@misc{:o,
  title = {Taking {{Parametric Assumptions Seriously}}: {{Arguments}} for the {{Use}} of {{Welch}}'s {{F-test}} Instead of the {{Classical F-test}} in {{One-Way ANOVA}} \textbar{} {{International Review}} of {{Social Psychology}}},
  urldate = {2025-12-27},
  howpublished = {https://rips-irsp.com/articles/10.5334/irsp.198},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/3WW675SY/irsp.html}
}

@article{Abdi:2007,
  title = {The {{Bonferonni}} and {{\v Sid\'ak Corrections}} for {{Multiple Comparisons}}},
  author = {Abdi, Herv{\'e}},
  editor = {Salkind, Neil J.},
  year = 2007,
  journal = {Encyclopedia of measurement and statistics},
  publisher = {Sage},
  address = {Thousand Oaks, CA},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/DGZBR96T/Abdi - 2006 - The Bonferonni and Šidák Corrections for Multiple Comparisons.pdf}
}

@book{Agresti:2010,
  title = {Analysis of {{Ordinal Categorical Data}}},
  author = {Agresti, Alan},
  year = 2010,
  month = mar,
  series = {Wiley {{Series}} in {{Probability}} and {{Statistics}}},
  edition = {1},
  publisher = {Wiley},
  doi = {10.1002/9780470594001},
  urldate = {2026-05-09},
  copyright = {http://doi.wiley.com/10.1002/tdm\_license\_1.1},
  isbn = {978-0-470-08289-8 978-0-470-59400-1},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/6VTIQ5AE/L-G-0000645264-0003879127.pdf}
}

@misc{AllenDowney:2023,
  title = {Never {{Test}} for {{Normality}}},
  author = {AllenDowney},
  year = 2023,
  month = jan,
  journal = {Probably Overthinking It},
  urldate = {2025-06-03},
  abstract = {Way back in 2013, I wrote this blog post explaining why you should never use a statistical test to check whether a sample came from a Gaussian distribution. I argued that data from the real world never come from a Gaussian distribution, or any other simple mathematical model, so the answer to the question is always no. And there are only two possible outcomes from the test: Either way, the result doesn't tell you anything useful. In this article, I... Read More Read More},
  langid = {american},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/GPJ3TGAH/never-test-for-normality.html}
}

@article{Allingham:2012,
  title = {Testing {{Equality}} of {{Variances}} for {{Multiple Univariate Normal Populations}}},
  author = {Allingham, David and Rayner, J. C. W.},
  year = 2012,
  month = sep,
  journal = {Journal of Statistical Theory and Practice},
  volume = {6},
  number = {3},
  pages = {524--535},
  issn = {1559-8608, 1559-8616},
  doi = {10.1080/15598608.2012.695703},
  urldate = {2025-06-29},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/DPA3PLFT/Allingham und Rayner - 2012 - Testing Equality of Variances for Multiple Univariate Normal Populations.pdf}
}

@article{Anscombe:1963,
  title = {The {{Examination}} and {{Analysis}} of {{Residuals}}},
  author = {Anscombe, F. J. and {\noopsort{tukey}}{and Tukey}, John W.},
  year = 1963,
  month = may,
  journal = {Technometrics},
  volume = {5},
  number = {2},
  pages = {141--160},
  publisher = {ASA Website},
  issn = {0040-1706},
  doi = {10.1080/00401706.1963.10490071},
  urldate = {2025-05-28},
  abstract = {A number of methods for examining the residuals remaining after a conventional analysis of variance or least-squares fitting have been explored during the past few years. These give information on various questions of interest, and in particular, aid in assessing the validity or appropriateness of the conventional analysis. The purpose of this paper is to make a variety of these techniques more easily available, so that they can be tried out more widely. Techniques of analysis, some graphical, some wholly numerical, and others mixed, are discussed in terms of the residuals that result from fitting row and column means to entries in a two-way array (or in several two-way arrays). Extensions to more complex situations, and some of the uses of the results of examination, are indicated.}
}

@article{Bartlett:1937,
  title = {Properties of Sufficiency and Statistical Tests},
  author = {Bartlett, M. S.},
  year = 1937,
  journal = {Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences},
  volume = {160},
  number = {901},
  pages = {268--282},
  doi = {10.1098/rspa.1937.0109}
}

@article{Blanca:2017,
  title = {Non-Normal Data: {{Is ANOVA}} Still a Valid Option?},
  shorttitle = {Non-Normal Data},
  author = {Blanca, Mar{\'i}a and Alarc{\'o}n, Rafael and Arnau, Jaume and Bono, Roser and Bendayan, Rebecca},
  year = 2017,
  month = nov,
  journal = {Psicothema},
  volume = {4},
  number = {29},
  pages = {552--557},
  issn = {0214-9915, 1886-144X},
  doi = {10.7334/psicothema2016.383},
  urldate = {2025-06-29},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/FQZ4SEFD/Blanca et al. - 2017 - Non-normal data Is ANOVA still a valid option.pdf}
}

@article{Breusch:1979,
  title = {A {{Simple Test}} for {{Heteroscedasticity}} and {{Random Coefficient Variation}}},
  author = {Breusch, T. S. and Pagan, A. R.},
  year = 1979,
  journal = {Econometrica},
  volume = {47},
  number = {5},
  eprint = {1911963},
  eprinttype = {jstor},
  pages = {1287--1294},
  publisher = {[Wiley, Econometric Society]},
  issn = {0012-9682},
  doi = {10.2307/1911963},
  urldate = {2025-12-29},
  abstract = {A simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test. For a wide range of heteroscedastic and random coefficient specifications, the criterion is given as a readily computed function of the OLS residuals. Some finite sampleevidence is presented to supplement the general asymptotic properties of Lagrangian multiplier tests.},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/2ZWR7ZY8/Breusch und Pagan - 1979 - A Simple Test for Heteroscedasticity and Random Coefficient Variation.pdf}
}

@article{Brown:1974,
  title = {Robust {{Tests}} for the {{Equality}} of {{Variances}}},
  author = {Brown, Morton B. and Forsythe, Alan B.},
  year = 1974,
  month = jun,
  journal = {Journal of the American Statistical Association},
  volume = {69},
  number = {346},
  pages = {364--367},
  issn = {0162-1459, 1537-274X},
  doi = {10.1080/01621459.1974.10482955},
  urldate = {2025-06-17},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/ABFAPTP8/Brown und Forsythe - 1974 - Robust Tests for the Equality of Variances.pdf}
}

@article{Chen:2015,
  title = {Statistical {{Inference}} in {{Generalized Linear Mixed Models}} by {{Joint Modelling Mean}} and {{Covariance}} of {{Non-Normal Random Effects}}},
  author = {Chen, Yin and Fei, Yu and Pan, Jianxin},
  year = 2015,
  journal = {OJS},
  volume = {05},
  number = {06},
  pages = {568--584},
  issn = {2161-718X, 2161-7198},
  doi = {10.4236/ojs.2015.56059},
  urldate = {2025-06-29},
  copyright = {http://creativecommons.org/licenses/by/4.0/},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/ZAW7YIGL/Chen et al. - 2015 - Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of N.pdf}
}

@article{Chernick:2011,
  title = {An {{Introduction}} to {{Bootstrap Methods}} with {{Applications}} to {{R}}},
  author = {Chernick, Michael and LaBudde, Robert},
  year = 2011,
  month = nov,
  journal = {Mathematics \& Statistics Faculty Books},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/G33FIFPZ/10.html}
}

@book{Christensen:2011,
  title = {Plane Answers to Complex Questions: The Theory of Linear Models},
  author = {Christensen, Ronald},
  year = 2011,
  publisher = {Springer Science \& Business Media}
}

@article{Cochran:1954,
  title = {The {{Combination}} of {{Estimates}} from {{Different Experiments}}},
  author = {Cochran, William G.},
  year = 1954,
  month = mar,
  journal = {Biometrics},
  volume = {10},
  number = {1},
  eprint = {3001666},
  eprinttype = {jstor},
  pages = {101},
  issn = {0006341X},
  doi = {10.2307/3001666},
  urldate = {2025-05-19},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/9ABTBY4F/1955-00087-001.html;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/9IW9ZBXF/1955-00087-001.html}
}

@article{Cohen:1968,
  title = {Multiple Regression as a General Data-Analytic System},
  author = {Cohen, Jacob},
  year = 1968,
  journal = {Psychological Bulletin},
  volume = {70},
  number = {6, Pt.1},
  pages = {426--443},
  publisher = {American Psychological Association},
  address = {US},
  issn = {1939-1455},
  doi = {10.1037/h0026714},
  abstract = {Presents techniques for using multiple regression (MR) as a general variance-accounting procedure of great flexibility, power, and fidelity to research aims in both manipulative and observational psychological research. The identity of MR and fixed-model analysis of variance/covariance (AV/ACV) is sketched. This requires an exposition of means of expressing nominal scale (qualitative) data as independent variables in MR. Attention is given to methods for handling interactions, curvilinearity, missing data, and covariates, for either uncorrelated or correlated independent variables in MR. The relative roles of AV/ACV and MR in data analysis are described, and the practical advantages of the latter are set forth. (16 ref.) (PsycInfo Database Record (c) 2025 APA, all rights reserved)},
  keywords = {Statistical Analysis},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/LGKFV84T/Cohen - 1968 - Multiple regression as a general data-analytic system.pdf}
}

@book{Cook:1982,
  title = {Residuals and {{Influence}} in {{Regression}}},
  author = {Cook, R. Dennis and Weisberg, Sanford},
  year = 1982,
  publisher = {{New York: Chapman and Hall}},
  urldate = {2026-05-09},
  isbn = {0-412-24280-0},
  langid = {american},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/BHN8FT9W/Cook und Weisberg - 1982 - Residuals and Influence in Regression.pdf}
}

@article{Delacre:2017,
  title = {Why Psychologists Should by Default Use {{Welch}}'s t-Test Instead of {{Student}}'s t-Test},
  author = {Delacre, Marie and Lakens, Dani{\"e}l and Leys, Christophe},
  year = 2017,
  journal = {International Review of Social Psychology},
  volume = {30},
  number = {1},
  pages = {92--101},
  publisher = {Ubiquity Press},
  doi = {10.5334/irsp.82},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/CNFQD5ZI/82-1-534-4-10-20221125.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/WMNMCFU3/Delacre et al. - 2017 - Why Psychologists Should by Default Use Welchâs t-test Instead of Studentâs t-test.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/ZZ8X255K/Delacre et al. - 2017 - Why Psychologists Should by Default Use Welchâs t-test Instead of Studentâs t-test.pdf}
}

@article{Delacre:2019,
  title = {Taking {{Parametric Assumptions Seriously}}: {{Arguments}} for the {{Use}} of {{Welch}}'s {{F-test}} Instead of the {{Classical F-test}} in {{One-Way ANOVA}}},
  shorttitle = {Taking {{Parametric Assumptions Seriously}}},
  author = {Delacre, Marie and Leys, Christophe and Mora, Youri L. and Lakens, Dani{\"e}l},
  year = 2019,
  month = aug,
  journal = {International Review of Social Psychology},
  volume = {32},
  number = {1},
  issn = {2397-8570},
  doi = {10.5334/irsp.198},
  urldate = {2025-06-30},
  abstract = {Student's t-test and classical F-test ANOVA rely on the assumptions that two or more samples are independent, and that independent and identically distributed residuals are normal and have equal variances between groups. We focus on the assumptions of normality and equality of variances, and argue that these assumptions are often unrealistic in the field of psychology. We underline the current lack of attention to these assumptions through an analysis of researchers' practices. Through Monte Carlo simulations, we illustrate the consequences of performing the classic parametric F-test for ANOVA when the test assumptions are not met on the Type I error rate and statistical power. Under realistic deviations from the assumption of equal variances, the classic F-test can yield severely biased results and lead to invalid statistical inferences. We examine two common alternatives to the F-test, namely the Welch's ANOVA (W-test) and the Brown-Forsythe test (F*-test). Our simulations show that under a range of realistic scenarios, the W-test is a better alternative and we therefore recommend using the W-test by default when comparing means. We provide a detailed example explaining how to perform the W-test in SPSS and R. We summarize our conclusions in practical recommendations that researchers can use to improve their statistical practices.},
  langid = {american},
  keywords = {ANOVA,Parametric assumptions,Parametric test,Replicability crisis,Welch test},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/54DF7CQK/Delacre et al. - 2019 - Taking parametric assumptions seriously arguments for the use of Welch’s F-test instead of the clas.pdf}
}

@article{Delacre:2022,
  title = {Correction: {{Why Psychologists Should}} by {{Default Use Welch}}'s t-Test {{Instead}} of {{Student}}'s t-Test},
  shorttitle = {Correction},
  author = {Delacre, Marie and Lakens, Dani{\"e}l and Leys, Christophe},
  year = 2022,
  month = nov,
  journal = {International Review of Social Psychology},
  volume = {35},
  number = {1},
  pages = {21},
  issn = {2119-4130},
  doi = {10.5334/irsp.661},
  urldate = {2025-12-27},
  abstract = {This article details a correction to: Delacre, M., Lakens, D., \& Leys, C. (2017). Why Psychologists Should by Default Use Welch's t-test Instead of Student's t-test. International Review of Social Psychology, 30(1), 92--101. DOI: https://doi.org/10.5334/ irsp.82.},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/ICJSWF4D/Delacre et al. - 2022 - Correction Why Psychologists Should by Default Use Welch’s t-test Instead of Student’s t-test.pdf}
}

@article{derrick2016why,
  title = {Why {{Welch}}'s Test Is {{Type I}} Error Robust},
  author = {Derrick, Ben and Toher, Deirdre and White, Paul},
  year = 2016,
  journal = {The Quantitative Methods for Psychology},
  volume = {12},
  number = {1},
  pages = {30--38},
  doi = {10.20982/tqmp.12.1.p030},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/3LHRYKLI/Derrick und White - 2016 - Why Welch's test is Type I error robust.pdf}
}

@book{Efron:1993,
  title = {An Introduction to the Bootstrap},
  author = {Efron, Bradley and Tibshirani, Robert},
  year = 1993,
  series = {Monographs on Statistics and Applied Probability},
  number = {57},
  publisher = {Chapman \& Hall},
  address = {New York},
  isbn = {978-0-412-04231-7},
  langid = {english},
  lccn = {QA276.8 .E3745 1993},
  keywords = {Bootstrap (Statistics)},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/5SL2CN8K/Efron und Tibshirani - 1993 - An introduction to the bootstrap.pdf}
}

@article{Fagerland:2009,
  title = {Performance of Five Two-Sample Location Tests for Skewed Distributions with Unequal Variances},
  author = {Fagerland, Morten W. and Sandvik, Leiv},
  year = 2009,
  month = sep,
  journal = {Contemporary Clinical Trials},
  volume = {30},
  number = {5},
  pages = {490--496},
  issn = {1551-7144},
  doi = {10.1016/j.cct.2009.06.007},
  urldate = {2025-06-04},
  abstract = {Tests for comparing the locations of two independent populations are associated with different null hypotheses, but results are often interpreted as evidence for or against equality of means or medians. We examine the appropriateness of this practice by investigating the performance of five frequently used tests: the two-sample T test, the Welch U test, the Yuen--Welch test, the Wilcoxon--Mann--Whitney test, and the Brunner--Munzel test. Under combined violations of normality and variance homogeneity, the true significance level and power of the tests depend on a complex interplay of several factors. In a wide ranging simulation study, we consider scenarios differing in skewness, skewness heterogeneity, variance heterogeneity, sample size, and sample size ratio. We find that small differences in distribution properties can alter test performance markedly, thus confounding the effort to present simple test recommendations. Instead, we provide detailed recommendations in Appendix A. The Welch U test is recommended most frequently, but cannot be considered an omnibus test for this problem.},
  keywords = {Brunner--Munzel test,Heteroscedasticity,Robustness,Skewness,test,Two-sample location problem,Welch test,Wilcoxon--Mann--Whitney test,Yuen--Welch test},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/T83TNKK2/S1551714409001098.html;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/UA44IKA4/S1551714409001098.html}
}

@article{Fagerland:2012,
  title = {T-Tests, Non-Parametric Tests, and Large Studies---a Paradox of Statistical Practice?},
  author = {Fagerland, Morten W.},
  year = 2012,
  month = jun,
  journal = {BMC Medical Research Methodology},
  volume = {12},
  number = {1},
  pages = {78},
  issn = {1471-2288},
  doi = {10.1186/1471-2288-12-78},
  urldate = {2025-06-04},
  abstract = {During the last 30 years, the median sample size of research studies published in high-impact medical journals has increased manyfold, while the use of non-parametric tests has increased at the expense of t-tests. This paper explores this paradoxical practice and illustrates its consequences.},
  keywords = {{Data Interpretation, Statistical},{Models, Statistical},{Statistics, Nonparametric},\textbraceleft Data Interpretation,\textbraceleft Models,\textbraceleft Statistics,Computer Simulation,Confidence Intervals,Humans,Non-parametric test,Nonparametric\textbraceright,Probability,Sample size,Statistical practice,Statistical\textbraceright,T-test,Welch test,Wilcoxon-Mann-Whitney test},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/5XG4W6SM/Fagerland - 2012 - t-tests, non-parametric tests, and large studies—a paradox of statistical practice.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/RZW5Z7N6/1471-2288-12-78.html;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/SXVHTLJ4/1471-2288-12-78.html}
}

@article{Field:2017,
  title = {Robust Statistical Methods: {{A}} Primer for Clinical Psychology and Experimental Psychopathology Researchers},
  shorttitle = {Robust Statistical Methods},
  author = {Field, Andy P. and Wilcox, Rand R.},
  year = 2017,
  month = nov,
  journal = {Behaviour Research and Therapy},
  volume = {98},
  pages = {19--38},
  issn = {00057967},
  doi = {10.1016/j.brat.2017.05.013},
  urldate = {2025-05-28},
  abstract = {This paper reviews and offers tutorials on robust statistical methods relevant to clinical and experimental psychopathology researchers. We review the assumptions of one of the most commonly applied models in this journal (the general linear model, GLM) and the effects of violating them. We then present evidence that psychological data are more likely than not to violate these assumptions. Next, we overview some methods for correcting for violations of model assumptions. The final part of the paper presents 8 tutorials of robust statistical methods using R that cover a range of variants of the GLM (t-tests, ANOVA, multiple regression, multilevel models, latent growth models). We conclude with recommendations that set the expectations for what methods researchers submitting to the journal should apply and what they should report.},
  langid = {english},
  keywords = {Assumptions,Bias,Robust statistical methods},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/JR9J929U/Field und Wilcox - 2017 - Robust statistical methods A primer for clinical psychology and experimental psychopathology resear.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/P67NK6RH/Field und Wilcox - 2017 - Robust statistical methods A primer for clinical psychology and experimental psychopathology resear.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/HCA83YUT/S0005796717301067.html}
}

@book{Fisher:1925,
  title = {Statistical Methods for Research Workers},
  author = {Fisher, Ronald Aylmer},
  year = 1925,
  publisher = {{Oliver and Boyd}}
}

@book{Fisher:1934,
  title = {Statistical {{Method For Research Workers}}},
  author = {Fisher, Roland A.},
  year = 1934,
  edition = {9th edition},
  urldate = {2025-05-20},
  abstract = {Book Source: Digital Library of India Item 2015.205971 dc.contributor.author: Fisher, R. A dc.date.accessioned: 2015-07-09T14:25:03Z dc.date.available: 2015-07-09T14:25:03Z dc.date.digitalpublicationdate: 2005-02-28 dc.date.citation: 1934 dc.identifier.barcode: 1040010075117 dc.identifier.origpath: /data\_copy/upload/0075/122 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/205971 dc.description.scannerno: 4 dc.description.scanningcentre: IISc, Bangalore dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 334 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Svinfo dc.publisher: Oliver And Boyd,london dc.rights: Out\_of\_copyright dc.source.library: Jrd Tata Library, Indian Institute Of Science, Bangalore dc.subject.classification: Social Sciences dc.subject.classification: Demography.statistics.sociology dc.subject.classification: Fundamentals.basics Of Statistics dc.subject.keywords: Statistical Method For Research Workers dc.title: Statistical Method For Research Workers},
  langid = {english},
  keywords = {Other}
}

@book{Fisher:1935,
  title = {The Design of Experiments},
  author = {Fisher, Roland A.},
  year = 1971,
  edition = {9th ed},
  publisher = {Macmillan},
  isbn = {978-0-02-844690-5},
  langid = {english},
  annotation = {OCLC: 316331623}
}

@article{Fisher:1935a,
  title = {The {{Logic}} of {{Inductive Inference}}},
  author = {Fisher, R. A.},
  year = 1935,
  journal = {Journal of the Royal Statistical Society},
  volume = {98},
  number = {1},
  eprint = {10.2307/2342435},
  eprinttype = {jstor},
  pages = {39},
  issn = {09528385},
  doi = {10.2307/2342435},
  urldate = {2025-06-23},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/EBK35EP8/Fisher - 1935 - The Logic of Inductive Inference.pdf}
}

@book{Fisher:1970,
  title = {Statistical Methods for Research Workers},
  author = {Fisher, Ronald Aylmer},
  year = 1970,
  edition = {14th ed., revised and enlarged},
  publisher = {{Oliver and Boyd}},
  address = {Edinburgh},
  isbn = {978-0-05-002170-5},
  lccn = {HA29 .F5 1970},
  keywords = {Biometry,Statistics}
}

@book{Fisher:1990,
  title = {Statistical {{Methods}}, {{Experimental Design}}, and {{Scientific Inference}}: {{A Re-issue}} of {{Statistical Methods}} for {{Research Workers}}, the {{Design}} of {{Experiments}} and {{Statistical Methods}} and {{Scientific Inference}}},
  shorttitle = {Statistical {{Methods}}, {{Experimental Design}}, and {{Scientific Inference}}},
  author = {Fisher, Ronald A. and Yates, F},
  editor = {Bennett, J H},
  year = 1990,
  month = apr,
  publisher = {Oxford University PressOxford},
  doi = {10.1093/oso/9780198522294.001.0001},
  urldate = {2025-05-29},
  abstract = {Abstract             R.A. Fisher has had more influence on the development of statistical theory and practice than any other twentieth-century statistician. His writings (both in paper and book form) have proved to be as relevant to present-day statisticians as they were when first published. This book brings together as a single volume three of Fisher's most influential textbooks: Statistical Methods for Research Workers, The Design of Experiments , and Statistical Methods and Scientific Inference . In this new edition Frank Yates has provided a foreword which sheds fresh light on Fisher's thinking and on the writing and reception of each of the books. He discusses some of the key issues tackled in the three books and reflects on how the ideas expressed have come to permeate modern statistical practice.R.A. Fisher has had more influence on the development of statistical theory and practice than any other twentieth-century statistician. His writings (both in paper and book form) have proved to be as relevant to present-day statisticians as they were when first published. This book brings together as a single volume three of Fisher's most influential textbooks: Statistical Methods for Research Workers, The Design of Experiments , and Statistical Methods and Scientific Inference . In this new edition Frank Yates has provided a foreword which sheds fresh light on Fisher's thinking and on the writing and reception of each of the books. He discusses some of the key issues tackled in the three books and reflects on how the ideas expressed have come to permeate modern statistical practice.},
  isbn = {978-0-19-852229-4 978-1-383-02363-3},
  langid = {english}
}

@book{Fox:2019,
  title = {An {{R}} Companion to Applied Regression},
  author = {Fox, John and Weisberg, Sanford},
  year = 2019,
  edition = {3},
  publisher = {Sage},
  address = {Thousand Oaks CA}
}

@article{Franc:2025,
  title = {The {{Misuse}} of {{Normality Tests}} as {{Gatekeepers}} for {{Research}} in {{Prehospital}} and {{Disaster Medicine}}},
  author = {Franc, Jeffrey Michael},
  year = 2025,
  month = oct,
  journal = {Prehospital and Disaster Medicine},
  volume = {40},
  number = {5},
  pages = {241--242},
  publisher = {Cambridge University Press},
  issn = {1049-023X, 1945-1938},
  doi = {10.1017/S1049023X25101465},
  urldate = {2025-12-08},
  abstract = {This editorial discusses the common practice of using normality tests as a preliminary step for choosing between parametric and non-parametric methods. The editorial argues that such pre-testing is theoretically unfounded and practically harmful, as parametric tests are robust to moderate deviations from normality, while reliance on normality tests can distort error rates and mislead researchers.},
  langid = {english},
  keywords = {normality tests,parametric tests,statistical analysis},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/9X3JXYRM/Franc - 2025 - The Misuse of Normality Tests as Gatekeepers for Research in Prehospital and Disaster Medicine.pdf}
}

@article{Games:1976,
  title = {Pairwise Multiple Comparison Procedures with Unequal {{N}}'s and/or Variances: {{A Monte Carlo}} Study},
  shorttitle = {Pairwise Multiple Comparison Procedures with Unequal {{N}}'s and/or Variances},
  author = {Games, Paul A. and Howell, John F.},
  year = 1976,
  journal = {Journal of Educational Statistics},
  volume = {1},
  number = {2},
  pages = {113--125},
  publisher = {American Educational Research Assn},
  address = {US},
  issn = {0362-9791},
  doi = {10.2307/1164979},
  abstract = {Three different methods for testing all pairs of Yk - Yk{$\prime$} were contrasted under varying sample size and variance conditions. With unequal n's of 6 and up, only the Behrens-Fisher statistic provided satisfactory control of both the familywise rate of Type I errors and Type I error rate on each contrast. Satisfactory control with unequal n's of 3 and up is dubious even with this statistic. (15 ref) (PsycINFO Database Record (c) 2016 APA, all rights reserved)},
  keywords = {Statistical Samples,Statistical Significance,Statistical Tests,Variability Measurement},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/QSFZ3UYD/1979-12392-001.html;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/QYBAE3M6/1979-12392-001.html}
}

@article{Games:1979,
  title = {Tests for Homogeneity of Variance in Factorial Designs.},
  author = {Games, Paul A. and Keselman, Harvey J. and Clinch, Jennifer J.},
  year = 1979,
  month = sep,
  journal = {Psychological Bulletin},
  volume = {86},
  number = {5},
  pages = {978--984},
  issn = {1939-1455, 0033-2909},
  doi = {10.1037/0033-2909.86.5.978},
  urldate = {2025-07-11},
  langid = {english}
}

@article{Ghasemi:2012,
  title = {Normality {{Tests}} for {{Statistical Analysis}}: {{A Guide}} for {{Non-Statisticians}}},
  shorttitle = {Normality {{Tests}} for {{Statistical Analysis}}},
  author = {Ghasemi, Asghar and Zahediasl, Saleh},
  year = 2012,
  month = dec,
  journal = {Int J Endocrinol Metab},
  volume = {10},
  number = {2},
  pages = {486--489},
  issn = {1726-913X, 1726-9148},
  doi = {10.5812/ijem.3505},
  urldate = {2025-05-29},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/U87LFJAQ/Ghasemi und Zahediasl - 2012 - Normality Tests for Statistical Analysis A Guide for Non-Statisticians.pdf}
}

@article{Gosselin:2024,
  title = {Testing for Normality: A User's (Cautionary) Guide},
  shorttitle = {Testing for Normality},
  author = {Gosselin, Romain-Daniel},
  year = 2024,
  month = oct,
  journal = {Lab Anim},
  volume = {58},
  number = {5},
  pages = {433--437},
  publisher = {SAGE Publications},
  issn = {0023-6772},
  doi = {10.1177/00236772241276808},
  urldate = {2025-06-28},
  abstract = {The normality assumption postulates that empirical data derives from a normal (Gaussian) population. It is a pillar of inferential statistics that enables the theorization of probability functions and the computation of p-values thereof. The breach of this assumption may not impose a formal mathematical constraint on the computation of inferential outputs (e.g., p-values) but may make them inoperable and possibly lead to unethical waste of laboratory animals. Various methods, including statistical tests and qualitative visual examination, can reveal incompatibility with normality and the choice of a procedure should not be trivialized. The following minireview will provide a brief overview of diagrammatical methods and statistical tests commonly employed to evaluate congruence with normality. Special attention will be given to the potential pitfalls associated with their application. Normality is an unachievable ideal that practically never accurately describes natural variables, and detrimental consequences of non-normality may be safeguarded by using large samples. Therefore, the very concept of preliminary normality testing is also, arguably provocatively, questioned.},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/J3AU2PJG/Gosselin - 2024 - Testing for normality a user’s (cautionary) guide.pdf}
}

@misc{Grace-Martin:2012,
  title = {Checking the {{Normality Assumption}} for an {{ANOVA Model}}},
  author = {{Grace-Martin}, Karen},
  year = 2012,
  month = may,
  journal = {The Analysis Factor},
  urldate = {2025-06-03},
  abstract = {The assumptions are exactly the same for ANOVA and regression models. The normality assumption is that residuals follow a normal distribution. You usually see it like this:  {$\varepsilon$}\textasciitilde{} i.i.d. N(0, {$\sigma^2$})  But what it's really getting at is the distribution of Y\textbar X.},
  langid = {american},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/49RTZ8YP/checking-normality-anova-model.html}
}

@manual{Graves:2026,
  type = {Manual},
  title = {{{multcompView}}: {{Visualizations}} of Paired Comparisons},
  author = {Graves, Spencer and Piepho, Hans-Peter and {\noopsort{sundar dorai-raj}}{with help from Sundar Dorai-Raj}, Luciano Selzer},
  year = 2026,
  doi = {10.32614/CRAN.package.multcompView}
}

@manual{Gross:2015,
  type = {Manual},
  title = {Nortest: {{Tests}} for Normality},
  author = {Gross, Juergen and Ligges, Uwe},
  year = 2015,
  doi = {10.32614/CRAN.package.nortest}
}

@book{Hochberg:1987,
  title = {Multiple {{Comparison Procedures}}},
  author = {Hochberg, Yosef and Tamhane, Ajit C.},
  year = 1987,
  month = sep,
  series = {Wiley {{Series}} in {{Probability}} and {{Statistics}}},
  edition = {1},
  publisher = {Wiley},
  issn = {1940-6347},
  doi = {10.1002/9780470316672},
  urldate = {2025-05-23},
  copyright = {http://doi.wiley.com/10.1002/tdm\_license\_1.1},
  isbn = {978-0-471-82222-6 978-0-470-31667-2}
}

@book{Hollander:2014,
  title = {Nonparametric Statistical Methods},
  author = {Hollander, Myles and Chicken, Eric and Wolfe, Douglas A.},
  year = 2014,
  series = {Wiley Series in Probability and Statistics},
  edition = {Third edition},
  publisher = {John Wiley \& Sons, Inc},
  address = {Hoboken, New Jersey},
  isbn = {978-0-470-38737-5 978-1-118-67799-5},
  langid = {english}
}

@article{Holm:1979,
  title = {A {{Simple Sequentially Rejective Multiple Test Procedure}}},
  author = {Holm, Sture},
  year = 1979,
  journal = {Scandinavian Journal of Statistics},
  volume = {6},
  number = {2},
  eprint = {4615733},
  eprinttype = {jstor},
  pages = {65--70},
  publisher = {[Board of the Foundation of the Scandinavian Journal of Statistics, Wiley]},
  issn = {0303-6898},
  urldate = {2025-05-19},
  abstract = {This paper presents a simple and widely applicable multiple test procedure of the sequentially rejective type, i.e. hypotheses are rejected one at a time until no further rejections can be done. It is shown that the test has a prescribed level of significance protection against error of the first kind for any combination of true hypotheses. The power properties of the test and a number of possible applications are also discussed.}
}

@article{Jorgensen:2001,
  title = {Exponential Dispersion Models and Extensions: {{A}} Review},
  author = {J{\o}rgensen, Bent},
  year = 2001,
  journal = {International Statistical Review},
  volume = {69},
  number = {1},
  pages = {27--52},
  publisher = {Wiley Online Library}
}

@article{Juarros-Basterretxea:2024,
  title = {Post-Hoc Tests in One-Way {{ANOVA}}: {{The}} Case for Normal Distribution},
  shorttitle = {Post-Hoc Tests in One-Way {{ANOVA}}},
  author = {{Juarros-Basterretxea}, Joel and {Aonso-Diego}, Gema and Postigo, {\'A}lvaro and {Montes-{\'A}lvarez}, Pelayo and {Men{\'e}ndez-Aller}, {\'A}lvaro and {Garc{\'i}a-Cueto}, Eduardo},
  year = 2024,
  month = jun,
  journal = {Methodology},
  volume = {20},
  number = {2},
  pages = {84--99},
  issn = {1614-2241},
  doi = {10.5964/meth.11721},
  urldate = {2025-07-03},
  abstract = {When one-way ANOVA is statistically significant, a multiple comparison problem arises, hence post-hoc tests are needed to elucidate between which groups significant differences are found. Different post-hoc tests have been proposed for each situation regarding heteroscedasticity and sample size groups. This study aims to compare the Type I error ({$\alpha$}) rate of 10 post-hoc tests in four different conditions based on heteroscedasticity and balance between-group sample size. A Montecarlo simulation study was carried out on a total of 28 data sets, with 10,000 resamples in each, distributed through four conditions. One-way ANOVA tests and post-hoc tests were conducted to estimate the {$\alpha$} rate at a 95\% confidence level. The percentage of times the null hypothesis was falsely refused is used to compare the tests. Three out of four conditions demonstrated considerable variability among sample sizes. However, the best post-hoc test in the second condition (heteroscedastic and balance group) did not depend on simple size. In some cases, inappropriate post-hoc tests were more accurate. Homoscedasticity and balance between-group sample size should be considered for appropriate post-hoc test selection.},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/2SVIIFLS/Juarros-Basterretxea et al. - 2024 - Post-hoc tests in one-way ANOVA The case for normal distribution.pdf}
}

@article{Kamath:2025,
  title = {Assessing the Robustness of Normality Tests under Varying Skewness and Kurtosis: A Practical Checklist for Public Health Researchers},
  shorttitle = {Assessing the Robustness of Normality Tests under Varying Skewness and Kurtosis},
  author = {Kamath, Asha and Poojari, Satyanarayana and Varsha, K.},
  year = 2025,
  month = sep,
  journal = {BMC Med Res Methodol},
  volume = {25},
  number = {1},
  pages = {206},
  issn = {1471-2288},
  doi = {10.1186/s12874-025-02641-y},
  urldate = {2025-12-08},
  abstract = {Many statistical methods used in public health research, namely t-tests, ANOVA correlation and regression, rely on the assumption of normality. Violation of the normality assumption can severely lead to biased parameter estimates, reduced test power, and impact the reliability and validity of the findings, impacting the real-world evidence. An attempt to provide guidelines for choice of appropriate tests for assessment in public health data analytics is being made in this article.},
  langid = {english},
  keywords = {Normality,Power,Sample size,Skewness and Kurtosis,Type 1 error rate},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/NQNG858C/Kamath et al. - 2025 - Assessing the robustness of normality tests under varying skewness and kurtosis a practical checkli.pdf}
}

@article{Katsileros:2024,
  title = {A Comparison of Tests for Homoscedasticity Using Simulation and Empirical Data},
  author = {Katsileros, Anastasios and Antonetsis, Nikolaos and Mouzaidis, Paschalis and Tani, Eleni and Bebeli, Penelope J. and Karagrigoriou, Alex},
  year = 2024,
  month = jan,
  journal = {Communications for Statistical Applications and Methods},
  volume = {31},
  number = {1},
  pages = {1--35},
  issn = {2287-7843},
  doi = {10.29220/CSAM.2024.31.1.001},
  urldate = {2025-06-16},
  abstract = {Anastasios Katsileros, Nikolaos Antonetsis, Paschalis Mouzaidis, Eleni Tani, Penelope J. Bebeli, Alex Karagrigoriou. CSAM 2024;31:1-35. https://doi.org/10.29220/CSAM.2024.31.1.001},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/76SQNLQR/Katsileros et al. - 2024 - A comparison of tests for homoscedasticity using simulation and empirical data.pdf}
}

@article{Kim:2019,
  title = {More about the Basic Assumptions of T-Test: Normality and Sample Size},
  shorttitle = {More about the Basic Assumptions of T-Test},
  author = {Kim, Tae Kyun and Park, Jae Hong},
  year = 2019,
  month = apr,
  journal = {Korean J Anesthesiol},
  volume = {72},
  number = {4},
  pages = {331--335},
  publisher = {Korean Society of Anesthesiologists},
  issn = {2005-6419, 2005-7563},
  doi = {10.4097/kja.d.18.00292},
  urldate = {2025-06-05},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/2BNZTQYP/Kim und Park - 2019 - More about the basic assumptions of t-test normality and sample size.pdf}
}

@article{Knief:2021,
  title = {Violating the Normality Assumption May Be the Lesser of Two Evils},
  author = {Knief, Ulrich and Forstmeier, Wolfgang},
  year = 2021,
  journal = {Behav Res Methods},
  volume = {53},
  number = {6},
  pages = {2576--2590},
  issn = {1554-351X},
  doi = {10.3758/s13428-021-01587-5},
  urldate = {2025-12-08},
  abstract = {When data are not normally distributed, researchers are often uncertain whether it is legitimate to use tests that assume Gaussian errors, or whether one has to either model a more specific error structure or use randomization techniques. Here we use Monte Carlo simulations to explore the pros and cons of fitting Gaussian models to non-normal data in terms of risk of type I error, power and utility for parameter estimation. We find that Gaussian models are robust to non-normality over a wide range of conditions, meaning that p values remain fairly reliable except for data with influential outliers judged at strict alpha levels. Gaussian models also performed well in terms of power across all simulated scenarios. Parameter estimates were mostly unbiased and precise except if sample sizes were small or the distribution of the predictor was highly skewed. Transformation of data before analysis is often advisable and visual inspection for outliers and heteroscedasticity is important for assessment. In strong contrast, some non-Gaussian models and randomization techniques bear a range of risks that are often insufficiently known. High rates of false-positive conclusions can arise for instance when overdispersion in count data is not controlled appropriately or when randomization procedures ignore existing non-independencies in the data. Hence, newly developed statistical methods not only bring new opportunities, but they can also pose new threats to reliability. We argue that violating the normality assumption bears risks that are limited and manageable, while several more sophisticated approaches are relatively error prone and particularly difficult to check during peer review. Scientists and reviewers who are not fully aware of the risks might benefit from preferentially trusting Gaussian mixed models in which random effects account for non-independencies in the data.},
  pmcid = {PMC8613103},
  pmid = {33963496},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/L96K42U3/Knief und Forstmeier - 2021 - Violating the normality assumption may be the lesser of two evils.pdf}
}

@article{Kozak:2018,
  title = {What's Normal Anyway? {{Residual}} Plots Are More Telling than Significance Tests When Checking {{{\textsc{ANOVA}}}} Assumptions},
  shorttitle = {What's Normal Anyway?},
  author = {Kozak, M. and Piepho, H.-P.},
  year = 2018,
  month = feb,
  journal = {J Agronomy Crop Science},
  volume = {204},
  number = {1},
  pages = {86--98},
  issn = {0931-2250, 1439-037X},
  doi = {10.1111/jac.12220},
  urldate = {2025-06-20},
  abstract = {Abstract                            We consider two questions important for applying analysis of variance (               ANOVA               ): Should normality be checked on the raw data or on the residuals (or is it immaterial which of the two approaches we take)? Should normality and homogeneity of variance be checked using significance tests or diagnostic plots (or both)? Based on two examples, we show that residuals should be used for model checking and that residual plots are better for checking               ANOVA               assumptions than statistical tests. We also discuss why one should be very cautious when using statistical tests to check the assumptions.},
  copyright = {http://onlinelibrary.wiley.com/termsAndConditions\#vor},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/88M9NAGB/Kozak und Piepho - 2018 - What's normal anyway Residual plots are more telling than significance tests when checking span st.pdf}
}

@article{Kruskal:1952,
  title = {Use of {{Ranks}} in {{One-Criterion Variance Analysis}}},
  author = {Kruskal, William H. and Wallis, W. Allen},
  year = 1952,
  journal = {Journal of the American Statistical Association},
  volume = {47},
  number = {260},
  eprint = {2280779},
  eprinttype = {jstor},
  pages = {583--621},
  publisher = {[American Statistical Association, Taylor \& Francis, Ltd.]},
  issn = {0162-1459},
  doi = {10.2307/2280779},
  urldate = {2025-05-19},
  abstract = {Given C samples, with n\textsubscript{i} observations in the ith sample, a test of the hypothesis that the samples are from the same population may be made by ranking the observations from from 1 to \$\textbackslash Sum n\_i\$ (giving each observation in a group of ties the mean of the ranks tied for), finding the C sums of ranks, and computing a statistic H. Under the stated hypothesis, H is distributed approximately as {$\chi$}\textsuperscript{2}(C - 1), unless the samples are too small, in which case special approximations or exact tables are provided. One of the most important applications of the test is in detecting differences among the population means.}
}

@book{Kutner:2005,
  title = {Applied Linear Statistical Models},
  author = {Kutner, Michael H.},
  year = 2005,
  publisher = {Boston : McGraw-Hill Irwin},
  urldate = {2025-06-29},
  abstract = {xxviii, 1396 pages : 24 cm +; Applied Linear Statistical Models", 5e, is the long established leading authoritative text and reference on statistical modeling. For students in most any discipline where statistical analysis or interpretation is used, ALSM serves as the standard work. The text includes brief introductory and review material, and then proceeds through regression and modeling for the first half, and through ANOVA and Experimental Design in the second half. All topics are presented in a precise and clear style supported with solved examples, numbered formulae, graphic illustrations, and "Notes" to provide depth and statistical accuracy and precision. Applications used within the text and the hallmark problems, exercises, and projects are drawn from virtually all disciplines and fields providing motivation for students in virtually any college. The Fifth edition provides an increased use of computing and graphical analysis throughout, without sacrificing concepts or rigor. In general, the 5e uses larger data sets in examples and exercises, and where methods can be automated within software without loss of understanding, it is so done; CD-ROM Title: Student CD-ROM to accompany applied linear statistical models, 5th ed; System requirements for accompanying CD-ROM: PC, pentium based processor; Microsoft Windows 98/2000/XP; IE explorer 5.5; MS Office or equivalent; Includes bibliographical references (pages 1374-1384) and index; Simple Linear Regression -- Multiple Linear Regression -- NonLinear Regression -- Design and Analysis of Single-Factor Studies -- Multi-Factor Studies -- Specialized Study Designs},
  collaborator = {{Internet Archive}},
  isbn = {978-0-07-238688-2 978-0-07-112221-4 978-0-07-310874-2 978-0-07-238690-5},
  langid = {english},
  keywords = {Regression analysis -- Textbooks}
}

@article{Kwak:2017,
  title = {Central Limit Theorem: The Cornerstone of Modern Statistics},
  shorttitle = {Central Limit Theorem},
  author = {Kwak, Sang Gyu and Kim, Jong Hae},
  year = 2017,
  month = apr,
  journal = {Korean J Anesthesiol},
  volume = {70},
  number = {2},
  pages = {144--156},
  issn = {2005-6419},
  doi = {10.4097/kjae.2017.70.2.144},
  urldate = {2025-06-05},
  abstract = {According to the central limit theorem, the means of a random sample of size, n, from a population with mean, \textmu, and variance, {$\sigma$}2, distribute normally with mean, \textmu, and variance, {$\sigma$}2n. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding.},
  pmcid = {PMC5370305},
  pmid = {28367284},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/3SF7FASB/Kwak und Kim - 2017 - Central limit theorem the cornerstone of modern statistics.pdf}
}

@article{Lantz:2013,
  title = {The Impact of Sample Non-normality on {{ANOVA}} and Alternative Methods},
  author = {Lantz, Bj{\"o}rn},
  year = 2013,
  month = may,
  journal = {Brit J Math \& Statis},
  volume = {66},
  number = {2},
  pages = {224--244},
  issn = {0007-1102, 2044-8317},
  doi = {10.1111/j.2044-8317.2012.02047.x},
  urldate = {2025-07-14},
  copyright = {http://onlinelibrary.wiley.com/termsAndConditions\#vor},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/6YRX7WYQ/Lantz - 2013 - The impact of sample non‐normality on ANOVA and alternative methods.pdf}
}

@article{LeBoedec:2016,
  title = {Sensitivity and Specificity of Normality Tests and Consequences on Reference Interval Accuracy at Small Sample Size: A Computer-Simulation Study},
  shorttitle = {Sensitivity and Specificity of Normality Tests and Consequences on Reference Interval Accuracy at Small Sample Size},
  author = {Le Boedec, Kevin},
  year = 2016,
  month = dec,
  journal = {Vet Clin Pathol},
  volume = {45},
  number = {4},
  pages = {648--656},
  issn = {1939-165X},
  doi = {10.1111/vcp.12390},
  abstract = {BACKGROUND: According to international guidelines, parametric methods must be chosen for RI construction when the sample size is small and the distribution is Gaussian. However, normality tests may not be accurate at small sample size. OBJECTIVES: The purpose of the study was to evaluate normality test performance to properly identify samples extracted from a Gaussian population at small sample sizes, and assess the consequences on RI accuracy of applying parametric methods to samples that falsely identified the parent population as Gaussian. METHODS: Samples of n = 60 and n = 30 values were randomly selected 100 times from simulated Gaussian, lognormal, and asymmetric populations of 10,000 values. The sensitivity and specificity of 4 normality tests were compared. Reference intervals were calculated using 6 different statistical methods from samples that falsely identified the parent population as Gaussian, and their accuracy was compared. RESULTS: Shapiro-Wilk and D'Agostino-Pearson tests were the best performing normality tests. However, their specificity was poor at sample size n = 30 (specificity for P {$<$} .05: .51 and .50, respectively). The best significance levels identified when n = 30 were 0.19 for Shapiro-Wilk test and 0.18 for D'Agostino-Pearson test. Using parametric methods on samples extracted from a lognormal population but falsely identified as Gaussian led to clinically relevant inaccuracies. CONCLUSIONS: At small sample size, normality tests may lead to erroneous use of parametric methods to build RI. Using nonparametric methods (or alternatively Box-Cox transformation) on all samples regardless of their distribution or adjusting, the significance level of normality tests depending on sample size would limit the risk of constructing inaccurate RI.},
  langid = {english},
  pmid = {27556235},
  keywords = {Animals,Computer Simulation,Data Accuracy,Gaussian distribution,nonparametric method,Normal Distribution,parametric method,Reference Values,Sample Size,Sensitivity and Specificity,Shapiro-Wilk test}
}

@incollection{Levene:1960,
  title = {Robust Tests for Equality of Variances},
  booktitle = {Contributions to Probability and Statistics: {{Essays}} in Honor of Harold Hotelling},
  author = {Levene, Howard},
  editor = {Olkin, Ingram},
  year = 1960,
  pages = {278--292},
  publisher = {Stanford University Press},
  address = {Stanford, CA}
}

@misc{Lindelov:2019,
  title = {Common Statistical Tests Are Linear Models (or: How to Teach Stats)},
  author = {Lindel{\o}v, Jonas Kristoffer},
  year = 2019
}

@phdthesis{Liu:,
  title = {Comparing {{Welch}}'s {{ANOVA}}, a {{Kruskal-Wallis}} Test and Traditional {{ANOVA}} in Case of {{Heterogeneity}} of {{Variance}}},
  author = {Liu, Hangcheng},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/BGVR2W7L/Liu - Comparing Welch's ANOVA, a Kruskal-Wallis test and traditional ANOVA in case of Heterogeneity of Var.pdf}
}

@article{Lix:1996,
  title = {Consequences of {{Assumption Violations Revisited}}: {{A Quantitative Review}} of {{Alternatives}} to the {{One-Way Analysis}} of {{Variance}} {{{\emph{F}}}} {{Test}}},
  shorttitle = {Consequences of {{Assumption Violations Revisited}}},
  author = {Lix, Lisa M. and Keselman, Joanne C. and Keselman, H. J.},
  year = 1996,
  month = dec,
  journal = {Review of Educational Research},
  volume = {66},
  number = {4},
  pages = {579--619},
  issn = {0034-6543, 1935-1046},
  doi = {10.3102/00346543066004579},
  urldate = {2025-07-04},
  abstract = {The presence of variance heterogeneity and nonnormality in educational and psychological data may frequently invalidate the use of the analysis of variance (ANOVA) F test in one-way independent groups designs. This article offers recommendations to applied researchers on the use of various parametric and nonparametric alternatives to the F test under assumption violation conditions. Meta-analytic techniques were used to summarize the statistical robustness literature on the Type I error properties of the Brown-Forsythe (Brown \& Forsythe, 1974 ), James (1951) second-order, Kruskal-Wallis ( Kruskal \& Wallis, 1952 ), and Welch (1951) tests. Two variables, based on the theoretical work of Box (1954) , are shown to be highly effective in deciding when a particular alternative procedure should be adopted. Based on the meta-analysis findings, it is recommended that researchers gain a clear understanding of the nature of their data before conducting statistical analyses. Of all of the procedures, the James and Welch tests performed best under violations of the variance homogeneity assumption, although their sensitivity to certain types of nonnormality may preclude their use in all data-analytic situations. Opportunities for further methodological studies of ANOVA alternative procedures are also discussed.},
  copyright = {https://journals.sagepub.com/page/policies/text-and-data-mining-license},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/EZIF5K7J/Lix et al. - 1996 - Consequences of Assumption Violations Revisited A Quantitative Review of Alternatives to the One-Wa.pdf}
}

@article{Lumley:2002,
  title = {The {{Importance}} of the {{Normality Assumption}} in {{Large Public Health Data Sets}}},
  author = {Lumley, Thomas and Diehr, Paula and Emerson, Scott and Chen, Lu},
  year = 2002,
  month = may,
  journal = {Annu. Rev. Public Health},
  volume = {23},
  number = {1},
  pages = {151--169},
  issn = {0163-7525, 1545-2093},
  doi = {10.1146/annurev.publhealth.23.100901.140546},
  urldate = {2025-06-03},
  abstract = {▪ Abstract\enspace{} It is widely but incorrectly believed that the t-test and linear regression are valid only for Normally distributed outcomes. The t-test and linear regression compare the mean of an outcome variable for different subjects. While these are valid even in very small samples if the outcome variable is Normally distributed, their major usefulness comes from the fact that in large samples they are valid for any distribution. We demonstrate this validity by simulation in extremely non-Normal data. We discuss situations in which in other methods such as the Wilcoxon rank sum test and ordinal logistic regression (proportional odds model) have been recommended, and conclude that the t-test and linear regression often provide a convenient and practical alternative. The major limitation on the t-test and linear regression for inference about associations is not a distributional one, but whether detecting and estimating a difference in the mean of the outcome answers the scientific question at hand.},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/5V5NQAXG/E662F882-7A81-4F34-9958-C30949933CA8.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/827EFYF5/E662F882-7A81-4F34-9958-C30949933CA8.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/CMENI3TQ/E662F882-7A81-4F34-9958-C30949933CA8.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/RQ6FBQZ5/E662F882-7A81-4F34-9958-C30949933CA8.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/SLGATDQ7/E662F882-7A81-4F34-9958-C30949933CA8.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/UUMIL633/Lumley et al. - 2002 - The Importance of the Normality Assumption in Large Public Health Data Sets.pdf}
}

@article{Mann:1947,
  title = {On a Test of Whether One of Two Random Variables Is Stochastically Larger than the Other},
  author = {Mann, Henry B. and Whitney, Donald R.},
  year = 1947,
  journal = {The Annals of Mathematical Statistics},
  volume = {18},
  number = {1},
  pages = {50--60},
  doi = {10.1214/aoms/1177730491}
}

@article{Marsaglia:2004,
  title = {Evaluating the {{Anderson-Darling Distribution}}},
  author = {Marsaglia, George and Marsaglia, John},
  year = 2004,
  month = feb,
  journal = {Journal of Statistical Software},
  volume = {9},
  pages = {1--5},
  issn = {1548-7660},
  doi = {10.18637/jss.v009.i02},
  urldate = {2026-05-12},
  abstract = {Except for n = 1, only the limit as n approaches infinity for the distribution of the Anderson-Darling test for uniformity has been found, and that in so complicated a form that published values for a few percentiles had to be determined by numerical integration, saddlepoint or other approximation methods. We give here our method for evaluating that asymptotic distribution to great accuracy--directly, via series with two-term recursions. We also give, for any particular n, a procedure for evaluating the distribution to the fourth digit, based on empirical CDF's from samples of size 1010 .},
  copyright = {Copyright (c) 2004 George Marsaglia, John Marsaglia},
  langid = {english}
}

@book{McCullagh:1989,
  title = {Generalized {{Linear Models}}},
  author = {McCullagh, P. and Nelder, J. A.},
  year = 1989,
  publisher = {Springer US},
  address = {Boston, MA},
  doi = {10.1007/978-1-4899-3242-6},
  urldate = {2025-06-29},
  copyright = {http://www.springer.com/tdm},
  isbn = {978-0-412-31760-6 978-1-4899-3242-6},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/IVYUHLEY/McCullagh und Nelder - 1989 - Generalized Linear Models.pdf}
}

@book{Meier:,
  title = {Statistik F\"ur {{Fortgeschrittene}} - {{Kommentare}} Zu {{R-Anwendungen}}},
  author = {Meier, L., M. Kalisch},
  urldate = {2025-06-27},
  abstract = {In diesem Dokument wird die Anwendung verschiedener Statistikmethoden an Beispielen illustiert. Die wichtigsten Punkte der zu Grunde liegenden Theorie werden dabei stichpunktartig wiederholt.},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/JDKMG73M/power.html}
}

@article{Micceri:1989,
  title = {The Unicorn, the Normal Curve, and Other Improbable Creatures.},
  author = {Micceri, Theodore},
  year = 1989,
  journal = {Psychological Bulletin},
  volume = {105},
  number = {1},
  pages = {156--166},
  issn = {1939-1455, 0033-2909},
  doi = {10.1037/0033-2909.105.1.156},
  urldate = {2025-07-11},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/CYRRHHV5/Micceri - 1989 - The unicorn, the normal curve, and other improbable creatures..pdf}
}

@article{Mishra:2019,
  title = {Descriptive {{Statistics}} and {{Normality Tests}} for {{Statistical Data}}},
  author = {Mishra, Prabhaker and Pandey, Chandra M and Singh, Uttam and Gupta, Anshul and Sahu, Chinmoy and Keshri, Amit},
  year = 2019,
  journal = {Ann Card Anaesth},
  volume = {22},
  number = {1},
  pages = {67--72},
  issn = {0971-9784},
  doi = {10.4103/aca.ACA_157_18},
  urldate = {2025-06-05},
  abstract = {Descriptive statistics are an important part of biomedical research which is used to describe the basic features of the data in the study. They provide simple summaries about the sample and the measures. Measures of the central tendency and dispersion are used to describe the quantitative data. For the continuous data, test of the normality is an important step for deciding the measures of central tendency and statistical methods for data analysis. When our data follow normal distribution, parametric tests otherwise nonparametric methods are used to compare the groups. There are different methods used to test the normality of data, including numerical and visual methods, and each method has its own advantages and disadvantages. In the present study, we have discussed the summary measures and methods used to test the normality of the data.},
  pmcid = {PMC6350423},
  pmid = {30648682},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/6BMKME5I/Mishra et al. - 2019 - Descriptive Statistics and Normality Tests for Statistical Data.pdf}
}

@article{Moser:1992,
  title = {Homogeneity of Variance in the Two-Sample Means Test},
  author = {Moser, B K and Stevens, G. R.},
  year = 1992,
  month = feb,
  journal = {The American Statistician},
  pages = {19--21},
  doi = {10.1080/00031305.1992.10475839},
  abstract = {Homogeneity of Variance in the Two-Sample Means Test Page 1 In this department The Amrricai? Starisrician publishes articles. reviews, and notes of interest to teachers of the first mathematical statistics cowbe and of applied statistics courses. The department includes the Accen( on Teaching Materials section; suitable contents for the section are described under the section heading. Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses \l dots},
  keywords = {Power,Preliminary variance test,Size},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/2EIU6DZC/moser1992.pdf}
}

@article{Nelder:1972,
  title = {Generalized Linear Models},
  author = {Nelder, John Ashworth and Wedderburn, Robert WM},
  year = 1972,
  journal = {Journal of the Royal Statistical Society: Series A (General)},
  volume = {135},
  number = {3},
  pages = {370--384},
  publisher = {Wiley Online Library},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/HCIYNIBZ/Nelder und Wedderburn - 1972 - Generalized Linear Models.pdf}
}

@article{Nimon:2017,
  title = {Regression as the {{Univariate General Linear Model}}: {{Examining Test Statistics}}, p Values, {{Effect Sizes}},and {{Descriptive Statistics Using R}}},
  shorttitle = {Regression as the {{Univariate General Linear Model}}},
  author = {Nimon, Kim and Mull, Mandolen and Berrios, Julia and Musgrave, Jon and Keiffer, Greggory L.},
  year = 2017,
  journal = {General Linear Model Journal},
  volume = {43},
  number = {1},
  pages = {50--82},
  issn = {2379-0105},
  doi = {10.31523/glmj.04301.004},
  urldate = {2025-12-30},
  abstract = {This paper presents regression as the univariate general linear model (GLM). Building on the work of Cohen (1968), McNeil (1974), and Zientek and Thompson (2009), the paper uses descriptive statistics to build a small, simulated dataset that readers can use to verify that multiple linear regression (MLR) subsumes the univariate parametric analyses in the GLM. Unlike other related works, we provide R syntax that demonstrates how MLR produces equivalent test statistics, p values, effect sizes, and descriptive statistics when compared to the univariate analyses that MLR subsumes. The paper diverges from Zientek and Thompson by presenting an expanded hierarchy for MLR and demonstrating why only the case of the chi-square test of independence where the criterion variable is dichotomous, and not the general case, is subsumed by MLR. Readers will find an accessible treatment of the GLM as well as R syntax, which they can use to report descriptive statistics, p values, and effect sizes associated with the univariate parametric statistics in the GLM.},
  copyright = {Copyright (c) 2017 Kim Nimon, Mandolen Mull, Julia Berrios, Jon Musgrave, Greggory L. Keiffer (Author)},
  langid = {english},
  keywords = {Univariate General Linear Model},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/QNPXEBJT/Nimon et al. - 2017 - Regression as the Univariate General Linear Model Examining Test Statistics, p values, Effect Sizes.pdf}
}

@article{Nuijten:2016,
  title = {The Prevalence of Statistical Reporting Errors in Psychology (1985-2013)},
  author = {Nuijten, Mich{\`e}le B. and Hartgerink, Chris H. J. and {\noopsort{assen}}{van Assen}, Marcel A. L. M. and Epskamp, Sacha and Wicherts, Jelte M.},
  year = 2016,
  month = dec,
  journal = {Behav Res Methods},
  volume = {48},
  number = {4},
  pages = {1205--1226},
  issn = {1554-3528},
  doi = {10.3758/s13428-015-0664-2},
  abstract = {This study documents reporting errors in a sample of over 250,000 p-values reported in eight major psychology journals from 1985 until 2013, using the new R package "statcheck." statcheck retrieved null-hypothesis significance testing (NHST) results from over half of the articles from this period. In line with earlier research, we found that half of all published psychology papers that use NHST contained at least one p-value that was inconsistent with its test statistic and degrees of freedom. One in eight papers contained a grossly inconsistent p-value that may have affected the statistical conclusion. In contrast to earlier findings, we found that the average prevalence of inconsistent p-values has been stable over the years or has declined. The prevalence of gross inconsistencies was higher in p-values reported as significant than in p-values reported as nonsignificant. This could indicate a systematic bias in favor of significant results. Possible solutions for the high prevalence of reporting inconsistencies could be to encourage sharing data, to let co-authors check results in a so-called "co-pilot model," and to use statcheck to flag possible inconsistencies in one's own manuscript or during the review process.},
  langid = {english},
  pmcid = {PMC5101263},
  pmid = {26497820},
  keywords = {Behavioral Research,Bias,False positives,Humans,NHST,p-values,Prevalence,Publication bias,Questionable research practices,Reporting errors,Significance},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/AWGNY7TX/Nuijten et al. - 2016 - The prevalence of statistical reporting errors in psychology (1985-2013).pdf}
}

@article{Olejnik:1987,
  title = {Type {{I Error Rates}} and {{Power Estimates}} of {{Selected Parametric}} and {{Nonparametric Tests}} of {{Scale}}},
  author = {Olejnik, Stephen F. and Algina, James},
  year = 1987,
  journal = {Journal of Educational Statistics},
  volume = {12},
  number = {1},
  eprint = {1164627},
  eprinttype = {jstor},
  pages = {45},
  issn = {03629791},
  doi = {10.2307/1164627},
  urldate = {2025-06-17},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/ZRXDDFRZ/Olejnik und Algina - 1987 - Type I Error Rates and Power Estimates of Selected Parametric and Nonparametric Tests of Scale.pdf}
}

@article{Patil:2021,
  title = {Visualizations with Statistical Details: {{The}} 'ggstatsplot' Approach},
  shorttitle = {Visualizations with Statistical Details},
  author = {Patil, Indrajeet},
  year = 2021,
  month = may,
  journal = {Journal of Open Source Software},
  volume = {6},
  number = {61},
  pages = {3167},
  issn = {2475-9066},
  doi = {10.21105/joss.03167},
  urldate = {2026-05-04},
  abstract = {Patil, I., (2021). Visualizations with statistical details: The 'ggstatsplot' approach. Journal of Open Source Software, 6(61), 3167, https://doi.org/10.21105/joss.03167},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/SLJXM2B9/Patil - 2021 - Visualizations with statistical details The 'ggstatsplot' approach.pdf}
}

@article{Patil:2021a,
  title = {{{statsExpressions}}: {{R Package}} for {{Tidy Dataframes}} and {{Expressions}} with {{Statistical Details}}},
  shorttitle = {{{statsExpressions}}},
  author = {Patil, Indrajeet},
  year = 2021,
  month = may,
  journal = {Journal of Open Source Software},
  volume = {6},
  number = {61},
  pages = {3236},
  issn = {2475-9066},
  doi = {10.21105/joss.03236},
  urldate = {2026-05-04},
  abstract = {Patil, I., (2021). statsExpressions: R Package for Tidy Dataframes and Expressions with Statistical Details. Journal of Open Source Software, 6(61), 3236, https://doi.org/10.21105/joss.03236},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/J9PPECU6/Patil - 2021 - statsExpressions R Package for Tidy Dataframes and Expressions with Statistical Details.pdf}
}

@article{Pearson:1900,
  title = {On the Criterion That a given System of Deviations from the Probable in the Case of a Correlated System of Variables Is Such That It Can Be Reasonably Supposed to Have Arisen from Random Sampling},
  author = {Pearson, Karl},
  year = 1900,
  month = jul,
  journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
  volume = {50},
  number = {302},
  pages = {157--175},
  issn = {1941-5982, 1941-5990},
  doi = {10.1080/14786440009463897},
  urldate = {2025-05-19},
  langid = {english}
}

@article{Rasch:2011,
  title = {The Two-Sample t Test: Pre-Testing Its Assumptions Does Not Pay Off},
  shorttitle = {The Two-Sample t Test},
  author = {Rasch, Dieter and Kubinger, Klaus D. and Moder, Karl},
  year = 2011,
  month = feb,
  journal = {Stat Papers},
  volume = {52},
  number = {1},
  pages = {219--231},
  issn = {0932-5026, 1613-9798},
  doi = {10.1007/s00362-009-0224-x},
  urldate = {2025-05-19},
  copyright = {http://www.springer.com/tdm},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/KADLMW3L/Ra-Ku-Mo_StatisticalPapers.pdf}
}

@article{Razali:2011,
  title = {Power Comparisons of {{Shapiro-Wilk}}, {{Kolmogorov-Smirnov}}, {{Lilliefors}} and {{Anderson-Darling}} Tests},
  author = {Razali, Nornadiah Mohd and Wah, Yap Bee},
  year = 2011,
  journal = {Journal of Statistical Modeling and Analytics},
  volume = {2},
  number = {1},
  pages = {21--33},
  publisher = {Scienpress Ltd}
}

@manual{RCoreTeam:2025,
  type = {Manual},
  title = {R: A Language and Environment for Statistical Computing},
  author = {{R Core Team}},
  year = 2025,
  address = {Vienna, Austria},
  institution = {R Foundation for Statistical Computing}
}

@article{Royston:1982,
  title = {An {{Extension}} of {{Shapiro}} and {{Wilk}}'s {{W Test}} for {{Normality}} to {{Large Samples}}},
  author = {Royston, J. P.},
  year = 1982,
  month = jun,
  journal = {J. R. Stat. Soc. Ser. C. Appl. Stat.},
  volume = {31},
  number = {2},
  pages = {115--124},
  issn = {0035-9254},
  doi = {10.2307/2347973},
  urldate = {2026-05-03},
  abstract = {Shapiro and Wilk's (1965) W statistic arguably provides the best omnibus test of normality, but is currently limited to sample sizes between 3 and 50. W is extended up to n = 2000 and an approximate normalizing transformation suitable for computer implementation is given. A novel application of W in transforming data to normality is suggested, using the three-parameter lognormal as an example.},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/6A4YUG6R/Royston - 1982 - An Extension of Shapiro and Wilk’s W Test for Normality to Large Samples.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/83FGLPUX/2347973.html}
}

@article{Ruxton:2006,
  title = {The Unequal Variance T-Test Is an Underused Alternative to {{Student}}'s t-Test and the {{Mann}}--{{Whitney U}} Test},
  author = {Ruxton, Graeme D},
  year = 2006,
  journal = {Behavioral Ecology},
  volume = {17},
  number = {4},
  pages = {688--690},
  publisher = {Oxford University Press},
  doi = {10.1093/beheco/ark016},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/RKPZY4TK/ark016.html}
}

@book{Salkind:2007,
  title = {Encyclopedia of Measurement and Statistics},
  author = {Salkind, Neil J. and Rasmussen, Kristin},
  year = 2007,
  publisher = {SAGE Publications},
  address = {Thousand Oaks, Calif.},
  abstract = {"The study of measurement and statistics can be less than inviting. However, in fields as varying as education, politics, and health care, assessment and the use of measurement and statistics have become integral parts of almost every activity undertaken. These activities require the organization of ideas, the generation of hypotheses, the collection of data, and the interpretation, illustration, and analysis of data. No matter where educated people look, this critical analysis is more important than ever in an age where information - and lots of it - is readily available. The Encyclopedia of Measurement and Statistics presents state-of-the-art information and ready-to-use facts from the fields of measurement and statistics in an unintimidating style. The ideas and tools contained in these pages are approachable and can be invaluable for understanding our very technical world and the increasing flow of information. Although there are references that cover statistics and assessment in depth, none provides as comprehensive a resource in as focused and accessible a manner as the two volumes of this encyclopedia. Through approximately 500 contributions, experts provide an overview and an explanation of the major topics in these two areas. Key Features Covers every major facet of these two different, but highly integrated disciplines - from mean, mode, and median to reliability, validity, significance, correlation, and much more - all without overwhelming the informed reader Offers cross-disciplinary coverage, with contributions from and applications to the fields of Psychology, Education, Sociology, Human Development, Political Science, Business and Management, Public Health, and others Provides cross-reference terms, a brief listing of further readings, and Web site URLs following most entries, as well as an extensive set of appendices and an annotated list of organizations relevant to measurement and statistics Appendices Features Appendix A is a guide to basic statistics for those readers who might like an instructional step-by-step presentation of basic concepts in statistics and measurement Appendix B is a table of critical values used in hypothesis testing and an important part of any reference in this area Appendix C represents a collection of some important and useful measurement and statistics Internet sites A primary goal of creating this set of volumes is to open up the broad discipline of measurement and statistics to a wider and more general audience than usual},
  isbn = {978-1-4129-3963-8},
  langid = {english},
  annotation = {OCLC: 162107519}
}

@article{Satterthwaite:1946,
  title = {An {{Approximate Distribution}} of {{Estimates}} of {{Variance Components}}},
  author = {Satterthwaite, F. E.},
  year = 1946,
  journal = {Biometrics Bulletin},
  volume = {2},
  number = {6},
  pages = {110--114},
  publisher = {[International Biometric Society, Wiley]},
  issn = {0099-4987},
  doi = {10.2307/3002019},
  urldate = {2025-05-19},
  jstor = {3002019}
}

@book{Searle:1971,
  title = {Linear Models},
  author = {Searle, Shayle R},
  year = 1971,
  publisher = {John Wiley \& Sons}
}

@article{Shapiro:1965,
  title = {An Analysis of Variance Test for Normality (Complete Samples)\dag},
  author = {Shapiro, S. S. and Wilk, M. B.},
  year = 1965,
  month = dec,
  journal = {Biometrika},
  volume = {52},
  number = {3-4},
  pages = {591--611},
  issn = {0006-3444},
  doi = {10.1093/biomet/52.3-4.591},
  urldate = {2025-06-05},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/CTQLTNS6/ShapiroWilk.pdf}
}

@article{Shatz:2024,
  title = {Assumption-Checking Rather than (Just) Testing: {{The}} Importance of Visualization and Effect Size in Statistical Diagnostics},
  shorttitle = {Assumption-Checking Rather than (Just) Testing},
  author = {Shatz, Itamar},
  year = 2024,
  month = feb,
  journal = {Behav Res},
  volume = {56},
  number = {2},
  pages = {826--845},
  issn = {1554-3528},
  doi = {10.3758/s13428-023-02072-x},
  urldate = {2025-06-05},
  abstract = {Statistical methods generally have assumptions (e.g., normality in linear regression models). Violations of these assumptions can cause various issues, like statistical errors and biased estimates, whose impact can range from inconsequential to critical. Accordingly, it is important to check these assumptions, but this is often done in a flawed way. Here, I first present a prevalent but problematic approach to diagnostics---testing assumptions using null hypothesis significance tests (e.g., the Shapiro--Wilk test of normality). Then, I consolidate and illustrate the issues with this approach, primarily using simulations. These issues include statistical errors (i.e., false positives, especially with large samples, and false negatives, especially with small samples), false binarity, limited descriptiveness, misinterpretation (e.g., of p-value as an~effect size), and potential testing failure due to unmet test assumptions. Finally, I synthesize the implications of these issues for statistical diagnostics, and provide practical recommendations for improving such diagnostics. Key recommendations include maintaining awareness of the issues with assumption tests (while recognizing they can be useful), using appropriate combinations of diagnostic methods (including visualization and effect sizes) while recognizing their limitations, and distinguishing between testing and checking assumptions. Additional recommendations include judging assumption violations as a complex spectrum (rather than a simplistic binary), using programmatic tools that increase replicability and decrease researcher degrees of freedom, and sharing the material and rationale involved in the diagnostics.},
  langid = {english},
  keywords = {Assessment and Testing,Assumption checks,Graphical methods,Logical Analysis,Null hypothesis significance testing,Psychological Assessment,Psychological Diagnostics,Psychological Testing,Software Testing,Statistical assumptions,Statistical diagnostics,Visualization},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/YPHKW4YD/Shatz - 2024 - Assumption-checking rather than (just) testing The importance of visualization and effect size in s.pdf}
}

@misc{Signorell:2025,
  title = {{{DescTools}}: {{Tools}} for {{Descriptive Statistics}}},
  shorttitle = {{{DescTools}}},
  author = {Signorell, Andri and Aho, Ken and Alfons, Andreas and Anderegg, Nanina and Aragon, Tomas and Arachchige, Chandima and Arppe, Antti and Baddeley, Adrian and Barton, Kamil and Bolker, Ben and Borchers, Hans W. and Caeiro, Frederico and Champely, Stephane and Chessel, Daniel and Chhay, Leanne and Cooper, Nicholas and Cummins, Clint and Dewey, Michael and Doran, Harold C. and Dray, Stephane and Dupont, Charles and Eddelbuettel, Dirk and Ekstrom, Claus and Elff, Martin and Enos, Jeff and Farebrother, Richard W. and Fox, John and Francois, Romain and Friendly, Michael and Galili, Tal and Gamer, Matthias and Gastwirth, Joseph L. and Gegzna, Vilmantas and Gel, Yulia R. and Graber, Sereina and Gross, Juergen and Grothendieck, Gabor and Jr, Frank E. Harrell and Heiberger, Richard and Hoehle, Michael and Hoffmann, Christian W. and Hojsgaard, Soeren and Hothorn, Torsten and Huerzeler, Markus and Hui, Wallace W. and Hurd, Pete and Hyndman, Rob J. and Jackson, Christopher and Kohl, Matthias and Korpela, Mikko and Kuhn, Max and Labes, Detlew and Leisch, Friederich and Lemon, Jim and Li, Dong and Maechler, Martin and Magnusson, Arni and Mainwaring, Ben and Malter, Daniel and Marsaglia, George and Marsaglia, John and Matei, Alina and Meyer, David and Miao, Weiwen and Millo, Giovanni and Min, Yongyi and Mitchell, David and Moser, Cyril Flurin and Mueller, Franziska and Naepflin, Markus and Navarro, Danielle and Nilsson, Henric and Nordhausen, Klaus and Ogle, Derek and Ooi, Hong and Parsons, Nick and Pavoine, Sandrine and Plate, Tony and Prendergast, Luke and Rapold, Roland and Revelle, William and Rinker, Tyler and Ripley, Brian D. and Rodriguez, Caroline and Russell, Nathan and Sabbe, Nick and Scherer, Ralph and Seshan, Venkatraman E. and Smithson, Michael and Snow, Greg and Soetaert, Karline and Stahel, Werner A. and Stephenson, Alec and Stevenson, Mark and Stubner, Ralf and Templ, Matthias and Lang, Duncan Temple and Therneau, Terry and Tille, Yves and Torgo, Luis and Trapletti, Adrian and Ulrich, Joshua and Ushey, Kevin and VanDerWal, Jeremy and Venables, Bill and Verzani, John and Iglesias, Pablo J. Villacorta and Warnes, Gregory R. and Wellek, Stefan and Wickham, Hadley and Wilcox, Rand R. and Wolf, Peter and Wollschlaeger, Daniel and Wood, Joseph and Wu, Ying and Yee, Thomas and Zeileis, Achim},
  year = 2025,
  month = mar,
  urldate = {2026-05-12},
  abstract = {A collection of miscellaneous basic statistic functions and convenience wrappers for efficiently describing data. The author's intention was to create a toolbox, which facilitates the (notoriously time consuming) first descriptive tasks in data analysis, consisting of calculating descriptive statistics, drawing graphical summaries and reporting the results. The package contains furthermore functions to produce documents using MS Word (or PowerPoint) and functions to import data from Excel. Many of the included functions can be found scattered in other packages and other sources written partly by Titans of R. The reason for collecting them here, was primarily to have them consolidated in ONE instead of dozens of packages (which themselves might depend on other packages which are not needed at all), and to provide a common and consistent interface as far as function and arguments naming, NA handling, recycling rules etc. are concerned. Google style guides were used as naming rules (in absence of convincing alternatives). The 'BigCamelCase' style was consequently applied to functions borrowed from contributed R packages as well.},
  copyright = {GPL-2 \textbar{} GPL-3 [expanded from: GPL ({$\geq$} 2)]},
  keywords = {AnomalyDetection,MissingData}
}

@article{Skovlund:2001,
  title = {Should We Always Choose a Nonparametric Test When Comparing Two Apparently Nonnormal Distributions?},
  author = {Skovlund, Eva and Fenstad, Grete U.},
  year = 2001,
  month = jan,
  journal = {Journal of Clinical Epidemiology},
  volume = {54},
  number = {1},
  pages = {86--92},
  issn = {0895-4356},
  doi = {10.1016/S0895-4356(00)00264-X},
  urldate = {2025-06-28},
  abstract = {When clinical data are subjected to statistical analysis, a common question is how to choose an appropriate significance test. Comparing two independent groups with observations measured on a continuous scale, the question is typically whether to choose the two-sample-t test or the Wilcoxon--Mann--Whitney test (WMW test). Similar results are often obtained, but which conclusion can be drawn if significance tests give highly different P-values? The t test is optimal for normally distributed observations with common variance and robust to deviations from normality if sample sizes are not very small. The WMW test makes no distributional assumptions, but depends heavily on equal shape and variance of the two distributions (homoscedasticity). We have compared the properties of the traditional two-sample t test, a modified t test allowing unequal variance, and the WMW test by stochastic simulation. All show acceptable behaviour when the two distributions have similar variance. When variances differ, the modified t test is superior to the other two.},
  keywords = {-Values,Heteroscedasticity,Stochastic simulation,Two-sample  test,Welch's test,Wilcoxon--Mann--Whitney test},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/R2XT8QEX/S089543560000264X.html}
}

@article{Strasak:2007,
  title = {The {{Use}} of {{Statistics}} in {{Medical Research}}: {{A Comparison}} of "{{The New England Journal}} of {{Medicine}}" and "{{Nature Medicine}}"},
  shorttitle = {The {{Use}} of {{Statistics}} in {{Medical Research}}},
  author = {Strasak, Alexander M. and Zaman, Qamruz and Marinell, Gerhard and Pfeiffer, Karl P. and Ulmer, Hanno},
  year = 2007,
  journal = {The American Statistician},
  volume = {61},
  number = {1},
  eprint = {27643837},
  eprinttype = {jstor},
  pages = {47--55},
  publisher = {[American Statistical Association, Taylor \& Francis, Ltd.]},
  issn = {0003-1305},
  urldate = {2026-05-11},
  abstract = {There is widespread evidence of the extensive use of statistical methods in medical research. Just the same, standards are generally low and a growing body of literature points to statistical errors in most medical journals. However, there is no comprehensive study contrasting the top medical journals of basic and clinical science for recent practice in their use of statistics. All original research articles in Volume 10, Numbers 1---6 of "Nature Medicine (Nat Med)" and Volume 350, Numbers 1---26 of "The New England Journal of Medicine (NEJM)" were screened for their statistical content. Types, frequencies, and complexity of applied statistical methods were systematically recorded. A 46-item checklist was used to evaluate statistical quality for a subgroup of papers. 94.5 percent (95\% CI 87.6---98.2) of NEJM articles and 82.4 percent (95\% CI 65.5---93.2) of Nat Med articles contained inferential statistics. NEJM papers were significantly more likely to use advanced statistical methods (p {$<$} 0.0001). Statistical errors were identified in a considerable proportion of articles, although not always serious in nature. Documentation of applied statistical methods was generally poor and insufficient, particularly in Nat Med. Compared to 1983, a vast increase in usage and complexity of statistical methods could be observed for NEJM papers. This does not necessarily hold true for Nat Med papers, as the results of the study indicate that basic science sticks with basic analysis. As statistical errors seem to remain common in medical literature, closser attention to statistical methodology should be seriously considered to raise standards.}
}

@article{Student:1908,
  title = {The Probable Error of a Mean},
  author = {{Student}},
  year = 1908,
  journal = {Biometrika},
  volume = {6},
  number = {1},
  pages = {1--25},
  publisher = {Oxford University Press}
}

@article{Sullivan:1992,
  title = {Robustness of the t {{Test Applied}} to {{Data Distorted}} from {{Normality}} by {{Floor Effects}}},
  author = {Sullivan, L.M. and D'Agostino, R.B.},
  year = 1992,
  month = dec,
  journal = {J Dent Res},
  volume = {71},
  number = {12},
  pages = {1938--1943},
  issn = {0022-0345, 1544-0591},
  doi = {10.1177/00220345920710121601},
  urldate = {2025-06-02},
  abstract = {In calculus, plaque, and gingivitis trials, measures are taken on subjects both prior to the use of an active treatment and after its use. When the trial is short-term, or when a cleaning of the mouth takes place after the baseline measurement, distributions of such measures (e.g., the Volpe-Manhold score or the Loe and Silness scale) are approximately normally distributed above zero but also can have a proportion of subjects who attain scores of zero. When the effects of an active treatment are compared with those of a control, the two-independent-sample t test can be applied to outcome scores or to differences between the baseline and outcome scores. Robustness of these t tests, in the presence of distributions "distorted" from normality as described, was investigated by computer simulation. In general, both t tests produced actual significance levels which were close to nominal significance levels, even in the presence of small samples and distributions in which as many as 50\% of the subjects attained scores of zero.},
  copyright = {https://journals.sagepub.com/page/policies/text-and-data-mining-license},
  langid = {english}
}

@article{Thompson:2015,
  title = {The {{Case}} for {{Using}} the {{General Linear Model}} as a {{Unifying Conceptual Framework}} for {{Teaching Statistics}} and {{Psychometric Theory}}},
  author = {Thompson, Bruce},
  year = 2015,
  month = feb,
  journal = {Journal of Methods and Measurement in the Social Sciences},
  volume = {6},
  number = {2},
  issn = {2159-7855},
  doi = {10.2458/v6i2.18801},
  urldate = {2025-12-30},
  copyright = {https://creativecommons.org/licenses/by-nc-nd/4.0},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/Q39NWQMR/Thompson - 2015 - The Case for Using the General Linear Model as a Unifying Conceptual Framework for Teaching Statisti.pdf}
}

@article{Tressoldi:2013,
  title = {High {{Impact}} = {{High Statistical Standards}}? {{Not Necessarily So}}},
  shorttitle = {High {{Impact}} = {{High Statistical Standards}}?},
  author = {Tressoldi, Patrizio E. and Giofr{\'e}, David and Sella, Francesco and Cumming, Geoff},
  year = 2013,
  month = feb,
  journal = {PLOS ONE},
  volume = {8},
  number = {2},
  pages = {e56180},
  publisher = {Public Library of Science},
  issn = {1932-6203},
  doi = {10.1371/journal.pone.0056180},
  urldate = {2026-05-11},
  abstract = {What are the statistical practices of articles published in journals with a high impact factor? Are there differences compared with articles published in journals with a somewhat lower impact factor that have adopted editorial policies to reduce the impact of limitations of Null Hypothesis Significance Testing? To investigate these questions, the current study analyzed all articles related to psychological, neuropsychological and medical issues, published in 2011 in four journals with high impact factors: Science, Nature, The New England Journal of Medicine and The Lancet, and three journals with relatively lower impact factors: Neuropsychology, Journal of Experimental Psychology-Applied and the American Journal of Public Health. Results show that Null Hypothesis Significance Testing without any use of confidence intervals, effect size, prospective power and model estimation, is the prevalent statistical practice used in articles published in Nature, 89\%, followed by articles published in Science, 42\%. By contrast, in all other journals, both with high and lower impact factors, most articles report confidence intervals and/or effect size measures. We interpreted these differences as consequences of the editorial policies adopted by the journal editors, which are probably the most effective means to improve the statistical practices in journals with high or low impact factors.},
  langid = {english},
  keywords = {Bibliometrics,Confidence intervals,Experimental psychology,Medical journals,Mental health and psychiatry,Neuropsychology,Psychology,Scientific publishing},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/IGR5GTWY/Tressoldi et al. - 2013 - High Impact = High Statistical Standards Not Necessarily So.pdf}
}

@article{Uhm:2023,
  title = {A Comparison of Normality Testing Methods by Empirical Power and Distribution of {{P-values}}},
  author = {Uhm, Taewoong and {\noopsort{yi}}{and Yi}, Seongbaek},
  year = 2023,
  month = sep,
  journal = {Communications in Statistics - Simulation and Computation},
  volume = {52},
  number = {9},
  pages = {4445--4458},
  publisher = {Taylor \& Francis},
  issn = {0361-0918},
  doi = {10.1080/03610918.2021.1963450},
  urldate = {2025-06-05},
  abstract = {Normal distribution is commonly assumed distribution in statistical inference. Therefore, goodness-of-fit test for normality is required as a preliminary procedure in the applications. Most relevant testing methods have been evaluated using empirical power. However, the power depends on significance level, sample size, and alternative distributions. This study compares normality testing methods which have been verified excellent based on power, considering significance levels, sample sizes, and alternative distributions in addition to their powers. Furthermore we evaluate the performance of the testing methods using the expected and median values of p-values of the corresponding test statistics.},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/BZ4LI3N6/Uhm und and Yi - 2023 - A comparison of normality testing methods by empirical power and distribution of P-values.pdf}
}

@article{Welch:1947,
  title = {The Generalization of `Student's' Problem When Several Different Population Variances Are Involved},
  author = {Welch, B. L.},
  year = 1947,
  journal = {Biometrika},
  volume = {34},
  number = {1--2},
  pages = {28--35},
  doi = {10.1093/biomet/34.1-2.28}
}

@article{Welch:1947a,
  title = {The {{Generalization}} of `{{Student}}'s' {{Problem}} When {{Several Different Population Variances}} Are {{Involved}}},
  author = {Welch, B. L.},
  year = 1947,
  journal = {Biometrika},
  volume = {34},
  number = {1/2},
  eprint = {2332510},
  eprinttype = {jstor},
  pages = {28--35},
  publisher = {[Oxford University Press, Biometrika Trust]},
  issn = {0006-3444},
  doi = {10.2307/2332510},
  urldate = {2025-06-26}
}

@article{Welch:1951,
  title = {On the {{Comparison}} of {{Several Mean Values}}: {{An Alternative Approach}}},
  shorttitle = {On the {{Comparison}} of {{Several Mean Values}}},
  author = {Welch, B. L.},
  year = 1951,
  journal = {Biometrika},
  volume = {38},
  number = {3/4},
  eprint = {2332579},
  eprinttype = {jstor},
  pages = {330--336},
  publisher = {[Oxford University Press, Biometrika Trust]},
  issn = {0006-3444},
  doi = {10.2307/2332579},
  urldate = {2025-05-20}
}

@article{West:2021,
  title = {Best Practice in Statistics: {{Use}} the {{Welch}} t-Test When Testing the Difference between Two Groups},
  author = {West, Brady T},
  year = 2021,
  journal = {Annals of Clinical Biochemistry},
  volume = {58},
  number = {4},
  pages = {267--269},
  publisher = {SAGE Publications},
  doi = {10.1177/0004563221992088},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/PJGLXFN2/West - 2021 - Best practice in statistics Use the Welch t-test when testing the difference between two groups.pdf}
}

@book{Wilcox:2001,
  title = {Fundamentals of {{Modern Statistical Methods}}: {{Substantially Improving Power}} and {{Accuracy}}},
  shorttitle = {Fundamentals of {{Modern Statistical Methods}}},
  author = {Wilcox, Rand},
  year = 2001,
  month = jan,
  journal = {Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy},
  doi = {10.1007/978-1-4419-5525-8},
  abstract = {Conventional statistical methods have a very serious flaw. They routinely miss differences among groups or associations among variables that are detected by more modern techniques, even under very small departures from normality. Hundreds of journal articles have described the reasons standard techniques can be unsatisfactory, but simple, intuitive explanations are generally unavailable. Situations arise where even highly nonsignificant results become significant when analyzed with more modern methods. Without assuming the reader has any prior training in statistics, Part I of this book describes basic statistical principles from a point of view that makes their shortcomings intuitive and easy to understand. The emphasis is on verbal and graphical descriptions of concepts. Part II describes modern methods that address the problems covered in Part I. Using data from actual studies, many examples are included to illustrate the practical problems with conventional procedures and how more modern methods can make a substantial difference in the conclusions reached in many areas of statistical research. The second edition of this book includes a number of advances and insights that have occurred since the first edition appeared. Included are new results relevant to medians, regression, measures of association, strategies for comparing dependent groups, methods for dealing with heteroscedasticity, and measures of effect size. Rand Wilcox is a professor of psychology at the University of Southern California. He is a fellow of the Royal Statistical Society and the Association for Psychological Science. Dr. Wilcox currently serves as an associate editor of Computational Statistics \& Data Analysis, Communications in Statistics: Theory and Methods, Communications in Statistics: Simulation and Computation, and Psychometrika. He has published more than 280 articles in a wide range of statistical journals and he is the author of six other books on statistics. \copyright{} Springer Science+Business Media, LLC 2010. All rights reserved.},
  isbn = {978-1-4419-5524-1},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/UMGBUQQX/Wilcox - 2001 - Fundamentals of Modern Statistical Methods Substantially Improving Power and Accuracy.pdf}
}

@book{Wilcox:2021,
  title = {Introduction to {{Robust Estimation}} and {{Hypothesis Testing}}},
  author = {Wilcox, Rand R.},
  year = 2021,
  month = sep,
  urldate = {2025-06-17},
  abstract = {Introduction to Robust Estimating and Hypothesis Testing, Fifth Edition is a useful `how-to' on the application of robust methods utilizing eas},
  isbn = {978-0-12-820098-8},
  langid = {american},
  annotation = {Wilcox:2021},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/RMINBM5C/978-0-12-820098-8.html;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/USBETENT/978-0-12-820098-8.html}
}

@article{WILK:1968,
  title = {Probability Plotting Methods for the Analysis for the Analysis of Data},
  author = {WILK, M. B. and GNANADESIKAN, R.},
  year = 1968,
  month = mar,
  journal = {Biometrika},
  volume = {55},
  number = {1},
  pages = {1--17},
  issn = {0006-3444},
  doi = {10.1093/biomet/55.1.1},
  urldate = {2025-05-28},
  abstract = {This paper describes and discusses graphical techniques, based on the primitive empirical cumulative distribution function and on quantile (Q-Q) plots, percent (p-p) plots and hybrids of these, which are useful in assessing a one-diamensional sample, either from original data or resulting from analysis. Areas of application include: the comparison of samples; the comparison of distributions; the presentation of results on sensitivities of statistical methods; the analysis of collections of contrasts and of collections of sample variances; the assessment of multivariate contrasts; and the structuring of analysis of variances; mean squares. Many of the objectives and techniques are illustrated by examples.},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/ZLZ92W7H/262814.html}
}

@article{Yap:2011,
  title = {Comparisons of Various Types of Normality Tests},
  author = {Yap, B. W. and Sim, C. H.},
  year = 2011,
  month = dec,
  journal = {Journal of Statistical Computation and Simulation},
  volume = {81},
  number = {12},
  pages = {2141--2155},
  issn = {0094-9655, 1563-5163},
  doi = {10.1080/00949655.2010.520163},
  urldate = {2025-05-29},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/BP34C34R/Yap und Sim - 2011 - Comparisons of various types of normality tests.pdf}
}

@article{Yates:1934,
  title = {Contingency {{Tables Involving Small Numbers}} and the {$\chi$}2 {{Test}}},
  author = {Yates, F.},
  year = 1934,
  month = jul,
  journal = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
  volume = {1},
  number = {2},
  pages = {217--235},
  issn = {1369-7412, 1467-9868},
  doi = {10.2307/2983604},
  urldate = {2025-06-17},
  copyright = {https://academic.oup.com/journals/pages/open\_access/funder\_policies/chorus/standard\_publication\_model},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/TQT7DCSX/Yates - 1934 - Contingency Tables Involving Small Numbers and the χ2 Test.pdf}
}

@article{Zhou:2023,
  title = {Statistical Tests for Homogeneity of Variance for Clinical Trials and Recommendations},
  author = {Zhou, Yuhang and Zhu, Yiyang and Wong, Weng Kee},
  year = 2023,
  month = mar,
  journal = {Contemp Clin Trials Commun},
  volume = {33},
  pages = {101119},
  issn = {2451-8654},
  doi = {10.1016/j.conctc.2023.101119},
  urldate = {2025-06-28},
  abstract = {In most clinical trials, the main interest is to test whether there are differences in the mean outcomes among the treatment groups. When the outcome is continuous, a common statistical test is a usual t-test for a two-group comparison. For more than 2 groups, an ANOVA setup is used and the test for equality for all groups is based on the F-distribution. A key assumption for these parametric tests is that data are normally, independently distributed and the response variances are equal. The robustness of these tests to the first two assumptions is quite well investigated, but the issues arising from heteroscedasticity are less studied. This paper reviews different methods for ascertaining homogeneity of variance across groups and investigates the consequences of heteroscedasticity on the tests. Simulations based on normal, heavy-tailed, and skewed normal data demonstrate that some of the less known methods, such as the Jackknife or Cochran's test, are quite effective in detecting differences in the variances.},
  pmcid = {PMC10151260},
  pmid = {37143826}
}

@article{Zimmerman:2004,
  title = {A Note on Preliminary Tests of Equality of Variances},
  author = {Zimmerman, Donald W},
  year = 2004,
  journal = {British Journal of Mathematical and Statistical Psychology},
  volume = {57},
  number = {1},
  pages = {173--181},
  publisher = {Wiley},
  doi = {10.1348/000711004849222},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/4C59EXMS/Zimmerman - 2004 - A note on preliminary tests of equality of variances.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/LLMB3N54/000711004849222.html}
}

@misc{Zrimsek:2024,
  title = {Quantifying {{Uncertainty}}: {{All We Need}} Is the {{Bootstrap}}?},
  shorttitle = {Quantifying {{Uncertainty}}},
  author = {Zrim{\v s}ek, Ur{\v s}a and {\v S}trumbelj, Erik},
  year = 2024,
  month = oct,
  number = {arXiv:2403.20182},
  eprint = {2403.20182},
  primaryclass = {stat},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2403.20182},
  urldate = {2025-06-27},
  abstract = {Quantifying uncertainty through standard errors, confidence intervals, hypothesis tests, and related measures is a fundamental aspect of statistical practice. However, these techniques involve a variety of methods, mathematical formulas, and underlying concepts, which can be complex. Could the non-parametric bootstrap, known for its simplicity and general applicability, serve as a universal alternative? In this study, we address this question through a review of existing literature and a simulation analysis of one- and two-sided confidence intervals across varying sample sizes, confidence levels, data-generating processes, and statistical functionals. Our findings indicate that the double bootstrap consistently performs best and is a promising alternative to traditional methods used for common statistical tasks. These results suggest that the bootstrap, particularly the double bootstrap, could simplify statistical education and practice without compromising effectiveness.},
  archiveprefix = {arXiv},
  keywords = {Statistics - Methodology},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/ZSEANGBL/Zrimšek und Štrumbelj - 2024 - Quantifying Uncertainty All We Need is the Bootstrap.pdf;/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/HGCSU68W/2403.html}
}

@article{Zygmont:2023,
  title = {Managing the {{Assumption}} of {{Normality}} within the {{General Linear Model}} with {{Small Samples}}: {{Guidelines}} for {{Researchers Regarding If}}, {{When}} and {{How}}.},
  shorttitle = {Managing the {{Assumption}} of {{Normality}} within the {{General Linear Model}} with {{Small Samples}}},
  author = {Zygmont, Conrad Stanis{\l}aw},
  year = 2023,
  month = dec,
  journal = {TQMP},
  volume = {19},
  number = {4},
  pages = {302--332},
  issn = {2292-1354},
  doi = {10.20982/tqmp.19.4.p302},
  urldate = {2026-04-29},
  abstract = {Academic textbooks, statistical literature, and publication guidelines provide conflicting, ambiguous and often incomplete answers to the question of how researchers should handle the normality assumption for classical general linear model tests when conducting their analyses. Previous studies have shown that normality violations can impact on type I errors, power, parameter estimates and standard error estimates of classical tests. This paper reviews the arguments in favour and against normality testing, the role of the central limit theorem, types of violations that tests within the general linear model are susceptible to, methods for evaluating the normality assumption, and the paradox that normality tests have low power in small sample sizes where the influence of assumption violations are likely to be most profound. A Monte Carlo simulation study was used to evaluate the power of 18 normality tests across 18 alternative distributions, and the effect of normality deviations on estimates of centrality, scatter and regression coefficients. The results demonstrate that the type of normality test and distribution matters, and that a conditional testing procedure utilising normality tests to select between classic, non-parametric and robust tests should not be used. Instead, an alternative procedure for managing the normality assumption is advised, and demonstrated in the supplementary materials using R code and data that are provided.},
  langid = {english},
  file = {/Users/sschilli/Library/CloudStorage/OneDrive-HochschuleLuzern/storage/J6ZGRZ6U/Zygmont - 2023 - Managing the Assumption of Normality within the General Linear Model with Small Samples Guidelines.pdf}
}

@preamble{ "\providecommand{\noopsort}[1]{} " }
