title: Normal probability plots with confidence.
abstract: Normal probability plots are widely used as a statistical tool for assessing whether an observed simple random sample is drawn from a normally distributed population. The users, however, have to judge subjectively, if no objective rule is provided, whether the plotted points fall close to a straight line. In this paper, we focus on how a normal probability plot can be augmented by intervals for all the points so that, if the population distribution is normal, then all the points should fall into the corresponding intervals simultaneously with probability 1-α. These simultaneous 1-α probability intervals provide therefore an objective mean to judge whether the plotted points fall close to the straight line: the plotted points fall close to the straight line if and only if all the points fall into the corresponding intervals. The powers of several normal probability plot based (graphical) tests and the most popular nongraphical Anderson-Darling and Shapiro-Wilk tests are compared by simulation. Based on this comparison, recommendations are given in Section 3 on which graphical tests should be used in what circumstances. An example is provided to illustrate the methods.
authors.affiliation: S3RI and School of Mathematics, University of Southampton, Southampton, SO17 1TB, UK.
authors.forename: Wanpen
authors.initials: W
authors.lastname: Chantarangsi
authors.forename: Wei
authors.initials: W
authors.lastname: Liu
authors.forename: Frank
authors.initials: F
authors.lastname: Bretz
authors.forename: Seksan
authors.initials: S
authors.lastname: Kiatsupaibul
authors.forename: Anthony J
authors.initials: AJ
authors.lastname: Hayter
authors.forename: Fang
authors.initials: F
authors.lastname: Wan
mesh_terms: D000181:Acrylonitrile / Q000031:analogs & derivatives / Q000378:metabolism; D001699:Biometry; D016001:Confidence Intervals; D016011:Normal Distribution; D011336:Probability; D011960:Receptors, Estrogen / Q000378:metabolism; D013223:Statistics as Topic / Q000379:methods*
chemical_list: D011960:Receptors, Estrogen; C040969:2,3,3-triphenylacrylonitrile; D000181:Acrylonitrile
keywords: Graphical method; Hypotheses testing; Normal distribution; Normal probability plot; Power; Simultaneous inference