Power Comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling Tests
Abstract and Figures
The importance of normal distribution is undeniable since it is an underlying assumption of many statistical procedures such as t-tests, linear regression analysis, discriminant analysis and Analysis of Variance (ANOVA). When the normality assumption is violated, interpretation and inferences may not be reliable or valid. The three common procedures in assessing whether a random sample of independent observations of size n come from a population with a normal distribution are: graphical methods (histograms, boxplots, Q-Q-plots), numerical methods (skewness and kurtosis indices) and formal normality tests. This paper* compares the power of four formal tests of normality: Shapiro-Wilk (SW) test, Kolmogorov-Smirnov (KS) test, Lilliefors (LF) test and Anderson-Darling (AD) test. Power comparisons of these four tests were obtained via Monte Carlo simulation of sample data generated from alternative distributions that follow symmetric and asymmetric distributions. Ten thousand samples of various sample size were generated from each of the given alternative symmetric and asymmetric distributions. The power of each test was then obtained by comparing the test of normality statistics with the respective critical values. Results show that Shapiro-Wilk test is the most powerful normality test, followed by Anderson-Darling test, Lilliefors test and Kolmogorov-Smirnov test. However, the power of all four tests is still low for small sample size.
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... While Kolmogorov-smirnov is the preferred method of assessing central tendency, it is not the preferred method for small data sets (grech & calleja, 2018). the shapiro-Wilk test is appropriate where fewer than 50 data points are being investigated (razali & Wah, 2011). the data points were evaluated for normality using statistical analysis software, statistical package for the social sciences (spss). ...
This paper measures the impact of IFRS 16 adoption on financial statements and key financial ratios of mining companies listed on the Johannesburg Stock Exchange (JSE). The IASB has requested research on the adoption of IFRS 16 to understand the impact and assist with post-implementation reviews. Limited studies have been conducted to evaluate the post-implementation impact of IFRS 16. The Wilcoxon signed-rank test was used to determine the impact on financial ratios, and the Kruskal-Wallis test was used to evaluate the impact based on company sizes. The findings illustrated that IFRS 16 increased total assets and liabilities post-adoption. Return-on-asset ratios were not significantly impacted; however, significant changes were noted in debt/equity and debt/asset ratios. Another novel finding is that companies of different sizes were similarly affected by adopting IFRS 16, indicating that the monetary impact of IFRS 16 does not bias based on company size. The research assists users of financial statements to understand the impact of the adoption of IFRS 16 and contributes to the post-implementation review process of the IASB. This article contributes insights into lease capitalisation studies by outlining the impact of IFRS 16’s impact on financial statements and relevant ratios.
... The statistical significance was accepted at p<0.05. Shapiro-Wilk test was conducted in order to check for normality (Razali and Wah, 2011). Table 2 showed that litter size at birth (total and live) and weaning significantly (P<0.05) ...
The present trial investigated the efficacy of dietary curcumin nanoparticles on reproductive performance,
haemato-biochemical parameters, antioxidants, immunity and in vitro embryo production of rabbit does. Mature rabbit does (APRI line) were distributed into 4 groups. Does in the first treatment were fed commercial
diet (CP) as the control group. The rabbits in 2nd, 3rd, and 4th were fed CP with curcumin nanoparticles
(CURNPs) at levels of 3,5, and 7 mg per kg diet respectively. All does were naturally mated with fertile APRI
bucks (five bucks per treatment). Results showed that does in all treatments showed significantly (P<0.05)
better in vivo reproductive efficiency in terms of rates of conception, kindling rate and litter size, as well as
total cholesterol, triglycerides, high and low density lipoproteins, antioxidant status such as concentrations of
total antioxidant capacity, glutathione, and malondialdehyde, as well as activity of glutathione peroxidase,
glutathione S-transferase, superoxide dismutase and catalase, immunity, ovulatory response of CLs number and ovulation rate), in vitro embryo quality, and hatched blastocysts production as compared to other treatments. In conclusion, dietary supplementation with curcumin nanoparticles had positive effects on in vivo
and in vitro reproductive efficiency of doe rabbits
... The matrix V, in turn, corresponds to the order statistics' covariance matrix. This metric is effective in detecting normalcy deviations across a variety of datasets [35]. ...
In response to the growing concerns regarding motorcyclists' safety and advancements in the motorcycle industry, this study investigated the potential of natural fibers as a sustainable approach for enhancing helmet protection, thus replacing the traditional use of expanded polystyrene. Utilizing statistical tools such as the Shapiro-Wilk test, Chau-venet's criterion, and the interquartile range, we compared the impact energy absorption of composites reinforced with natural fibers, including sugarcane bagasse, coconut, and sisal, added to expanded polyurethane prototypes. The results, evaluated through confidence intervals, indicated that composites reinforced with 5% sugarcane bagasse, 5% and 10% coconut, and 10% and 15% sisal exhibited significantly superior impact absorption performance compared to pure expanded polyurethane. Composites with agave sisalana fibers exhibited low variability and reliable performance, with the 10% concentration showing the best results. Sugarcane bagasse fiber demonstrated strong stability, especially at a 5% concentration. Coconut fiber performed well at both 5% and 10% concentrations but showed the greatest variability among the fibers tested. These findings underscore the potential of natural fibers in enhancing helmet safety and suggest promising directions for future research into the ideal composite materials for motorcycle helmets, an inquiry that is currently underway.
... Se ha calculado para cada escala del cuestionario los estadísticos descriptivos de la muestra, examinando diferentes propiedades para observar si los datos tienen una distribución normal: medias, desviaciones típicas, asimetría y curtosis. Además, con el objetivo de explorar la relación entre las variables de cada escala, se han analizado las correlaciones no paramétricas de los ítems por medio del coeficiente de correlación de Spearman dado que la muestra es inferior a 50 sujetos (Razali y Wah, 2011). Posteriormente, se ha analizado la consistencia interna de las escalas calculando el coeficiente Alfa de Cronbach a fin de identificar ítems poco consistentes (se han excluido ítems con valores α=<0,3). ...
La promoción de la salud en edades tempranas a través de la tecnología gamificada ha emergido en los últimos años como una estrategia innovadora con grandes posibilidades educativas para mejorar áreas específicas de los hábitos saludables como la higiene, la alimentación, la actividad física o la educación digital entre otras, siendo necesaria la implicación de todos los ámbitos que rodean a niños, niñas y adolescentes, especialmente del contexto familiar, con el fin de alcanzar un bienestar integral. En concreto, destacan las aplicaciones móviles (apps) que incorporan contenidos relacionados con la salud y están dirigidas a niños, niñas y adolescentes. Sin embargo, la gran mayoría no cuentan con respaldo científico basado en conocimiento experto. Este estudio busca crear un instrumento sólido y fiable para que las familias evalúen la calidad de este software, asegurando su uso educativo y seguro. Se trata de un cuestionario de 39 ítems organizados en seis dimensiones. Tras una prueba piloto con 33 familias, los resultados de los análisis estadísticos realizados han revelado unas propiedades psicométricas muy favorables, sugiriendo la utilidad del instrumento para apoyar a las familias en la selección de este tipo de apps educativas.
... As for the testing analysis, the Shapiro-Wilk statistical test for normality (less than 50 cities) shows that the data obtained do not follow a normal distribution (Finch, 2005;Lemeshko & Lemeshko, 2008;Mohd Razali & Bee Wah, 2011). Therefore, a non-parametric test should be used due to the sample size -less than 50- (Bonett & Wright, 2000) and to the values which are not tied. ...
The rapid growth of the population in cities has given rise to major urban challenges. This has led city governments to use technical solutions based on Information and Communication Technologies (ICTs), arising the concept of smart city (SC). However, the strategy followed to become smart is still very diffuse. This paper seeks to analyze the opinion of the ICT managers of local governments in their initial stage of cities to become smart. To achieve this aim, we have conducted empirical research in Costa Rican cities, which are initiating the SC process, but emphasizing the technological implementation strategy they are using. Concretely, this paper analyzes variables such as the number of ICT projects, dimensions, goals and expected impacts as well as their association. Findings provide technological strategies that can be used and thus facilitate the implementation process of cities to become smart as well as the achievement of results.
... As for the testing analysis, the Shapiro-Wilk statistical test for normality (less than 50 cities) shows that the data obtained do not follow a normal distribution (Finch, 2005;Lemeshko & Lemeshko, 2008;Mohd Razali & Bee Wah, 2011). Therefore, a non-parametric test should be used due to the sample size -less than 50- (Bonett & Wright, 2000) and to the values which are not tied. ...
The rapid growth of the population in cities has given rise to major urban challenges. This has led city governments to use technical solutions based on Information and Communication Technologies (ICTs), arising the concept of smart city (SC). However, the strategy followed to become smart is still very diffuse. This paper seeks to analyze the opinion of the ICT managers of local governments in their initial stage of cities to become smart. To achieve this aim, we have conducted empirical research in Costa Rican cities, which are initiating the SC process, but emphasizing the technological implementation strategy they are using. Concretely, this paper analyzes variables such as the number of ICT projects, dimensions, goals and expected impacts as well as their association. Findings provide technological strategies that can be used and thus facilitate the implementation process of cities to become smart as well as the achievement of results.
... Data were edited in MS Excel (Microsoft Corporation, Redmond, WA, United States). The Levene and Shapiro-Wilk tests were conducted in order to check for normality and homogeneity of variance (Razali and Wah, 2011). One way-Anova of statistical analysis system (SAS, 2012) was used for assessing gene transcription of treC, fimA, mrkA, and espA. ...
Background: Klebsiella pneumoniae is a significant nosocomial pathogen that has developed resistance to multiple antibiotics, often forming biofilms that enhance its virulence. This study investigated the efficacy of a novel nanoformulation, AgNPs@chitosan-NaF, in combating K. pneumoniae biofilms. Methods: Antimicrobial susceptibility testing was performed to assess the antibiotic resistance profile of K. pneumoniae isolates. The antibiofilm activity of AgNPs@ chitosan-NaF was evaluated using crystal violet staining and scanning electron microscopy. The underlying mechanisms of action were investigated through gene expression analysis. Results: The majority of K. pneumoniae isolates exhibited high levels of multidrug resistance. AgNPs@chitosan-NaF demonstrated superior biofilm inhibition compared to AgNPs@chitosan, significantly reducing biofilm biomass and disrupting biofilm architecture at MICs ranging from 0.125 to 1 μg/mL. Mechanistic studies revealed that the nanoformulation downregulated the expression of key biofilm-associated genes, including treC, fimA, mrkA, and ecpA. While AgNPs@chitosan-NaF exhibited a concentration-dependent cytotoxic effect on both normal and cancer cell lines, minimal cytotoxicity was observed at concentrations below 31.25 μg/mL. Conclusion: This study highlights the synergistic effect of silver nanoparticles, chitosan, and sodium fluoride in combating K. pneumoniae biofilms. The nanoformulation, AgNPs@chitosan-NaF, emerges as a promising therapeutic strategy to address the challenge of multidrug-resistant bacterial infections.
Effective development of virtual reality (VR) applications is heavily reliant on the evaluation of user experience (UX). However, traditional methods such as questionnaires have inherent limitations which hinder their ability to capture nuanced behavioral responses and impede the agility of VR content creation: They are time-consuming, burdensome for users, and require significant human effort for interpretation. This study introduces an automated framework aimed at addressing the limitations of questionnaire-based evaluations to assess UX in VR. Our primary focus is to validate the concept of this framework through assessment of the sense of presence (SOP), a crucial psychological perception with significant impact on VR UX. Our proposed framework utilizes a deep neural network (DNN) to analyze patterns in multimodal behavioral cues, including facial expressions, head movements, and hand movements, to predict scores from the Igroup Presence Questionnaire (IPQ). Additionally, we introduce two statistical profiles: the Visual Entropy Profile (VEP), which offers insights into visual complexity by depicting scene entropy, and the Experiential Presence Profile (EPP), which is designed to capture users’ historical SOP levels to enable personalized baseline and sensitivity estimation. The proposed framework achieves a significant correlation between actual and predicted IPQ scores, with a Spearman’s rank correlation coefficient of 0.7303, showcasing the potential of DNNs in analyzing complex behavioral signals and automating SOP assessment. This study represents a pioneering effort in leveraging DNNs for the automatic assessment of SOP and paves the way for future advances in automatically assessing VR UX and unlocking new opportunities in the field.
Introduction:
Mathematical models are very useful tools for the operational control of the extraction stage in the raw sugar manufacturing process.
Objective:
To obtain a mathematical model to predict, based on the operational conditions of milling and imbibition which are applied, the sucrose content in bagasse.
Materials and Methods:
The mathematical model is developed by means of multiple linear regression based on experimental information obtained at industrial scale. Several statistical tests are used to guarantee an adequate adjustment of the mathematical model and to evaluate its predictive performance. The application range is established using “hidden extrapolation” analysis.
Results and Discussion:
This mathematical model is valid for an imbibition ratio between 0.80-2.90; imbibition water temperature between 40-80 oC and sucrose content in primary juice between 15.1-19.2 %. The mathematical model demonstrates that the sucrose content in bagasse has a non-linear dependence on the amount of imbibition applied and provides new statistical evidence proving the significant influence of the imbibition temperature on sucrose extraction. The procedure used is of great utility as methodological material for the development and evaluation of linear regression models in operational research.
Conclusions:
Through the use of the mathematical model as a predictive analysis tool, it is possible to improve the operational performance of the extraction stage by reducing sucrose losses in bagasse.
Background: An important aspect of the "description" of a variable is the shape of its distribution, which tells you the frequency of values from different ranges of the variable. Typically, as most of the statistical tests are based on the normality assumption, a researcher is interested in how well the distribution can be approximated by the normal distribution. Unless there are extreme violations of the normality assumptions, approved statistical tests usually provide accurate results. Although simple descriptive statistics can provide some information relevant to this issue, more precise information can be obtained by performing one of the tests of normality to determine whether the sample comes from a normally distributed population or not. Aim: Lilliefors corrected Kolmogorov-Smirnov, Shapiro-Wilk, D'Agostino Pearson and Jarqua-Bera tests were aimed to be compared in terms of Type I error and power of the tests. Materials and Methods: The simulation was run 1000 times for 23 different sample sizes and for 8 different distributions. Lilliefors corrected Kolmogorov-Smirnov, Shapiro-Wilk, D'Agostino Pearson and Jarqua-Bera tests were compared in terms of Type I error and power of the tests. Results: The most powerful results for normal distributions were given by the Jarqua-Bera and for nonnormal distributions by the Shapiro-Wilk test. Conclusions: As it had the lowest Type I error rate, the Jarqua-Bera test was superior for normal and standard normal distributions. For nonnormal distributions, achieving sufficient power at smaller sample sizes, the Shapiro-Wilk was the most powerful.
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.
Some (large sample) significance points are tabulated for a distribution-free test of goodness of fit which was introduced earlier by the authors. The test, which uses the actual observations without grouping, is sensitive to discrepancies at the tails of the distribution rather than near the median. An illustration is given, using a numerical example used previously by Birnbaum in illustrating the Kolmogorov test.