animal Behaviour · doi:10.1016/j.anbehav.2016.06.014 · Cited by 125 · see citing works
Bunn, C., Läderach, P., Perez-Jimenez, J. G., Montagnon, C., & Schilling, T. (2015) · PLoS ONE · doi:10.1371/journal.pone.0140490 · Cited by 108 · see citing works
“We based the AEZ descriptions on the differences of the group means from the grand mean and calculated their confidence intervals using R’s multcomp package [34].”
MethodVogel, C., Heister, K., Buegger, F., Tanuwidjaja, I., Haug, S., Schloter, M., & Kögel‐Knabner, I. (2015) · Biology and Fertility of Soils · doi:10.1007/s00374-014-0987-7 · Cited by 122 · see citing works
“To compare the influence of different soil types and time levels, we conducted a Tukey’s test using the R package multcomp (Bretz 2011).”
Xu, J., Ou, J., Luo, S., Wang, Z., Chang, E. C., Novak, C. J., Shen, J., Zheng, S., & Wang, Y. (2020) · Frontiers in Psychology · doi:10.3389/fpsyg.2020.566965 · Cited by 125 · see citing works
“Then, for perceived social support measured at all three time points, the Bonferroni-corrected post hoc test was conducted using the multcomp package in R (Bretz et al., 2016).”
MethodAssessing Distraction Potential of Augmented Reality Head-Up Displays for Vehicle Drivers
Kim, H., & Gabbard, J. L. (2019) · Human Factors The Journal of the Human Factors and Ergonomics Society · doi:10.1177/0018720819844845 · Cited by 123 · see citing works
“…we found significant main effects, we performed appropriate post hoc tests depending on the types of dependent variables, such as paired t -tests or McNemar tests with Tukey’s adjustment or false discovery rate adjustments to account for multiple comparisons (Bretz, Westfall, & Hothorn, 2016).”
MethodChang, A., Le, C. P., Walker, A. K., Creed, S. J., Pon, C. K., Albold, S., Carroll, D., Halls, M. L., Lane, J. R., Riedel, B., et al. (2016) · Brain Behavior and Immunity · doi:10.1016/j.bbi.2016.06.011 · Cited by 115 · see citing works
Advanced multiplicity adjustment methods in clinical trials
Alosh, M., Bretz, F., & Huque, M. F. (2013) · Statistics in Medicine · doi:10.1002/sim.5974 · Cited by 112 · see citing works
Self-citationIshibashi, H., Crittenden, D. B., Miyauchi, A., Libanati, C. R., Maddox, J., Fan, M., Chen, L., & Grauer, A. (2017) · Bone · doi:10.1016/j.bone.2017.07.005 · Cited by 110 · see citing works
Lozano, Y. M., Aguilar‐Trigueros, C. A., Roy, J., & Rillig, M. C. (2021) · New Phytologist · doi:10.1111/nph.17707 · Cited by 110 · see citing works
Zi, X.-M., Sheng, C.-L., Goodale, U. M., Shao, S., & Gao, J. (2014) · Mycorrhiza · doi:10.1007/s00572-014-0565-8 · Cited by 108 · see citing works
“05 (Bretz et al. 2010).”
Rahnenführer, J., de Bin, R., Benner, A., Ambrogi, F., Lusa, L., Boulesteix, A., Migliavacca, E., Binder, H., Michiels, S., Sauerbrei, W., et al. (2023) · BMC Medicine · doi:10.1186/s12916-023-02858-y · Cited by 103 · see citing works
Correlated Evolution of Two Copulatory Organs via a Single Cis-Regulatory Nucleotide ChangePreprint
Nagy, O., Nuez, I., Savisaar, R., Peluffo, A. E., Yassin, A., Lang, M., Stern, D. L., Matute, D. R., David, J. R., & Courtier‐Orgogozo, V. (2018) · SSRN Electronic Journal · doi:10.2139/ssrn.3188440 · Cited by 109 · see citing works
Piepho, H., & Edmondson, R. N. (2018) · Journal of Agronomy and Crop Science · doi:10.1111/jac.12267 · Cited by 104 · see citing works
Madembo, C., Mhlanga, B., & Thierfelder, C. (2020) · Agricultural Systems · doi:10.1016/j.agsy.2020.102921 · Cited by 104 · see citing works
Carrino‐Kyker, S. R., Kluber, L. A., Petersen, S. M., Coyle, K. P., Hewins, C. R., DeForest, J. L., Smemo, K. A., & Burke, D. J. (2016) · FEMS Microbiology Ecology · doi:10.1093/femsec/fiw024 · Cited by 102 · see citing works
Rapid publication-ready MS-Word tables for two-way ANOVA
Assaad, H., Hou, Y., Zhou, L. F., Carroll, R. J., & Wu, G. (2015) · SpringerPlus · doi:10.1186/s40064-015-0795-z · Cited by 99 · see citing works
“In this section, we merely scratch the surface of the complex topic of multiple hypotheses testing; the interested reader may find the books by Westfall et al. (2011) and Bretz et al. (2010) extremely helpful.”
BackgroundA conditional error function approach for subgroup selection in adaptive clinical trials
Friede, T., Parsons, N., & Stallard, N. (2012) · Statistics in Medicine · doi:10.1002/sim.5541 · Cited by 97 · see citing works
Gamba, M., Torti, V., Estienne, V., Randrianarison, R. M., Valente, D., Rovara, P., Bonadonna, G., Friard, O., & Giacoma, C. (2016) · Frontiers in Neuroscience · doi:10.3389/fnins.2016.00249 · Cited by 97 · see citing works
“We analyzed pitch variability by setting a frequency range from theminimum to themaximum of each unit in a DP and then calculating the frequency value at the upper limit of the second (Q50) quartile of energy (Figure 2).”
MethodFeatures and distribution patterns of Chinese endemic seed plant species
Huang, J., Jian‐Hua, C. H. E. N., Jun‐Sheng, Y. I. N. G., & Ma, K. (2011) · Journal of Systematics and Evolution · doi:10.1111/j.1759-6831.2011.00119.x · Cited by 97 · see citing works
“ANOVA and Tukey’s multiple comparisons (Bretz et al., 2010) were carried out to assess endemism differences in floristic elements and taxonomic groups.”
MethodSpano, G. M., Banningh, S. W., Marshall, W., de Vivo, L., Bellesi, M., Loschky, S. S., Tononi, G., & Cirelli, C. (2019) · Journal of Neuroscience · doi:10.1523/jneurosci.0380-19.2019 · Cited by 96 · see citing works
“Post hoc tests were performed using the glht() function of the multcomp package in R, with p values adjusted for multiple comparisons using the single-step method (Bretz et al., 2011).”
MethodZhou, V., MUNSON, J. A., Greenson, J., Hou, Y. F., Rogers, S. J., & Estes, A. M. (2017) · Autism · doi:10.1177/1362361317743251 · Cited by 94 · see citing works
“Due to the exploratory nature of this project and the small sample sizes, Bonferroni correction was considered overly stringent, and the results were reported both with and without this correction (Bretz et al., 2011).”
Demanuele, C., Bartsch, U., Baran, B., Khan, S., Vangel, M. G., Cox, R., Hämäläinen, M., Jones, M. W., Stickgold, R., & Manoach, D. S. (2016) · SLEEP · doi:10.1093/sleep/zsw013 · Cited by 91 · see citing works
β2-adrenoceptor signaling regulates invadopodia formation to enhance tumor cell invasion
Creed, S. J., Le, C. P., Hassan, M., Pon, C. K., Albold, S., Chan, K. T., Berginski, M. E., Huang, Z., Bear, J. E., Lane, J. R., et al. (2015) · Breast Cancer Research · doi:10.1186/s13058-015-0655-3 · Cited by 91 · see citing works
Curiosity Killed the Cat, but Makes Crowdwork Better
Law, E., Yin, M., Goh, J., Chen, K., Terry, M. A., & Gajos, K. Z. (2016) · CHI Conference on Human Factors in Computing Systems · doi:10.1145/2858036.2858144 · Cited by 91 · see citing works
Zhang, G., Chen, F., & Gan, Y. (2016) · Journal of Geophysical Research Atmospheres · doi:10.1002/2016jd024928 · Cited by 91 · see citing works
“Tukey's test [Tukey, 1949; Bretz et al., 2010] was employed to analyze whether the performances of any two schemes of the same subprocess differed.”
MethodCatuara‐Solarz, S., Espinosa‐Carrasco, J., Erb, I., Langohr, K., González, J. R., Notredame, C., & Dierssen, M. (2016) · eNeuro · doi:10.1523/eneuro.0103-16.2016 · Cited by 87 · see citing works
Myelin modifications after chronic sleep loss in adolescent mice
Bellesi, M., Haswell, J. D., de Vivo, L., Marshall, W., Roseboom, P. H., Tononi, G., & Cirelli, C. (2018) · SLEEP · doi:10.1093/sleep/zsy034 · Cited by 89 · see citing works
The Gut Microbiota Can Provide Viral Tolerance in the Honey Bee
Dosch, C., Manigk, A., Streicher, T., Tehel, A., Paxton, R. J., & Tragust, S. (2021) · Microorganisms · doi:10.3390/microorganisms9040871 · Cited by 91 · see citing works
Hahn, K. R., Myers, N. E., Prigarin, S. M., Rodenacker, K., Kurz, A., Förstl, H., Zimmer, C., Wohlschläger, A. M., & Sorg, C. (2013) · NeuroImage · doi:10.1016/j.neuroimage.2013.05.011 · Cited by 86 · see citing works
Impact of Invasive Tree Species on Natural Regeneration Species Composition, Diversity, and Density
Dyderski, M. K., & Jagodziński, A. M. (2020) · Forests · doi:10.3390/f11040456 · Cited by 87 · see citing works
“We evaluated influence of forest type using Tukey’s posteriori test, implemented in the multcomp package [82].”
BackgroundMethodSpalek, K., Gotzner, N., & Wartenburger, I. (2013) · Journal of Memory and Language · doi:10.1016/j.jml.2013.09.001 · Cited by 86 · see citing works
The shape of success in a turbulent world: wave exposure filtering of coral reef herbivory
Bejarano, S., Jouffray, J., Chollett, I., Allen, R., Roff, G., Marshell, A., Steneck, R. S., Ferse, S. C. A., & Mumby, P. J. (2017) · Functional Ecology · doi:10.1111/1365-2435.12828 · Cited by 85 · see citing works
STATISTICAL ANALYSIS OF THE MARIANA TRENCH GEOMORPHOLOGY USING R PROGRAMMING LANGUAGE
Lemenkova, P. (2019) · Geodesy and Cartography · doi:10.3846/gac.2019.3785 · Cited by 83 · see citing works
Diagnostic gene expression biomarkers of coral thermal stress
Kenkel, C. D., Sheridan, C., Leal, M. C., Bhagooli, R., Castillo, K. D., Kurata, N. P., McGinty, E. S., Goulet, T. L., & Matz, M. V. (2013) · Molecular Ecology Resources · doi:10.1111/1755-0998.12218 · Cited by 83 · see citing works
Research Design in Clinical Psychology
Kazdin, A. E. (2021) · doi:10.1017/9781108993647 · Cited by 240 · see citing works
Quantitative Designs and Statistical Techniques
Gries, S. Τ. (2015) · Cambridge University Press eBooks · doi:10.1017/9781009477888.004 · Cited by 81 · see citing works
Quantitative Methods in Archaeology Using R
Carlson, D. L. (2017) · Cambridge University Press eBooks · doi:10.1017/9781139628730 · Cited by 81 · see citing works
Tang, X., Pei, X., Lei, N., Luo, X., Liu, L., Shi, L., Chen, G., & Liang, J. (2020) · Geoderma · doi:10.1016/j.geoderma.2020.114339 · Cited by 80 · see citing works
Corlatti, L., Béthaz, S., von Hardenberg, A., Bassano, B., Palme, R., & Lovari, S. (2012) · Animal Behaviour · doi:10.1016/j.anbehav.2012.08.005 · Cited by 80 · see citing works
Longitudinal Analysis of Progression in Glaucoma Using Spectral-Domain Optical Coherence Tomography
Wessel, J. M., Horn, F. K., Tornow, R. P., Schmid, M. C., Mardin, C. Y., Kruse, F. E., Juenemann, A. G. M., & Lämmer, R. (2013) · Investigative Ophthalmology & Visual Science · doi:10.1167/iovs.12-9786 · Cited by 80 · see citing works
Deep soil flipping increases carbon stocks of New Zealand grasslands
Schiedung, M., Tregurtha, C. S., Beare, M., Thomas, S. M., & Don, A. (2019) · Global Change Biology · doi:10.1111/gcb.14588 · Cited by 79 · see citing works
The effects of land use characteristics on urban stormwater quality and watershed pollutant loads.
Yazdi, M. N., Sample, D., Scott, D., Wang, X.-X., & Ketabchy, M. (2021) · Science of the Total Environment · doi:10.1016/j.scitotenv.2021.145358 · Cited by 62 · see citing works
Interaction of methyl viologen-induced chloroplast and mitochondrial signalling in Arabidopsis
Cui, F., Brosché, M., Shapiguzov, A., He, X., Vainonen, J. P., Leppälä, J., Trotta, A., Kangasjärvi, S., Salojärvi, J., Kangasjärvi, J., et al. (2019) · Free Radical Biology and Medicine · doi:10.1016/j.freeradbiomed.2019.02.006 · Cited by 77 · see citing works
Dolný, A., & Harabiš, F. (2011) · Biological Conservation · doi:10.1016/j.biocon.2011.10.020 · Cited by 76 · see citing works
Recommendation domains to scale out climate change adaptation in cocoa production in Ghana
Bunn, C., Läderach, P., Quaye, A. K., Muilerman, S., Noponen, M., & Lundy, M. (2019) · Climate Services · doi:10.1016/j.cliser.2019.100123 · Cited by 74 · see citing works
Dolný, A., Harabiš, F., & Mižičová, H. (2014) · PLoS ONE · doi:10.1371/journal.pone.0100408 · Cited by 74 · see citing works
A Versatile Method for Confirmatory Evaluation of the Effects of a Covariate in Multiple Models
Pipper, C. B., Ritz, C., & Bisgaard, H. F. (2011) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/j.1467-9876.2011.01005.x · Cited by 74 · see citing works
“A very practical and popular solution to this problem is provided in current state of the art procedures (Hothorn et al., 2008; Herberich et al., 2010; Bretz et al., 2010).”
BackgroundMethodInfluentialMultimodal learning analytics to investigate cognitive load during online problem solving
Larmuseau, C., Cornelis, J. P., Lancieri, L., Desmet, P., & Depaepe, F. (2020) · British Journal of Educational Technology · doi:10.1111/bjet.12958 · Cited by 73 · see citing works
Pocnet, C., Antonietti, J., Strippoli, M. F., Glaus, J., Preisig, M., & Rossier, J. (2016) · Quality of Life Research · doi:10.1007/s11136-016-1296-4 · Cited by 78 · see citing works
“events, perceived social support, personality traits, and QoL (the p-values were corrected using Holm’s method to counteract the problem of multiple comparisons that occurs when one considers a set of statistical inference simultaneously [39, 40]).”
MethodHiatus Resolution in American English: The Case Against Glide Insertion
Davidson, L., & Erker, D. (2014) · Language · doi:10.1353/lan.2014.0028 · Cited by 72 · see citing works
“…be modal than fast tokens, and VBV is less likely to be modal than VGV, but there is no significant difference between VGV and VV. Post-hoc Tukey tests using the multcomp package in R (Bretz et al. 2010) show that VV is significantly more likely to be modal than VBV (β = 3.40, z = 5.99, p < 0.001).”
MethodInfluentialWang, J., Chatzidimitriou, E., Wood, L., Hasanaliyeva, G., Markellou, E., Iversen, P. O., Seal, C. J., Barański, M., Vigar, V., Ernst, L., et al. (2020) · Food Chemistry X · doi:10.1016/j.fochx.2020.100091 · Cited by 71 · see citing works
Quigley, K. M., Willis, B. L., & Bay, L. K. (2016) · Royal Society Open Science · doi:10.1098/rsos.160471 · Cited by 71 · see citing works
Nicotine in floral nectar pharmacologically influences bumblebee learning of floral features
Baracchi, D., Marples, A., Jenkins, A. J., Leitch, A. R., & Chıttka, L. (2017) · Scientific Reports · doi:10.1038/s41598-017-01980-1 · Cited by 71 · see citing works
Flavonoids as Putative Inducers of the Transcription Factors Nrf2, FoxO, and PPARγ
Pallauf, K., Duckstein, N., Hasler, M., Klotz, L., & Rimbach, G. H. (2017) · Oxidative Medicine and Cellular Longevity · doi:10.1155/2017/4397340 · Cited by 71 · see citing works
Husted, G. R., Thorsteinsson, B., Esbensen, B. A., Gluud, C. N., Winkel, P., Hommel, E. E., & Zoffmann, V. (2014) · Trials · doi:10.1186/1745-6215-15-321 · Cited by 70 · see citing works
“to control the family-wise error rate [35].”
BackgroundMethodInfluentialOn Using the Bootstrap for Multiple Comparisons
Westfall, P. H. (2011) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2011.607751 · Cited by 70 · see citing works
Self-citation
- Authors
- Bretz, F., Hothorn, T., & Westfall, P.
- Affiliations
- Texas Tech University (US)
- Venue
- Chapman & Hall/CRC eBooks
- Publisher
- Chapman and Hall/CRC
- Published
- 2016-04-19
- OpenAlex
- W396053900
- Cited by
- 1,233
- References
- 93
- Citations by year
- 2026: 20 · 2025: 57 · 2024: 96 · 2023: 70 · 2022: 97 · 2021: 146 · 2020: 99 · 2019: 133 · 2018: 98 · 2017: 89 · 2016: 78 · 2015: 66 · 2014: 61 · 2013: 52 · 2012: 49
- FWCI
- 12.36
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Chapman & Hall/CRC eBooks (publishedVersion)
- Thammasat University Digital Collections (submittedVersion)
- TU Digital Collections (Thammasat University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Computer Science › Artificial Intelligence › Data Analysis with R
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- multiple comparisons, R software, statistical software implementation, hypothesis testing
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 ›
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