Comparison of Type I Error Rates of Siegel-Tukey and Savage Tests among Non-Parametric Tests

This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.

Study on Key Biological Indicators of Diabetes Based on Statistical Tests

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.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

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.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

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.

Statistical Tests of the Validation of TCO Satellite Measurements, Recorded Simultaneously by TOMS-OMI (2005) and OMI-OMPS (2012-2018)

Two statistical validation methods were used to evaluate the confidence level of the Total Column Ozone (TCO) measurements recorded by satellite systems measuring simultaneously, one using the normal distribution and another using the Mann-Whitney test. First, the reliability of the TCO measurements was studied hemispherically. While similar coincidences and levels of significance > 0.05 were found with the two statistical tests, an enormous variability in the levels of significance throughout the year was also exposed. Then, using the same statistical comparison methods, a latitudinal study was carried out in order to elucidate the geographical distribution that gave rise to this variability. Our study reveals that between the TOMS and OMI measurements in 2005 there was only a coincidence in 50% of the latitudes, which explained the variability. This implies that for 2005, the TOMS measurements are not completely reliable, except between the -50° and -15° latitude band in the southern hemisphere and between +15° and +50° latitude band in the northern hemisphere. In the case of OMI-OMPS, we observe that between 2011 and 2016 the measurements of both satellite systems are reasonably similar with a confidence level higher than 95%. However, in 2017 a band with a width of 20° latitude centered on the equator appeared, in which the significance levels were much less than 0.05, indicating that one of the measurement systems had begun to fail. In 2018, the fault was not only located in the equator, but was also replicated in various bands in the Southern Hemisphere. We interpret this as evidence of irreversible failure in one of the measurement systems.

New Fatigue Test and Statistical Method for Metallic Materials Used in Vehicle Transmissions

Aim To improve the efficiency of fatigue material tests and relevant statistical treatment of test data. Methods\ Least square approach and other special treatments were used. Results and Conclusion\ The concepts of each phase in fatigue tests and statistical treatment are clarified. The method proposed leads to three important properties. Reduced number of specimens brings to the advantage of lowering test expenditures. The whole test procedure has more flexibility for there is no need to conduct many tests at the same stress level as in traditional cases.

Statistical analysis of nondestructive testing results of cast steel joints in civil engineering structures

To study the distribution law and random characteristics of casting defects in steel castings,24 civil engineering structural cast steel joints were divided into two groups:simple cast steel joints and complex cast steel joints.Three kinds of nondestructive testing(NDT)methods,namely,visual,magnetic particle,and ultrasonic inspections,were used to detect the macroscopic defects in joints.The NDT results were then statistically analyzed.The results show that the unfused core support is a common defect of complex cast steel joints,and the defect can be seen visually,so excavation and repair welding should be carried out before castings leave factories.Casting cracks are extremely likely to occur in the intersection area of tubes,which is called the ultrasonic inspection blind zone.The occurrence probability of gas pores on simple cast steel joints is the largest,and the occurrence probability of core support incomplete fusions on complex cast steel joints is the largest.However,when cast steel joints are counted as a whole sample,the occurrence probability of gas pores is larger than that of core support incomplete fusions.Therefore,it is the most common defect in cast steel joints.

A Statistical Power Comparison of the Kolmogorov-Smirnov Two-Sample Test and the Wald Wolfowitz Test in Terms of Fixed Skewness and Fixed Kurtosis in Large Sample Sizes

In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.

STATISTICAL TESTS FOR THE COMPARISON OF THE INCIDENCE OR MORTALITY RATES IN CANCER REGISTRY AND DESCRIPTIVE EPIDEMIOLOGY──A MICROCOMPUTER PROGRAM IN BASIC

This paper describes the statistical methods of the comparison of the incidence or mortality rates in cancer registry and descriptive epidemiology, and the features of microcomputer program (CANTEST) which was designed to perform the methods. The program was written in IBM BASIC language. Using the program CANTEST we presented here the user can do several statistical tests or estimations as follow: 1. the comparison of the adjusted rates which were calculated by directly or indirectly standardized methods, 2. the calculation of the slope of regression line for testing the linear trends of the adjusted rates, 3. the estimation of the 95% or 99%conndence intervals of the directly adjusted rates, of the cumulative rates (0-64 and 0-74), and of the cumulative risk. Several examples are presented for testing the performances of the program.

SiteTesting with IRA-935 Hygrometer and Statistical Analyses

A brief description of infrared IRA-935 water vapour measuring instrument is presented and integrated vertical water vapour content W 0 in the atmosphere at Gaomeigu and Fenghuangshan sites and precision analyses are given in the paper. The daily variation and distributions of W 0 in a whole year and monthly average W 0 measurements at these two sites are discussed in more detail. The statistical results of the observational data in the whole year are also analysed and discussed.

Reply to 'Statistical testing and distribution for lead chloride toxicity'

We are very grateful for the letter written by Dr Lange,and indeed apologize for the mistakes noted in the word-ing of our text regarding statistical analysis.This wasdue to changes carried out while revising the manuscriptat the request of reviewers,whom we thank for,point-ing out several issues that were actually similar to thosenoted by Dr.Lange.Unfortunately,we were unable todescribe and discuss our findings properly in the context

The Statistical Significance Test of Regional Climate Change Caused by Land Use and Land Cover Variation in West China

The West Development Policy being implemented in China is causing significant land use and land cover （LULC） changes in West China. With the up-to-date satellite database of the Global Land Cover Characteristics Database （GLCCD） that characterizes the lower boundary conditions, the regional climate model RIEMS-TEA is used to simulate possible impacts of the significant LULC variation. The model was run for five continuous three-month periods from 1 June to 1 September of 1993, 1994, 1995, 1996, and 1997, and the results of the five groups are examined by means of a student t-test to identify the statistical significance of regional climate variation. The main results are： （1） The regional climate is affected by the LULC variation because the equilibrium of water and heat transfer in the air-vegetation interface is changed. （2） The integrated impact of the LULC variation on regional climate is not only limited to West China where the LULC varies, but also to some areas in the model domain where the LULC does not vary at all. （3） The East Asian monsoon system and its vertical structure are adjusted by the large scale LULC variation in western China, where the consequences are the enhancement of the westward water vapor transfer from the east oast and the relevant increase of wet-hydrostatic energy in the middle-upper atmospheric layers. （4） The ecological engineering in West China affects significantly the regional climate in Northwest China, North China and the middle-lower reaches of the Yangtze River; there are obvious effects in South, Northeast, and Southwest China, but minor effects in Tibet.

Sample Size Determination and Statistical Hypothesis Testing for Core Centration in Press Coated Tablets

A novel statistical approach to evaluate the manufacturing quality of press coated tablets in terms of the centering of their core is presented. We also provide a formula to determine the necessary sample size. This approach is applied to real data.

Effectiveness Assessment of the Search-Based Statistical Structural Testing

Search-based statistical structural testing(SBSST)is a promising technique that uses automated search to construct input distributions for statistical structural testing.It has been proved that a simple search algorithm,for example,the hill-climber is able to optimize an input distribution.However,due to the noisy fitness estimation of the minimum triggering probability among all cover elements(Tri-Low-Bound),the existing approach does not show a satisfactory efficiency.Constructing input distributions to satisfy the Tri-Low-Bound criterion requires an extensive computation time.Tri-Low-Bound is considered a strong criterion,and it is demonstrated to sustain a high fault-detecting ability.This article tries to answer the following question:if we use a relaxed constraint that significantly reduces the time consumption on search,can the optimized input distribution still be effective in faultdetecting ability?In this article,we propose a type of criterion called fairnessenhanced-sum-of-triggering-probability(p-L1-Max).The criterion utilizes the sum of triggering probabilities as the fitness value and leverages a parameter p to adjust the uniformness of test data generation.We conducted extensive experiments to compare the computation time and the fault-detecting ability between the two criteria.The result shows that the 1.0-L1-Max criterion has the highest efficiency,and it is more practical to use than the Tri-Low-Bound criterion.To measure a criterion’s fault-detecting ability,we introduce a definition of expected faults found in the effective test set size region.To measure the effective test set size region,we present a theoretical analysis of the expected faults found with respect to various test set sizes and use the uniform distribution as a baseline to derive the effective test set size region’s definition.

ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICTY IN GROWTH CURVE MODELS

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.

Statistic Analysis on Quantitative Characteristics for Developing the DUS Test Guideline of Ranunculus asiaticus L.

Selection of quantitative characteristics, division of their expression ranges, and selection of example varieties are key issues on developing DUS Test Guidelines, which are more crucial for quantitative characteristics since their expressions vary in different degrees. Taking the development of DUS Test Guideline of Ranunculus asiaticus L. as an example, this paper applied statistic-based approaches for the analyses of quantitative characteristics. We selected 9 quantitative characteristics from 18 pre-selected characteristics, based on within-variety uniformity, stability between different growing cycles, and correlation among characteristics, by the analyses of coefficient of variation, paired-samples t-test and partial correlation. The expression ranges of the 9 selected quantitative characteristics were divided into different states using descriptive statistics and distribution frequency of varieties. Eight of the 9 selected quantitative characteristics were categorized as standard characteristics as they showed one peak in distribution frequency of 120 varieties in various expressions of the characteristics, whereas, plant height can be categorized as grouping characteristic since it gave two peaks, and can group the varieties into pot and cut varieties. Finally, box-plot was applied to visually select the example varieties, and varieties 7, 12, and 28 were determined as the example varieties for plant height. The methods described in this paper are effective for the selection of quantitative characteristics, division of expression ranges, and selection of example varieties in Ranunculus asiaticus L. for DUS test, and may also be interest for other plant genera.

Application of Statistical Tools for Data Analysis and Interpretation in Rice Plant Pathology

There has been a significant advancement in the application of statistical tools in plant pathology during the past four decades. These tools include multivariate analysis of disease dynamics involving principal component analysis, cluster analysis, factor analysis, pattern analysis, discriminant analysis, multivariate analysis of variance, correspondence analysis, canonical correlation analysis, redundancy analysis, genetic diversity analysis, and stability analysis, which involve in joint regression, additive main effects and multiplicative interactions, and genotype-by-environment interaction biplot analysis. The advanced statistical tools, such as non-parametric analysis of disease association, meta-analysis, Bayesian analysis, and decision theory, take an important place in analysis of disease dynamics. Disease forecasting methods by simulation models for plant diseases have a great potentiality in practical disease control strategies. Common mathematical tools such as monomolecular, exponential, logistic, Gompertz and linked differential equations take an important place in growth curve analysis of disease epidemics. The highly informative means of displaying a range of numerical data through construction of box and whisker plots has been suggested. The probable applications of recent advanced tools of linear and non-linear mixed models like the linear mixed model, generalized linear model, and generalized linear mixed models have been presented. The most recent technologies such as micro-array analysis, though cost effective, provide estimates of gene expressions for thousands of genes simultaneously and need attention by the molecular biologists. Some of these advanced tools can be well applied in different branches of rice research, including crop improvement, crop production, crop protection, social sciences as well as agricultural engineering. The rice research scientists should take advantage of these new opportunities adequately in adoption of the new highly potential advanced technologies while planning experimental designs, data collection, analysis and interpretation of their research data sets.

MAXIMUM TEST FOR A SEQUENCE OF QUADRATIC FORM STATISTICS ABOUT SCORE TEST IN LOGISTIC REGRESSION MODEL

This article proposes the maximum test for a sequence of quadratic form statistics about score test in logistic regression model which can be applied to genetic and medicine fields.Theoretical properties about the maximum test are derived.Extensive simulation studies are conducted to testify powers robustness of the maximum test compared to other two existed test.We also apply the maximum test to a real dataset about multiple gene variables association analysis.

A Statistical Analysis of the Modulus of Elasticity and Compressive Strength of Concrete C45/55 for Pre-stressed Precast Beams

Random behavior of concrete C45/55 XF2 used for prefabricated pre-stressed bridge beams is described on the basis of evaluating a vast set of measurements. A detailed statistical analysis is carried out on 133 test results of cylinders 150 ~ 300 mm in size. The tests have been running in laboratories of the Klokner Institute. A single worker took all specimens throughout the period, and the subsequent measurements of the static modulus of elasticity and the compressive strength of the concrete were performed. The measurements were made at the age of 28 days after specimens casting, and only one testing machine with the same capping method was used. Suitable theoretical models of division are determined on the basis of tests in good congruence, with the use of Z2 and the Bernstein criterion. A set of concrete compressive strength （carried out on 133 test results of cylinders 150 ~ 300 mm after test of static modulus of elasticity） shows relatively high skewness in this specific case. This cause that limited beta distribution is better than generally recommended theoretical distribution for strength the normal or lognormal. The modulus of elasticity is not significantly affected due to skewness because the design value is based on mean value.