JMASM 49: A Compilation of Some Popular Goodness of Fit Tests for Normal Distribution: Their Algorithms and MATLAB Codes (MATLAB)

Öner, Metin; Kocakoç, İpek Deveci

doi:10.22237/jmasm/1509496200

Cited by 69 publications

(48 citation statements)

References 16 publications

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“…As noted by Zimmerman et al (2003) concerning the utility of applying an r-based adjustment, "...if one is troubled by the slight bias in the correlation coefficient for normal populations, it is clear that it can be largely eliminated by the Fisher approximate unbiased estimator or by the Olkin and Pratt estimator" (p. 155). The main purpose of this study is to review calculation algorithms for some of the most common non-parametric and omnibus tests for normality, and to provide them as a compiled MATLAB function.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Through a simulation study, Zimmerman et al (2003) reported that the r OP and the r FAU adjustments were effectively the same when N ≥ 20, but when N < 20, r OP corrected bias more precisely than r FAU . This finding was also corroborated in a simulation conducted by Walker (2016).…”

Section: R-based Bias Adjustmentsmentioning

confidence: 99%

“…Fisher (1915Fisher ( , 1921Fisher ( , 1924 found that the correlation coefficient was comprised of an asymmetrical distribution, which also influenced this index's standard error, causing r to be a biased estimator of ρ under normal distribution conditions particularly with small sample sizes (i.e., for Fisher, "small" N = 18). Zimmerman, Zumbo, and Williams (2003) pointed out that the notion of "bias" in this situation is derived specifically from the sample mean associated with the r metric. Additionally, Zimmerman et al noted that, practically, This discrepancy [bias] may not be crucial if one is simply investigating whether or not a correlation exists.…”

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confidence: 99%

“…(p. 134) Bishara and Hittner (2015) established that the threshold for a "small" sample size was N < 20, where "… the absolute bias becomes negligible (less than .01) for a sample size greater than 20" (p. 786); noting that the bias decreased as the N increased. Further, Zimmerman et al (2003) determined that the extent of the aforementioned estimation issue, where r could underestimate ρ by "…as much as .03 or .04 under some realistic conditions…" (p. 134). They also noted that r r AND r BIASED ADJUSTMENT INDICES 542 could achieve a positive bias as high as 0.05 under non-normal distribution conditions.…”

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Vol. 16, No. 2 (Full Issue)

2017

J. Mod. App. Stat. Meth.

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EDITORIAL ASSISTANCEJMASM (ISSN 1538−9472, http://digitalcommons.wayne.edu/jmasm) is an independent, open access electronic journal, published biannually in May and November by JMASM Inc. (PO Box 48023, Oak Park, MI, 48237) in collaboration with the Wayne State University Library System. JMASM seeks to publish (1) new statistical tests or procedures, or the comparison of existing statistical tests or procedures, using computer-intensive Monte Carlo, bootstrap, jackknife, or resampling methods, (2) the study of nonparametric, robust, permutation, exact, and approximate randomization methods, and (3) applications of computer programming, preferably in Fortran (all other programming environments are welcome), related to statistical algorithms, pseudo-random number generators, simulation techniques, and self-contained executable code to carry out new or interesting statistical methods.Journal correspondence (other than manuscript submissions) and requests for advertising may be forwarded to ea@jmasm.com. See back matter for instructions for authors. IntroductionComputer simulation studies represent an important tool for investigating statistical procedures difficult or impossible to study using mathematical theory or real data. Descriptors of these studies vary (e.g., statistical experiment, Monte Carlo simulation, computer experiment), but the examples of Hoaglin and Andrews (1975) and Hauck and Anderson (1984) are followed here with use of the term simulation studies. Extensive descriptions of simulation studies can be found in Lewis and Orav (1989) and Santner, Williams, and Notz (2003). In the behavioral sciences simulation studies have been used to study a wide array of statistical methods (e.g., Cribbie, Fiksenbaum, & Wilcox, 2012; Depaoli, 2012; Enders, Baraldi, & Cham, 2014; Hu & Bentler, 1999; Tomarken & Serlin, 1986). The general goal of these studies is to provide evidence of the behavior of statistical methods under a variety of data conditions that improves statistical practice and informs future statistical research. The goal here is to encourage methodological researchers to treat these studies as statistical sampling EXPERIMENTAL DESIGN AND DATA ANALYSIS IN SIMULATION 4 experiments subject to established principles of experimental design and data analysis.An underappreciated facet of simulation studies in statistics is their role in enhancing the reproducibility of scientific findings. The importance of reproducibility has gained momentum in numerous scientific arenas because of growing evidence that many findings cannot be replicated (Stodden, 2015). Concerns over reproducibility and the role of statistics were captured in Statistics and science: A report of the London workshop on the future of the statistical sciences (2014) which noted: "The reproducibility problem goes far beyond statistics, of course, because it involves the entire reward structure of the scientific enterprise. Nevertheless, statistics is a very important ingredient in both the problem and the remedy." (p. 27) Simulati...

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: R-based Bias Adjustmentsmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Vol. 16, No. 2 (Full Issue)

2017

J. Mod. App. Stat. Meth.

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Intervals of color mismatch in chromaticity coordinates and in cone‐fundamental‐based (LMS) space

Carreño¹

2022

Color Research & Application

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We discuss the uncertainties in chromaticity coordinates in the color matching experiment reported by MacAdam [J. Opt. Soc. Am 32, 247 (1942)]. We also derive the uncertainties in cone-pigments based excitation space. The observer made color matchings by tuning the angle of a Rochon prism. The intervals of color mismatch were obtained using the average value and the standard deviations of the angle settings. We use in this work a rigorous statistical method to derive the probability density functions of chromaticity coordinates assuming a Gaussian distribution for the Rochon prism angle.We also derive the probability density functions of the L-, M-, and S-tristimulus values. We analyze how much the actual probability density functions deviate from the Gaussian. Finally, we determine the bounds of the intervals of color mismatch assuming that the areas of the tails of each probability density function are equal. The so derived intervals are compared to those reported in the original investigation due to MacAdam. We show that color-differences for a certain confidence level cannot be obtained as a simple common scaling factor of the color differences computed for a lower confidence level. The results obtained in LMS space at corneal level exhibit asymmetries between increment and decrement thresholds.

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The role of iron and myelin in orientation dependent R₂^* of white matter

et al. 2019

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Brain myelin and iron content are important parameters in neurodegenerative diseases such as multiple sclerosis (MS). Both myelin and iron content influence the brain's R2* relaxation rate. However, their quantification based on R2* maps requires a realistic tissue model that can be fitted to the measured data. In structures with low myelin content, such as deep gray matter, R2* shows a linear increase with increasing iron content. In white matter, R2* is not only affected by iron and myelin but also by the orientation of the myelinated axons with respect to the external magnetic field. Here, we propose a numerical model which incorporates iron and myelin, as well as fibre orientation, to simulate R2* decay in white matter. Applying our model to fibre orientation‐dependent in vivo R2* data, we are able to determine a unique solution of myelin and iron content in global white matter. We determine an averaged myelin volume fraction of 16.02 ± 2.07% in non‐lesional white matter of patients with MS, 17.32 ± 2.20% in matched healthy controls, and 18.19 ± 2.98% in healthy siblings of patients with MS. Averaged iron content was 35.6 ± 8.9 mg/kg tissue in patients, 43.1 ± 8.3 mg/kg in controls, and 47.8 ± 8.2 mg/kg in siblings. All differences in iron content between groups were significant, while the difference in myelin content between MS patients and the siblings of MS patients was significant. In conclusion, we demonstrate that a model that combines myelin‐induced orientation‐dependent and iron‐induced orientation‐independent components is able to fit in vivo R2* data.

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JMASM 49: A Compilation of Some Popular Goodness of Fit Tests for Normal Distribution: Their Algorithms and MATLAB Codes (MATLAB)

Cited by 69 publications

References 16 publications

Vol. 16, No. 2 (Full Issue)

Vol. 16, No. 2 (Full Issue)

Intervals of color mismatch in chromaticity coordinates and in cone‐fundamental‐based (LMS) space

The role of iron and myelin in orientation dependent R₂^* of white matter

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JMASM 49: A Compilation of Some Popular Goodness of Fit Tests for Normal Distribution: Their Algorithms and MATLAB Codes (MATLAB)

Cited by 69 publications

References 16 publications

Vol. 16, No. 2 (Full Issue)

Vol. 16, No. 2 (Full Issue)

Intervals of color mismatch in chromaticity coordinates and in cone‐fundamental‐based (LMS) space

The role of iron and myelin in orientation dependent R2* of white matter

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The role of iron and myelin in orientation dependent R₂^* of white matter