Normal probability plots with confidence

Chantarangsi, Wanpen; Liu, Wei; Bretz, Frank; Kiatsupaibul, Seksan; Hayter, Anthony J.; Wan, Fang

doi:10.1002/bimj.201300244

Cited by 18 publications

(18 citation statements)

References 15 publications

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“…Data are presented as scatter plots over time and histograms showing the distribution of data. The database and TPS subset are tested for normality using a normal probability plot,16 a linear regression tool, whereby a normal distribution will lie on a straight line. The purpose of this tool is to assess whether setting action levels based on the standard normal distribution is appropriate and if so then action levels (AL Δ ) and tolerances (TL Δ ) will then be set at μ ± 2σ and μ ± 3σ, respectively.…”

Section: Methodsmentioning

confidence: 99%

A clinical database to assess action levels and tolerances for the ongoing use of Mobius3D

Jolly

Dunn

Kenny

2016

J Applied Clin Med Phys

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In radiation therapy, calculation of dose within the patient contains inherent uncertainties, inaccuracies, limitations, and the potential for random error. Thus, point dose‐independent verification of such calculations is a well‐established process, with published data to support the setting of both action levels and tolerances. Mobius3D takes this process one step further with a full independent calculation of patient dose and comparisons of clinical parameters such as mean target dose and voxel‐by‐voxel gamma analysis. There is currently no published data to directly inform tolerance levels for such parameters, and therefore this work presents a database of 1000 Mobius3D results to fill this gap. The data are tested for normality using a normal probability plot and found to fit this distribution for three sub groups of data; Eclipse, iPlan and the treatment site Lung. The mean (μ) and standard deviation (σ) of these sub groups is used to set action levels and tolerances at μ ± 2σ and μ ± 3σ, respectively. A global (3%, 3 mm) gamma tolerance is set at 88.5%. The mean target dose tolerance for Eclipse data is the narrowest at ± 3%, whilst iPlan and Lung have a range of −5.0 to 2.2% and −1.8 to 5.0%, respectively. With these limits in place, future results failing the action level or tolerance will fall within the worst 5% and 1% of historical results and an informed decision can be made regarding remedial action prior to treatment.

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Section: Methodsmentioning

confidence: 99%

A clinical database to assess action levels and tolerances for the ongoing use of Mobius3D

Jolly

Dunn

Kenny

2016

J Applied Clin Med Phys

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“…In order to provide an objective judgement on whether the points (z k , Y [k] ) fall close to a straight line and building on the work of Michael (1983). Chantarangsi et al (2015) consider augmenting the normal probability plot by providing an interval for each Y [k] (k = 1, . .…”

Section: Introductionmentioning

confidence: 99%

“…, n) so that, if the population is normally distributed then all the Y [k] (k = 1, · · · , n) will fall into the corresponding intervals simultaneously with probability 1 − α. In this paper, the authors use the idea of Chantarangsi et al (2015) on Q-Q plots to judge whether a sample is drawn from the Weibull or exponential distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 presents the methods of parameter estimation for Weibull and exponential distributions. Section 3 then constructs graphical tests for testing Weibull and exponential distributions based on the tests proposed in Chantarangsi et al (2015) [5]. The powers of these graphical and two non-graphical tests are then compared in a simulation study in order to identify the tests that have overall good power in Section 4.…”

Section: Introductionmentioning

confidence: 99%

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Q-Q plots with confidence for testing Weibull and exponential distributions

Chantarangsi¹,

Liu²,

Bretz³

et al. 2015

HJMS

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One of the basic graphical methods for assessing the validity of a distributional assumption is the Q-Q plot which compares quantiles of a sample against the quantiles of the distribution. In this paper, we focus on how a Q-Q plot can be augmented by intervals for all the points so that, if the population distribution is Weibull or exponential then all the points should fall inside 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 within the corresponding intervals. The powers of five Q-Q plot based graphical tests and the most popular non-graphical Anderson-Darling and Cramér-von-Mises tests are compared by simulation. Based on this power study, the tests that have better powers are identified and recommendations are given on which graphical tests should be used in what circumstances. Examples are provided to illustrate the methods.

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“…In general, analyses of normality based on Q-Q plots are more reliable for large-scale samples (> 5,000 units), when tests of normality can greatly inflate type II error (reducing sensitivity). 7,8 There are dozens of statistical tests for verifying the fit of data to a normal distribution, based on different assumptions and using different algorithms. All of them test the null hypothesis (H0) that the data are normal, and so they return p-value > 0.05 if the result shows that data do fit the parameters for normality.…”

mentioning

confidence: 99%