A Practical Guide to Statistical Tests in the Biomedical Field: From Parametric to Nonparametric, Where and How?

Healthcare decisions are based on scientific evidence obtained from medical studies by gathering data and analyzing it to obtain the best results. When analyzing data, biostatistics is a powerful tool, but healthcare professionals lack knowledge in this field. This lack of knowledge can manifest itself in situations such as choosing the wrong statistical test for the right situation or applying a statistical test without checking its assumptions, leading to inaccurate results and misleading conclusions. With the help of this “narrative review”, the aim is to bring biostatistics closer to healthcare professionals by answering certain questions: how to describe the distribution of data? how to assess the normality of data? how to transform data? and how to choose between nonparametric and parametric tests? Through this work, our hope is that the reader will be able to choose the right test for the right situation, in order to obtain the most accurate results.

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.

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.

Testing Result Statistics-Based Rapid Testing Method for Safety-Critical System

Safety-critical system （SCS） has highly demand for dependability, which requires plenty of resource to ensure that the system under test （SUT） satisfies the dependability requirement. In this paper, a new SCS rapid testing method is proposed to improve SCS adaptive dependability testing. The result of each test execution is saved in calculation memory unit and evaluated as an algorithm model. Then the least quantity of scenario test case for next test execution will be calculated according to the promised SUT＇s confidence level. The feedback data are generated to weight controller as the guideline for the further testing. Finally, a compre- hensive experiment study demonstrates that this adaptive testing method can really work in practice. This rapid testing method, testing result statistics-based adaptive control, makes the SCS dependability testing much more effective.

TESTS OF ELLIPTICAL SYMMETRY AND THE ASYMPTOTIC TAIL BEHAVIOR OF THE STATISTICS

In this paper, some test statistics of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high\|dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis. The asymptotic properties of Bootstrap approximation are investigated and the tail behaviors of the statistics are studied.

Test for Homogeneity of Odds Ratios Using <i>U</i>-Statistics

There are a few statistics testing the homogeneity of odds ratios across strata. Asymptotic statistics lose their power in the “sparse-data” setting. Both asymptotic statistics and exact tests have low power when the sample sizes are small. We created a set of U statistics and compared them with some existing statistics in testing homogeneity of OR at different data settings. We evaluated their performance in terms of the empirical size and power via Monto Carlo simulations. Our results showed that two of the U-statistics under our study had higher power for testing homogeneity of odds ratios for 2 by 2 contingency tables. The application of the tests was illustrated in two real examples.

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.

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.

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.

Radio Frequency Interference Mitigation and Statistics in the Spectral Observations of FAST

In radio astronomy,radio frequency interference(RFI)becomes more and more serious for radio observational facilities.The RFI always influences the search and study of the interesting astronomical objects.Mitigating the RFI becomes an essential procedure in any survey data processing.The Five-hundred-meter Aperture Spherical radio Telescope(FAST)is an extremely sensitive radio telescope.It is necessary to find out an effective and precise RFI mitigation method for FAST data processing.In this work,we introduce a method to mitigate the RFI in FAST spectral observation and make a statistic for the RFI using~300 h FAST data.The details are as follows.First,according to the characteristics of FAST spectra,we propose to use the Asymmetrically Reweighted Penalized Least Squares algorithm for baseline fitting.Our test results show that it has a good performance.Second,we flag the RFI with four strategies,which are to flag extremely strong RFI,flag long-lasting RFI,flag polarized RFI,and flag beam-combined RFI,respectively.The test results show that all the RFI above a preset threshold could be flagged.Third,we make a statistic for the probabilities of polarized XX and YY RFI in FAST observations.The statistical results could tell us which frequencies are relatively quiescent.With such statistical data,we are able to avoid using such frequencies in our spectral observations.Finally,based on the~300 h FAST data,we obtained an RFI table,which is the most complete database currently for FAST.

Higher-Order Statistics for Automatic Weld Defect Detection

Image processing and image analysis are the main aspects for obtaining information from digital image owing to the fact that this techniques give the desired details in most of the applications generally and Non-Destructive testing specifically. This paper presents a proposed method for the automatic detection of weld defects in radiographic images. Firstly, the radiographic images were enhanced using adaptive histogram equalization and are filtered using mean and wiener filters. Secondly, the welding area is selected from the radiography image. Thirdly, the Cepstral features are extracted from the Higher-Order Spectra (Bispectrum and Trispectrum). Finally, neural networks are used for feature matching. The proposed method is tested using 100 radiographic images in the presence of noise and image blurring. Results show that in spite of time consumption, the proposed method yields best results for the automatic detection of weld defects in radiography images when the features were extracted from the Trispectrum of the image.

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.

Quantification constraints on time gap for comagmatic gold deposits:Evidence from chronological statistics

The time gap between diagenesis and mineralization (TGDM) for comagmatic gold deposits (CGD) plays an important role in confirming the genetic relationship between gold deposits and their related intrusions. With the help of preciously published isotopic ages of some typical gold deposits and their related rocks in China,the authors have discussed and quantified the distribution characteristics and scope of the TGDM. Statistical analyses and Kolmogorov tests showed that mineralizing events are either contemporaneous with or slightly postdate their cognate magma. The TGDM conforms with normal distributions at a 0.05 confidence level and clusters between 0 and 16.0 Ma with a mean of 7.0 Ma. Thus,if the TGDM of CGD is less than 16.0 Ma,it is reasonable to consider,with the aid of other evidence,the possibility of its comagmatic genetic affiliation. The authors also emphasized that to get a precise time gap it is necessary to strengthen the diagenesis-mineralization geological background of the deposits studied,and to pay attention to the study of time gap in combination with trace elements and isotope tracing.

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.