Many‐One Comparisons and Contrast Tests
Multiple Contrast Tests in the Presence of Heteroscedasticity
Abstract
This paper proposes a general approach for handling multiple contrast tests for normally distributed data in the presence of heteroscedasticity. Three candidate procedures are described and compared by simulations. Only the procedure with both comparison‐specific degrees of freedom and a correlation matrix depending on sample variances maintains the α‐level over all situations. Other approaches may fail notably as the variances differ more. Furthermore, related approximate simultaneous confidence intervals are given. The approach will be applied to a toxicological experiment. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Citing Literature
Number of times cited according to CrossRef: 50
- Steffen Beck-Broichsitter, Marisa R. Gerriets, Horst H. Gerke, Martina Sobotkova, Jaromir Dusek, Reiner Dohrmann, Rainer Horn, Brilliant Blue sorption characteristics of clay-organic aggregate coatings from Bt horizons, Soil and Tillage Research, 10.1016/j.still.2020.104635, 201, (104635), (2020).
- Steffen Beck-Broichsitter, Heiner Fleige, Horst H. Gerke, Rainer Horn, Effect of artificial soil compaction in landfill capping systems on anisotropy of air‐permeability , Journal of Plant Nutrition and Soil Science, 10.1002/jpln.201900281, 183, 2, (144-154), (2020).
- Junjiang Zhong, Miin-Jye Wen, Siu Hung Cheung, Wai-Yin Poon, Simultaneous tests of non inferiority and superiority in three-arm clinical studies with heterogeneous variance, Communications in Statistics - Theory and Methods, 10.1080/03610926.2020.1747082, (1-18), (2020).
- Felix M. Kluxen, Ludwig A. Hothorn, Alternatives to statistical decision trees in regulatory (eco-)toxicological bioassays, Archives of Toxicology, 10.1007/s00204-020-02690-w, (2020).
- Manoj Kumar Jena, Brajaballav Kar, Stages and Methods for Cleaning Large Secondary Data Using R, Methodological Issues in Management Research: Advances, Challenges, and the Way Ahead, 10.1108/9781789739732, (285-304), (2019).
- Stéphanie C. Michl, Matt Beyer, Jenni-Marie Ratten, Mario Hasler, Julie LaRoche, Carsten Schulz, A diet-change modulates the previously established bacterial gut community in juvenile brown trout (Salmo trutta), Scientific Reports, 10.1038/s41598-019-38800-7, 9, 1, (2019).
- Claudia Torno, Stefanie Staats, Anna Fickler, Sonia de Pascual-Teresa, María Soledad Izquierdo, Gerald Rimbach, Carsten Schulz, Combined effects of nutritional, biochemical and environmental stimuli on growth performance and fatty acid composition of gilthead sea bream (Sparus aurata), PLOS ONE, 10.1371/journal.pone.0216611, 14, 5, (e0216611), (2019).
- Robin Ristl, Ludwig Hothorn, Christian Ritz, Martin Posch, Simultaneous inference for multiple marginal generalized estimating equation models, Statistical Methods in Medical Research, 10.1177/0962280219873005, (096228021987300), (2019).
- Wenfu Xu, Jingya Gao, Feifang Hu, Siu Hung Cheung, Response-adaptive treatment allocation for non-inferiority trials with heterogeneous variances, Computational Statistics & Data Analysis, 10.1016/j.csda.2018.03.005, 124, (168-179), (2018).
- Maria Umlauft, Marius Placzek, Frank Konietschke, Markus Pauly, Wild bootstrapping rank-based procedures: Multiple testing in nonparametric factorial repeated measures designs, Journal of Multivariate Analysis, 10.1016/j.jmva.2018.12.005, (2018).
- Kathrin Steinberg, Jan Zimmermann, Stefan Meyer, Carsten Schulz, Start-up of recirculating aquaculture systems: How do water exchange rates influence pikeperch (Sander lucioperca) and water composition?, Aquacultural Engineering, 10.1016/j.aquaeng.2018.10.006, (2018).
- Sarah Friedrich, Markus Pauly, MATS: Inference for potentially singular and heteroscedastic MANOVA, Journal of Multivariate Analysis, 10.1016/j.jmva.2017.12.008, 165, (166-179), (2018).
- Claudia Torno, Stefanie Staats, Gerald Rimbach, Carsten Schulz, Effects of resveratrol and genistein on nutrient digestibility and intestinal histopathology of rainbow trout (Oncorhynchus mykiss), Aquaculture, 10.1016/j.aquaculture.2018.03.020, 491, (114-120), (2018).
- Anneka Mordhorst, Iris Zimmermann, Heiner Fleige, Rainer Horn, Improvement of oxygen transport functions in grave soils due to quicklime application depending on soil texture, Geoderma, 10.1016/j.geoderma.2018.06.013, 331, (18-28), (2018).
- Philip Pallmann, Christian Ritz, Ludwig A. Hothorn, Simultaneous small‐sample comparisons in longitudinal or multi‐endpoint trials using multiple marginal models, Statistics in Medicine, 10.1002/sim.7610, 37, 9, (1562-1576), (2018).
- Claudia Torno, Stefanie Staats, Stéphanie Michl, Sonia de Pascual-Teresa, Marisol Izquierdo, Gerald Rimbach, Carsten Schulz, Fatty Acid Composition and Fatty Acid Associated Gene-Expression in Gilthead Sea Bream (Sparus aurata) are Affected by Low-Fish Oil Diets, Dietary Resveratrol, and Holding Temperature, Marine Drugs, 10.3390/md16100379, 16, 10, (379), (2018).
- C. Torno, S. Staats, S. de Pascual-Teresa, G. Rimbach, C. Schulz, Effects of resveratrol and genistein on growth, nutrient utilization and fatty acid composition of rainbow trout, animal, 10.1017/S1751731118002458, (1-8), (2018).
- Henrike Möhler, Tim Diekötter, John D. Herrmann, Tobias W. Donath, Allelopathic vs. autotoxic potential of a grassland weed—evidence from a seed germination experiment, Plant Ecology & Diversity, 10.1080/17550874.2018.1541487, (1-11), (2018).
- Frank Konietschke, Randolph R. Aguayo, Wieland Staab, Simultaneous inference for factorial multireader diagnostic trials, Statistics in Medicine, 10.1002/sim.7507, 37, 1, (28-47), (2017).
- Gunda Schulte auf’m Erley, Li Wang, Anna-Catharina Wollmer, Julia Rudloff, Heiko C. Becker, Karl H. Mühling, Classification of oilseed rape accessions according to sulfur-related plant traits in short-term experiments reflects agronomic performance in field experiments, Industrial Crops and Products, 10.1016/j.indcrop.2017.05.036, 107, (73-80), (2017).
- Hideaki Ishibashi, Daria B. Crittenden, Akimitsu Miyauchi, Cesar Libanati, Judy Maddox, Michelle Fan, Li Chen, Andreas Grauer, Romosozumab increases bone mineral density in postmenopausal Japanese women with osteoporosis: A phase 2 study, Bone, 10.1016/j.bone.2017.07.005, 103, (209-215), (2017).
- Stéphanie Céline Michl, Benjamin Weis, Jeffrey A. Hutchings, Carsten Schulz, Plastic responses by wild brown trout ( Salmo trutta ) to plant-based diets, Aquaculture, 10.1016/j.aquaculture.2017.04.006, 476, (19-28), (2017).
- Anneka Mordhorst, Iris Zimmermann, Heiner Fleige, Rainer Horn, Changes in soil aeration and soil respiration of simulated grave soils after quicklime application, Journal of Plant Nutrition and Soil Science, 10.1002/jpln.201600351, 180, 2, (153-164), (2017).
- Gemechis D. Djira, Ludwig A. Hothorn, Detecting Relative Changes in Multiple Comparisons with an Overall Mean, Journal of Quality Technology, 10.1080/00224065.2009.11917760, 41, 1, (60-65), (2017).
- Stéphanie Céline Michl, Jenni-Marie Ratten, Matt Beyer, Mario Hasler, Julie LaRoche, Carsten Schulz, The malleable gut microbiome of juvenile rainbow trout (Oncorhynchus mykiss): Diet-dependent shifts of bacterial community structures, PLOS ONE, 10.1371/journal.pone.0177735, 12, 5, (e0177735), (2017).
- Sinem Zeytin, Carsten Schulz, Bernd Ueberschär, Diurnal patterns of tryptic enzyme activity under different feeding regimes in gilthead sea bream (Sparus aurata) larvae, Aquaculture, 10.1016/j.aquaculture.2016.02.017, 457, (85-90), (2016).
- Philip Pallmann, Ludwig A. Hothorn, Analysis of means: a generalized approach using R, Journal of Applied Statistics, 10.1080/02664763.2015.1117584, 43, 8, (1541-1560), (2016).
- Julia Santiago, Benjamin Brandt, Mari Wildhagen, Ulrich Hohmann, Ludwig A Hothorn, Melinka A Butenko, Michael Hothorn, Mechanistic insight into a peptide hormone signaling complex mediating floral organ abscission, eLife, 10.7554/eLife.15075, 5, (2016).
- Christoph-Martin Geilfus, Karsten Niehaus, Victoria Gödde, Mario Hasler, Christian Zörb, Karin Gorzolka, Mareike Jezek, Mehmet Senbayram, Jutta Ludwig-Müller, Karl H. Mühling, Fast responses of metabolites in Vicia faba L. to moderate NaCl stress, Plant Physiology and Biochemistry, 10.1016/j.plaphy.2015.04.008, 92, (19-29), (2015).
- Mario Hasler, Comment on multiple comparisons with a control under heteroscedasticity, Journal of Applied Statistics, 10.1080/02664763.2015.1005582, 42, 8, (1757-1758), (2015).
- Mario Hasler, Heteroscedasticity: multiple degrees of freedom vs. sandwich estimation, Statistical Papers, 10.1007/s00362-014-0640-4, 57, 1, (55-68), (2014).
- Li-Ching Huang, Miin-Jye Wen, Siu Hung Cheung, Noninferiority Studies with Multiple New Treatments and Heterogeneous Variances, Journal of Biopharmaceutical Statistics, 10.1080/10543406.2014.920346, 25, 5, (958-971), (2014).
- A. Kitsche, F. Schaarschmidt, Analysis of Statistical Interactions in Factorial Experiments, Journal of Agronomy and Crop Science, 10.1111/jac.12076, 201, 1, (69-79), (2014).
- Ludwig A. Hothorn, Statistical evaluation of toxicological bioassays – a review, Toxicol. Res., 10.1039/C4TX00047A, 3, 6, (418-432), (2014).
- Karin Müller, Stephanie Koster, Johanna Painer, Arne Söderberg, Dolores Gavier-Widèn, Edgar Brunner, Martin Dehnhard, Katarina Jewgenow, Testosterone production and spermatogenesis in free-ranging Eurasian lynx (Lynx lynx) throughout the year, European Journal of Wildlife Research, 10.1007/s10344-014-0821-4, 60, 4, (569-577), (2014).
- Mario Hasler, Multiple Contrast Tests for Multiple Endpoints in the Presence of Heteroscedasticity, The International Journal of Biostatistics, 10.1515/ijb-2012-0015, 10, 1, (2014).
- Ulrike Hinterseher, Annette Wunderlich, Silvia Roth, Annette Ramaswamy, Detlef K. Bartsch, Stefan Hauptmann, Brandon H. Greene, Volker Fendrich, Sebastian Hoffmann, Expression of hedgehog signalling pathway in anaplastic thyroid cancer, Endocrine, 10.1007/s12020-013-0015-y, 45, 3, (439-447), (2013).
- Thomas Jaki, Ludwig A. Hothorn, Statistical evaluation of toxicological assays: Dunnett or Williams test—take both, Archives of Toxicology, 10.1007/s00204-013-1065-x, 87, 11, (1901-1910), (2013).
- Mario Hasler, Kathrin Böhlendorf, Multiple Comparisons for Multiple Endpoints in Agricultural Experiments, Journal of Agricultural, Biological, and Environmental Statistics, 10.1007/s13253-013-0149-7, 18, 4, (578-593), (2013).
- Frank Schaarschmidt, Simultaneous confidence intervals for multiple comparisons among expected values of log-normal variables, Computational Statistics & Data Analysis, 10.1016/j.csda.2012.08.011, 58, (265-275), (2013).
- Christian Zörb, Karl Hermann Mühling, Mario Hasler, Victoria Gödde, Karsten Niehaus, Dirk Becker, Christoph‐Martin Geilfus, Metabolomic responses in grain, ear, and straw of winter wheat under increasing sulfur treatment, Journal of Plant Nutrition and Soil Science, 10.1002/jpln.201300163, 176, 6, (964-970), (2013).
- C. Dietz, S. Kroeckel, C. Schulz, A. Susenbeth, Energy requirement for maintenance and efficiency of energy utilization for growth in juvenile turbot (Psetta maxima, L.): The effect of strain and replacement of dietary fish meal by wheat gluten, Aquaculture, 10.1016/j.aquaculture.2012.06.028, 358-359, (98-107), (2012).
- Frank Konietschke, Ludwig A. Hothorn, Evaluation of Toxicological Studies Using a Nonparametric Shirley-Type Trend Test for Comparing Several Dose Levels with a Control Group, Statistics in Biopharmaceutical Research, 10.1080/19466315.2011.633861, 4, 1, (14-27), (2012).
- Hong Li, Wei Ning, Multiple comparisons with a control under heteroscedasticity, Journal of Applied Statistics, 10.1080/02664763.2012.706269, 39, 10, (2275-2283), (2012).
- Mario Hasler, Multiple comparisons to both a negative and a positive control, Pharmaceutical Statistics, 10.1002/pst.503, 11, 1, (74-81), (2012).
- Frank Konietschke, Ondrej Libiger, Ludwig A. Hothorn, Nonparametric Evaluation of Quantitative Traits in Population-Based Association Studies when the Genetic Model is Unknown, PLoS ONE, 10.1371/journal.pone.0031242, 7, 2, (e31242), (2012).
- Adrian G Cummins, Basile G Alexander, Adrian Chung, Edward Teo, Josh A Woenig, John B J Field, Fiona M Thompson, Ian C Roberts-Thomson, Morphometric Evaluation of Duodenal Biopsies in Celiac Disease, American Journal of Gastroenterology, 10.1038/ajg.2010.313, 106, 1, (145-150), (2011).
- Haydar Demirhan, Nimet Anıl Dolgun, Yaprak Parlak Demirhan, Muhsin Özgür Dolgun, Performance of some multiple comparison tests under heteroscedasticity and dependency, Journal of Statistical Computation and Simulation, 10.1080/00949650902962253, 80, 10, (1083-1100), (2010).
- Ludwig A. Hothorn, Statistical issues in drug development (2nd edn). Stephen Senn, John Wiley & Sons Ltd, Chichester, 2007. No. of pages: xix + 498. Price: $130.00. ISBN 978‐0‐470‐01877‐4, Statistics in Medicine, 10.1002/sim.3515, 28, 7, (1177-1178), (2009).
- Peter Frommolt, Martin Hellmich, Resampling in Multiple‐Dose Factorial Designs, Biometrical Journal, 10.1002/bimj.200900129, 51, 6, (915-931), (2009).
