Normal probability plots with confidence

Mathematics and Statistics

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Normal probability plots with confidence. / Chantarangsi, Wanpen; Liu, Wei; Bretz, Frank et al.
In: Biometrical Journal, Vol. 57, No. 1, 01.2015, p. 52-53.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Chantarangsi, W, Liu, W, Bretz, F, Kiatsupaibul, S, Hayter, A & Wan, F 2015, 'Normal probability plots with confidence', Biometrical Journal, vol. 57, no. 1, pp. 52-53. https://doi.org/10.1002/bimj.201300244

APA

Chantarangsi, W., Liu, W., Bretz, F., Kiatsupaibul, S., Hayter, A., & Wan, F. (2015). Normal probability plots with confidence. Biometrical Journal, 57(1), 52-53. https://doi.org/10.1002/bimj.201300244

Vancouver

Chantarangsi W, Liu W, Bretz F, Kiatsupaibul S, Hayter A, Wan F. Normal probability plots with confidence. Biometrical Journal. 2015 Jan;57(1):52-53. Epub 2014 Oct 21. doi: 10.1002/bimj.201300244

Author

Chantarangsi, Wanpen ; Liu, Wei ; Bretz, Frank et al. / Normal probability plots with confidence. In: Biometrical Journal. 2015 ; Vol. 57, No. 1. pp. 52-53.

Bibtex

@article{7d279c7374e44bbe9d8f3b42a9569e12,

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 inline image. These simultaneous inline image 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.",

keywords = "Graphical method, Hypotheses testing, Normal distribution, Normal probability plot, Power, Simultaneous inference",

author = "Wanpen Chantarangsi and Wei Liu and Frank Bretz and Seksan Kiatsupaibul and Anthony Hayter and Fang Wan",

year = "2015",

month = jan,

doi = "10.1002/bimj.201300244",

language = "English",

volume = "57",

pages = "52--53",

journal = "Biometrical Journal",

issn = "0323-3847",

publisher = "Wiley-VCH Verlag",

number = "1",

}

RIS

TY - JOUR

T1 - Normal probability plots with confidence

AU - Chantarangsi, Wanpen

AU - Liu, Wei

AU - Bretz, Frank

AU - Kiatsupaibul, Seksan

AU - Hayter, Anthony

AU - Wan, Fang

PY - 2015/1

Y1 - 2015/1

N2 - 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 inline image. These simultaneous inline image 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.

AB - 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 inline image. These simultaneous inline image 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.

KW - Graphical method

KW - Hypotheses testing

KW - Normal distribution

KW - Normal probability plot

KW - Power

KW - Simultaneous inference

U2 - 10.1002/bimj.201300244

DO - 10.1002/bimj.201300244

M3 - Journal article

VL - 57

SP - 52

EP - 53

JO - Biometrical Journal

JF - Biometrical Journal

SN - 0323-3847

IS - 1

ER -

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