normality assumption
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2021 ◽  
Vol 10 (3) ◽  
pp. 206
Author(s):  
Fisa Amanah ◽  
Nina Zulida Situmorang ◽  
Fatwa Tentama

Penelitian ini bertujuan untuk mengetahui pengaruh antara hope, employability dengan Subjective well-being pada mahasiswa profesi apoteker Universitas Ahmad Dahlan. Subjek yang digunakan dalam penelitian ini adalah mahasiswa profesi Apoteker Universitas Ahmad Dahlan yang berjumlah 80 orang. Metode penelitian yang digunakan adalah metode kuantitatif, alat pengumpulan data menggunakan skala hope, skala employability dan skala Subjective well-being. hasil dari uji asumsi normalitas pada penelitian ini yaitu diketahui bahwa subjective well-being memiliki p = 0,695 (p > 0,05), selanjutnya hope memiliki p = 0,458 (p > 0,05), dan employability p = 0,507 (p > 0,05). hasil uji normalitas menunjukkan bahwa ketiga variabel memiliki distribusi skor yang normal. Analisis regresi berganda penelitian memperoleh nilai koefisien R sebesar 0,499 dengan taraf signifikansi (p) sebesar 0,000 (p<0,05). Hal ini menunjukan bahwa adanya pengaruh yang signifikan antara hope, employability dengan Subjective well-being pada mahasiswa profesi apoteker Universitas Ahmad Dahlan.   This study aims to see the influence between hope, employability, and subjective well-being of the Ahmad Dahlan University pharmacist profession students. The subjects used in this study were the Ahmad Dahlan University Pharmacist profession which assessed 80 people. The research method used is quantitative methods, data aids using the scale of hope, employability scale and subjective well-being scale. The results of the normality assumption test in this study that it is not known that subjective welfare has p = 0.695 (p> 0.05), then it is expected to have p = 0.458 (p> 0.05), and work ability p = 0.507 (p> 0), 05). The results of the normality test show that the three variables have a normal score distribution. Multiple regression analysis obtained an R coefficient value of 0.499 with a significance level (p) of 0.000 (p <0.05). This shows that there is a significant influence between expectations, work ability and subjective welfare in the pharmacist professional students of Ahmad Dahlan University.


2021 ◽  
Vol 13 (14) ◽  
pp. 7917
Author(s):  
Sangsung Park ◽  
Seongyong Choi ◽  
Sunghae Jun

To perform technology analysis, we usually search patent documents related to target technology. In technology analysis using statistics and machine learning algorithms, we have to transform the patent documents into structured data that is a matrix of patents and keywords. In general, this matrix is very sparse because its most elements are zero values. The data is not satisfied with data normality assumption. However, most statistical methods require the assumption for data analysis. To overcome this problem, we propose a patent analysis method using Bayesian structure learning and visualization. In addition, we apply the proposed method to technology analysis of extended reality (XR). XR technology is integrated technology of virtual and real worlds that includes all of virtual, augmented and mixed realities. This technology is affecting most of our society such as education, healthcare, manufacture, disaster prevention, etc. Therefore, we need to have correct understanding of this technology. Lastly, we carry out XR technology analysis using Bayesian structure learning and visualization.


2021 ◽  
Vol 9 (2) ◽  
pp. 101-110
Author(s):  
Dini Shelvia Monica ◽  
Anton Prasetyo

The purpose of this study was to determine the effect of job satisfaction and compasation on intention to stay with organizational commitment as an intervening variable. The sampling method used in this study nonprofit sampling with purposive technique. The total sample in this study was 40 respondents. The method of collecting data using a questionnaire. The data analysis used was the validity and reliability instrument, the classical assumption test, hypothesis test and path analysis using the SPSS 25 for windows program. The results of this study indicate that all items of each variable are valid and reliable. The first model fulfills the criteria for the classical assumption test with no multicolonierity, heteroscedasticity, and fulfills the normality assumption, but in the second model there is multicolonierity. Based on the t test, it shows that job satisfaction and compensation have a significant effect on organizational commitment, job satisfaction and compensation have a significant effect on intention to stay, organizational commitment has a significant effect on intention to stay.


2021 ◽  
pp. 001316442110102
Author(s):  
Kaiwen Man ◽  
Randall Schumacker ◽  
Monica Morell ◽  
Yurou Wang

While hierarchical linear modeling is often used in social science research, the assumption of normally distributed residuals at the individual and cluster levels can be violated in empirical data. Previous studies have focused on the effects of nonnormality at either lower or higher level(s) separately. However, the violation of the normality assumption simultaneously across all levels could bias parameter estimates in unforeseen ways. This article aims to raise awareness of the drawbacks associated with compounded nonnormality residuals across levels when the number of clusters range from small to large. The effects of the breach of the normality assumption at both individual and cluster levels were explored. A simulation study was conducted to evaluate the relative bias and the root mean square of the model parameter estimates by manipulating the normality of the data. The results indicate that nonnormal residuals have a larger impact on the random effects than fixed effects, especially when the number of clusters and cluster size are small. In addition, for a simple random-effects structure, the use of restricted maximum likelihood estimation is recommended to improve parameter estimates when compounded residuals across levels show moderate nonnormality, with a combination of small number of clusters and a large cluster size.


Author(s):  
Ulrich Knief ◽  
Wolfgang Forstmeier

AbstractWhen data are not normally distributed, researchers are often uncertain whether it is legitimate to use tests that assume Gaussian errors, or whether one has to either model a more specific error structure or use randomization techniques. Here we use Monte Carlo simulations to explore the pros and cons of fitting Gaussian models to non-normal data in terms of risk of type I error, power and utility for parameter estimation. We find that Gaussian models are robust to non-normality over a wide range of conditions, meaning that p values remain fairly reliable except for data with influential outliers judged at strict alpha levels. Gaussian models also performed well in terms of power across all simulated scenarios. Parameter estimates were mostly unbiased and precise except if sample sizes were small or the distribution of the predictor was highly skewed. Transformation of data before analysis is often advisable and visual inspection for outliers and heteroscedasticity is important for assessment. In strong contrast, some non-Gaussian models and randomization techniques bear a range of risks that are often insufficiently known. High rates of false-positive conclusions can arise for instance when overdispersion in count data is not controlled appropriately or when randomization procedures ignore existing non-independencies in the data. Hence, newly developed statistical methods not only bring new opportunities, but they can also pose new threats to reliability. We argue that violating the normality assumption bears risks that are limited and manageable, while several more sophisticated approaches are relatively error prone and particularly difficult to check during peer review. Scientists and reviewers who are not fully aware of the risks might benefit from preferentially trusting Gaussian mixed models in which random effects account for non-independencies in the data.


2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Xin Tong

Semiparametric Bayesian methods have been proposed in the literature for growth curve modeling to reduce the adverse effect of having nonnormal data. The normality assumption of measurement errors in traditional growth curve models was {replaced} by a random distribution with Dirichlet process mixture priors. However, both the random effects and measurement errors are equally likely to be nonnormal. Therefore, in this study, three types of robust distributional growth curve models are proposed from a semiparametric Bayesian perspective, in which random coefficients or measurement errors follow either normal distributions or unknown random distributions with Dirichlet process mixture priors. Based on a Monte Carlo simulation study, we evaluate the performance of the robust models and demonstrate that selecting an appropriate model for practical data analyses is very important, by comparing the three types of robust distributional models as well as the traditional growth curve models with the normality assumption. We also provide a straightforward strategy to select the appropriate model.


Author(s):  
Dewi Wulandari ◽  
Sutrisno Sutrisno ◽  
Muhammad Bayu Nirwana

In Multivariate regression, we need to assess normality assumption simultaneously, not univariately. Univariate normal distribution does not guarantee the occurrence of multivariate normal distribution [1]. So we need to extend the assessment of univariate normal distribution into multivariate methods. One extended method is skewness and kurtosis as proposed by Mardia [2]. In this paper, we introduce the method, present the procedure of this method, and show how to examine normality assumption in multivariate regression study case using this method and expose the use of statistics software to help us in numerical calculation. Received February 20, 2021Revised March 8, 2021Accepted March 10, 2021


2021 ◽  
Vol 60 (4) ◽  
pp. 595-605
Author(s):  
Dario Ruggiu ◽  
Francesco Viola ◽  
Andreas Langousis

AbstractWe develop a nonparametric procedure to assess the accuracy of the normality assumption for annual rainfall totals (ART), based on the marginal statistics of daily rainfall. The procedure is addressed to practitioners and hydrologists that operate in data-poor regions. To do so we use 1) goodness-of-fit metrics to conclude on the approximate convergence of the empirical distribution of annual rainfall totals to a normal shape and classify 3007 daily rainfall time series from the NOAA/NCDC Global Historical Climatology Network database, with at least 30 years of recordings, into Gaussian (G) and non-Gaussian (NG) groups; 2) logistic regression analysis to identify the statistics of daily rainfall that are most descriptive of the G/NG classification; and 3) a random-search algorithm to conclude on a set of constraints that allows classification of ART samples on the basis of the marginal statistics of daily rain rates. The analysis shows that the Anderson–Darling (AD) test statistic is the most conservative one in determining approximate Gaussianity of ART samples (followed by Cramer–Von Mises and Lilliefors’s version of Kolmogorov–Smirnov) and that daily rainfall time series with fraction of wet days fwd < 0.1 and daily skewness coefficient of positive rain rates skwd > 5.92 deviate significantly from the normal shape. In addition, we find that continental climate (type D) exhibits the highest fraction of Gaussian distributed ART samples (i.e., 74.45%; AD test at α = 5% significance level), followed by warm temperate (type C; 72.80%), equatorial (type A; 68.83%), polar (type E; 62.96%), and arid (type B; 60.29%) climates.


2021 ◽  
Vol 6 ◽  
Author(s):  
Seohyun Kim ◽  
Xin Tong ◽  
Zijun Ke

Growth mixture modeling is a popular analytic tool for longitudinal data analysis. It detects latent groups based on the shapes of growth trajectories. Traditional growth mixture modeling assumes that outcome variables are normally distributed within each class. When data violate this normality assumption, however, it is well documented that the traditional growth mixture modeling mislead researchers in determining the number of latent classes as well as in estimating parameters. To address nonnormal data in growth mixture modeling, robust methods based on various nonnormal distributions have been developed. As a new robust approach, growth mixture modeling based on conditional medians has been proposed. In this article, we present the results of two simulation studies that evaluate the performance of the median-based growth mixture modeling in identifying the correct number of latent classes when data follow the normality assumption or have outliers. We also compared the performance of the median-based growth mixture modeling to the performance of traditional growth mixture modeling as well as robust growth mixture modeling based on t distributions. For identifying the number of latent classes in growth mixture modeling, the following three Bayesian model comparison criteria were considered: deviance information criterion, Watanabe-Akaike information criterion, and leave-one-out cross validation. For the median-based growth mixture modeling and t-based growth mixture modeling, our results showed that they maintained quite high model selection accuracy across all conditions in this study (ranged from 87 to 100%). In the traditional growth mixture modeling, however, the model selection accuracy was greatly influenced by the proportion of outliers. When sample size was 500 and the proportion of outliers was 0.05, the correct model was preferred in about 90% of the replications, but the percentage dropped to about 40% as the proportion of outliers increased to 0.15.


Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 173
Author(s):  
Ayman Alzaatreh ◽  
Mohammad Aljarrah ◽  
Ayanna Almagambetova ◽  
Nazgul Zakiyeva

The traditional linear regression model that assumes normal residuals is applied extensively in engineering and science. However, the normality assumption of the model residuals is often ineffective. This drawback can be overcome by using a generalized normal regression model that assumes a non-normal response. In this paper, we propose regression models based on generalizations of the normal distribution. The proposed regression models can be used effectively in modeling data with a highly skewed response. Furthermore, we study in some details the structural properties of the proposed generalizations of the normal distribution. The maximum likelihood method is used for estimating the parameters of the proposed method. The performance of the maximum likelihood estimators in estimating the distributional parameters is assessed through a small simulation study. Applications to two real datasets are given to illustrate the flexibility and the usefulness of the proposed distributions and their regression models.


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