Normality testing is a fundamental hypothesis test in the statistical analysis of key biological indicators of diabetes.If this assumption is violated,it may cause the test results to deviate from the true value,leadi...Normality testing is a fundamental hypothesis test in the statistical analysis of key biological indicators of diabetes.If this assumption is violated,it may cause the test results to deviate from the true value,leading to incorrect inferences and conclusions,and ultimately affecting the validity and accuracy of statistical inferences.Considering this,the study designs a unified analysis scheme for different data types based on parametric statistical test methods and non-parametric test methods.The data were grouped according to sample type and divided into discrete data and continuous data.To account for differences among subgroups,the conventional chi-squared test was used for discrete data.The normal distribution is the basis of many statistical methods;if the data does not follow a normal distribution,many statistical methods will fail or produce incorrect results.Therefore,before data analysis and modeling,the data were divided into normal and non-normal groups through normality testing.For normally distributed data,parametric statistical methods were used to judge the differences between groups.For non-normal data,non-parametric tests were employed to improve the accuracy of the analysis.Statistically significant indicators were retained according to the significance index P-value of the statistical test or corresponding statistics.These indicators were then combined with relevant medical background to further explore the etiology leading to the occurrence or transformation of diabetes status.展开更多
In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditiona...In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.展开更多
In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review effici...In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.展开更多
The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’...The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’s W test and D’Agostino-Belanger-D’Agostino K-squared test. An experiment with 384 conditions was simulated. The conditions were generated by crossing 24 sample sizes and 16 types of continuous distributions: one normal and 15 non-normal. The percentage of success in maintaining the null hypothesis of normality against normal samples and in rejecting the null hypothesis against non-normal samples (accuracy) was calculated. In addition, the type II error against normal samples and the statistical power against normal samples were computed. Comparisons of percentage and means were performed using Cochran’s Q-test, Friedman’s test, and repeated measures analysis of variance. With sample sizes of 150 or greater, high accuracy and mean power or type II error (≥0.70 and ≥0.80, respectively) were achieved. All three normality tests were similarly accurate;however, the PSNS-based test showed lower mean power than K-squared and W tests, especially against non-normal samples of symmetrical-platykurtic distributions, such as the uniform, semicircle, and arcsine distributions. It is concluded that the PSNS-based omnibus test is accurate and powerful for testing normality with samples of at least 150 observations.展开更多
Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） o...Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） of eigenvalues of the Wigner matrix is deduced. A numerical Kullback-Leibler divergence of the empiric-d spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak SIPSK signal detection in the single-input single-output （SISO） system and the single-input multiple-output （SIMO） system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.展开更多
In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test s...In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.展开更多
In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature ...In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.展开更多
One hundred and twenty normal subjects (240 eyes) agedfrom 10 to 69 were tested with FM 100-hue test.They were divided into6 groups according to their age.It was shown that there were no statisti-cally significant dif...One hundred and twenty normal subjects (240 eyes) agedfrom 10 to 69 were tested with FM 100-hue test.They were divided into6 groups according to their age.It was shown that there were no statisti-cally significant difference in the total error score (TES) between the malesand females or between the right and left eyes,but there existed some rela-tionships between the TES and age.The total error score (TES) was thelowest in the 20-29 age group and increased gradually with aging.Theanalysis of the partial...展开更多
The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper in...The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.展开更多
Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Kn...Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.展开更多
Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Kn...Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.展开更多
基金National Natural Science Foundation of China(No.12271261)Postgraduate Research and Practice Innovation Program of Jiangsu Province,China(Grant No.SJCX230368)。
文摘Normality testing is a fundamental hypothesis test in the statistical analysis of key biological indicators of diabetes.If this assumption is violated,it may cause the test results to deviate from the true value,leading to incorrect inferences and conclusions,and ultimately affecting the validity and accuracy of statistical inferences.Considering this,the study designs a unified analysis scheme for different data types based on parametric statistical test methods and non-parametric test methods.The data were grouped according to sample type and divided into discrete data and continuous data.To account for differences among subgroups,the conventional chi-squared test was used for discrete data.The normal distribution is the basis of many statistical methods;if the data does not follow a normal distribution,many statistical methods will fail or produce incorrect results.Therefore,before data analysis and modeling,the data were divided into normal and non-normal groups through normality testing.For normally distributed data,parametric statistical methods were used to judge the differences between groups.For non-normal data,non-parametric tests were employed to improve the accuracy of the analysis.Statistically significant indicators were retained according to the significance index P-value of the statistical test or corresponding statistics.These indicators were then combined with relevant medical background to further explore the etiology leading to the occurrence or transformation of diabetes status.
文摘In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.
文摘In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.
文摘The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’s W test and D’Agostino-Belanger-D’Agostino K-squared test. An experiment with 384 conditions was simulated. The conditions were generated by crossing 24 sample sizes and 16 types of continuous distributions: one normal and 15 non-normal. The percentage of success in maintaining the null hypothesis of normality against normal samples and in rejecting the null hypothesis against non-normal samples (accuracy) was calculated. In addition, the type II error against normal samples and the statistical power against normal samples were computed. Comparisons of percentage and means were performed using Cochran’s Q-test, Friedman’s test, and repeated measures analysis of variance. With sample sizes of 150 or greater, high accuracy and mean power or type II error (≥0.70 and ≥0.80, respectively) were achieved. All three normality tests were similarly accurate;however, the PSNS-based test showed lower mean power than K-squared and W tests, especially against non-normal samples of symmetrical-platykurtic distributions, such as the uniform, semicircle, and arcsine distributions. It is concluded that the PSNS-based omnibus test is accurate and powerful for testing normality with samples of at least 150 observations.
基金Supported by the National Natural Science Foundation of China under Grant No 61371170the Fundamental Research Funds for the Central Universities under Grant Nos NP2015404 and NS2016038+1 种基金the Aeronautical Science Foundation of China under Grant No 20152052028the Funding of Jiangsu Innovation Program for Graduate Education under Grant No KYLX15_0282
文摘Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） of eigenvalues of the Wigner matrix is deduced. A numerical Kullback-Leibler divergence of the empiric-d spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak SIPSK signal detection in the single-input single-output （SISO） system and the single-input multiple-output （SIMO） system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.
基金National Natural Science Foundation of China(1047112610671176).
文摘In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.
文摘In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.
文摘One hundred and twenty normal subjects (240 eyes) agedfrom 10 to 69 were tested with FM 100-hue test.They were divided into6 groups according to their age.It was shown that there were no statisti-cally significant difference in the total error score (TES) between the malesand females or between the right and left eyes,but there existed some rela-tionships between the TES and age.The total error score (TES) was thelowest in the 20-29 age group and increased gradually with aging.Theanalysis of the partial...
文摘The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.
文摘Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.
文摘Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.
