R-Factor Analysis of Data Based on Population Models Comprising R- and Q-Factors Leads to Biased Loading Estimates

Effects of performing an R-factor analysis of observed variables based on population models comprising R- and Q-factors were investigated. Although R-factor analysis of data based on a population model comprising R- and Q-factors is possible, this may lead to model error. Accordingly, loading estimates resulting from R-factor analysis of sample data drawn from a population based on a combination of R- and Q-factors will be biased. It was shown in a simulation study that a large amount of Q-factor variance induces an increase in the variation of R-factor loading estimates beyond the chance level. Tests of the multivariate kurtosis of observed variables are proposed as an indicator of possible Q-factor variance in observed variables as a prerequisite for R-factor analysis.

Improved statistical fluctuation analysis for two decoy-states phase-matching quantum key distribution

Phase-matching quantum key distribution is a promising scheme for remote quantum key distribution,breaking through the traditional linear key-rate bound.In practical applications,finite data size can cause significant system performance to deteriorate when data size is below 1010.In this work,an improved statistical fluctuation analysis method is applied for the first time to two decoy-states phase-matching quantum key distribution,offering a new insight and potential solutions for improving the key generation rate and the maximum transmission distance while maintaining security.Moreover,we also compare the influence of the proposed improved statistical fluctuation analysis method on system performance with those of the Gaussian approximation and Chernoff-Hoeffding boundary methods on system performance.The simulation results show that the proposed scheme significantly improves the key generation rate and maximum transmission distance in comparison with the Chernoff-Hoeffding approach,and approach the results obtained when the Gaussian approximation is employed.At the same time,the proposed scheme retains the same security level as the Chernoff-Hoeffding method,and is even more secure than the Gaussian approximation.

Statistical analysis on the influence of mechanical parameters in the vibration of pylons

We present a statistical investigation of the degree of influence that assumptions made in relation to the mechanical parameters of a pylon have on its ground-induced vibrations.The study is set up by using as a key kinematic variable the displacement at the top of a reference,a stand-alone pylon with a uniform cross-section and fixity at its base.Next,statistics are produced using a dimensionless displacement ratio defined between the‘parental’and the‘subsidiary’cases,the latter defined for the pylon(a)resting on compliant soil,(b)having an attached top mass,and(c)being non-uniform with height.Furthermore,two materials are examined,namely,steel and reinforced concrete(R/C).More specifically,this displacement ratio is independent of the excitation and plays the role of a transfer function between the base and the top of the pylon.Both horizontal and vertical motions are considered,and the equations of motion are solved in the frequency domain.The ensuing statistical analysis is conducted for the following parameter combinations:(a)pylon founded on soft,intermediate,and stiff soil;(b)low,intermediate,and high-mass ratios of the attached mass to the pylon′s mass;(c)a constant and quadratic degree of pylon tapering with height.Spearman correlation coefficients are calculated for all the above combinations to arrive at statistical results that establish validity bounds and quantify the degree of influence of each assumption on the pylon′s response.

Effect of Jianpi Bushen formula for colon cancer patients who underwent adjuvant chemotherapy:Statistical analysis plan for a multicenter trial

Background:Patients with colon cancer who receive chemotherapy usually experience various gastrointestinal adverse reactions,including nausea,vomiting,and diarrhea,which make it challenging for them to adhere to treatment.As an effective traditional Chinese medicine,the Jianpi Bushen formula has been widely used to alleviate the side effects of chemotherapy.Objective:To evaluate the efficacy and safety of Jianpi Bushen formulae for patients who undergo chemotherapy.This statistical analysis plan(SAP)is intended to enhance the transparency and research quality of our randomized controlled trial.Methods:Our study is a multicenter,double-blind,randomized controlled clinical trial.This trial aimed to compare the completion rate of chemotherapy in colon cancer patients who are using and not using Jianpi Bushen formula.To attenuate possible selection bias in the final report,we declared the overall trial design,outcome measures,subgroup analyses,and safety measures.Also,we described the data management and statistical analysis methods in detail.Conclusion:The SAP provides more detailed information than the trial protocol for data management and statistical analysis methods.Further post-hoc analyses can be performed by referring to the SAP,and possible selection bias can be attenuated.

Dealing with Multicollinearity in Factor Analysis: The Problem, Detections, and Solutions

Multicollinearity in factor analysis has negative effects, including unreliable factor structure, inconsistent loadings, inflated standard errors, reduced discriminant validity, and difficulties in interpreting factors. It also leads to reduced stability, hindered factor replication, misinterpretation of factor importance, increased parameter estimation instability, reduced power to detect the true factor structure, compromised model fit indices, and biased factor loadings. Multicollinearity introduces uncertainty, complexity, and limited generalizability, hampering factor analysis. To address multicollinearity, researchers can examine the correlation matrix to identify variables with high correlation coefficients. The Variance Inflation Factor (VIF) measures the inflation of regression coefficients due to multicollinearity. Tolerance, the reciprocal of VIF, indicates the proportion of variance in a predictor variable not shared with others. Eigenvalues help assess multicollinearity, with values greater than 1 suggesting the retention of factors. Principal Component Analysis (PCA) reduces dimensionality and identifies highly correlated variables. Other diagnostic measures include the condition number and Cook’s distance. Researchers can center or standardize data, perform variable filtering, use PCA instead of factor analysis, employ factor scores, merge correlated variables, or apply clustering techniques for the solution of the multicollinearity problem. Further research is needed to explore different types of multicollinearity, assess method effectiveness, and investigate the relationship with other factor analysis issues.

Analysis of inhomogeneity of solidified microstructure of continuous casting copper tubular billet based on factor analysis

The horizontal continuous casting process,the initial step in TP2 copper tubular processing,directly determines the microstructure and properties of copper tubular.However,the process parameters of the continuous casting characterize time variation,multiple disturbances and strong coupling.As a consequence,their influence on a casting billet is difficult to be determined.Due to the above issues,the common factor and special factor analysis of the factor analysis model were used in this study,and the casting experiment and billet metallographic experiment were carried out to diagnose and analyze the reason of the microstructure inhomogeneity.The multiple process parameters were studied and classified using common factor analysis,2 the cast billets with abnormal microstructures were identified by GT^(2) statistics,and the most important factors affecting the microstructural homogeneity were found by special factor analysis.The calculated and experimental results show that the principal parameters influencing the inhomogeneity of solidified microstructure are the primary inlet water pressure and the primary outlet water temperature.According to the consequence of the above investigation,the inhomogeneity of the copper billet microstructure can be effectively improved when the process parameters are controlled and adjusted.

Using Factor Analysis to Determine the Factors Impacting Learning Python for Non-Technical Business Analytics Graduate Students

This pioneering research represents a unique and singular study conducted within the United States, with a specific focus on non-technical graduate students pursuing degrees in business analytics. The primary impetus behind this study stems from the escalating demand for data-driven professionals, the diverse academic backgrounds of students, the imperative for adaptable pedagogical methods, the ever-evolving landscape of curriculum designs, and the overarching commitment to fostering educational equity. To investigate these multifaceted dynamics, we employed a data collection method that included the distribution of an online survey on platforms such as LinkedIn. Our survey reached and engaged 74 graduate students actively pursuing degrees in Business Analytics within the United States. This comprehensive research is the first and only one of its kind conducted in this context, and it serves as a vanguard exploration into the challenges and influences that shape the learning journey of Python among non-technical graduate Business Analytics students. The analytical insights derived from this research underscore the pivotal role of hands-on learning strategies, exemplified by practice exercises and assignments. Moreover, the study highlights the positive and constructive influence of collaboration and peer support in the process of learning Python. These invaluable findings significantly augment the existing body of knowledge in the field of business analytics. Furthermore, they offer an essential resource for educators and institutions seeking to optimize the educational experiences of non-technical students as they acquire essential Python skills.

Statistical Analysis and Countermeasures for Specimen Rejection in the Emergency Department

The rejected specimens from the Emergency Department of the Center of Clinical Laboratory from January 1,2022 to January 1,2023 were analyzed to reduce the specimen rejection rates and to improve the quality of inspection.The results showed that there were 1488 samples of rejected specimens and the non-conforming rate was 0.58%.The departments involved were mainly the Emergency Department,the Hematology Department,the Cardiology Department,the Intensive Care Department,and the Brain Surgery Department.Among the reasons for rejection,blood hemolysis accounted for 43.15%,blood coagulation accounted for 26.61%,and the rate of insufficient specimens was 17.14%.Among them,the sample rejection rate for arterial blood gas analysis was the highest,which accounted for 1.74%;followed by specimens for coagulation test,which was 1.18%.These results indicate the main reason for producing rejected specimens is mainly due to not following the standard operating procedure.Specimen rejection can largely be avoided if the standards for specimen collection are strictly followed.

3D Modeling and Determination of Factors Responsible for Zinc-Lead Mineralization in the Mehdiabad Deposit,Central Iran,based on Statistical Analysis of Geochemical Data

Although the Mehdiabad zinc-lead deposit is one of the most well-known deposits in the central Iran structural zone,the genesis of the deposit remains controversial.The host rock of the ore is a dolomitic limestone of the Lower Cretaceous Taft Formation.In the two main orebodies of the deposit,which includes the Black Hill and East Ridge ore zones,the oxide and sulfide ores are observed at the surface and at depth,respectively.The elements Zn,Fe,Mn and Mg are more abundant in the East Ridge ore zone(in both sulfide and oxide ores),with Ba,Pb,Ag and Cu being more abundant in the Black Hill oxide ore.Based on the distribution of elements and their correlation with each other in these ore zones,the elements are divided into three general groups,that of terrigenous elements,chemically-deposited elements and oreforming(hydrothermally deposited)elements,a division that is supported by the results of factor analyses.The spatial distribution of elements is jointly affected by contact with host rocks,the boundary of oxide-sulfide ores and fault zones.The main factors governing the distribution of elements are the mechanical transfer of detrital sediments,chemical sedimentation,transfer by hydrothermal fluids,oxidation and surface dissolution,all of which affected the spatial distribution of elements.The ore-forming elements are mostly affected by hydrothermal fluids and oxidation.This study not only provides additional information about the genesis of the Mehdiabad deposit,but also could assist in the exploitation of ore and further exploration purposes.The results of this study can aid in the exploration and exploitation of the Mehdiabad deposit and similar deposits in the region.

GREY RELATIONAL ANALYSIS: A NEW STATISTICAL METHOD OF MULTIFACTORIAL ANALYSIS IN MEDICINE

The concept, fundamental theory, analytical steps and formulae of grey relational analysis (GRA)-a new statistical method or multifactorial analysis in the field of medicine were introduced. GRA of grouping sequence that is applied to medical study was built by the authors. An example was given to demonstrate it. The superiority of GRA was recounted briefly.

Influencing factor analysis of interception probability and classification-regression neural network based estimation

The interception probability of a single missile is the basis for combat plan design and weapon performance evaluation,while its influencing factors are complex and mutually coupled.Existing calculation methods have very limited analysis of the influence mechanism of influencing factors,and none of them has analyzed the influence of the guidance law.This paper considers the influencing factors of both the interceptor and the target more comprehensively.Interceptor parameters include speed,guidance law,guidance error,fuze error,and fragment killing ability,while target performance includes speed,maneuverability,and vulnerability.In this paper,an interception model is established,Monte Carlo simulation is carried out,and the influence mechanism of each factor is analyzed based on the model and simulation results.Finally,this paper proposes a classification-regression neural network to quickly estimate the interception probability based on the value of influencing factors.The proposed method reduces the interference of invalid interception data to valid data,so its prediction accuracy is significantly better than that of pure regression neural networks.

Statistical Approach to Basketball Players’Skill Level

In basketball, each player’s skill level is the key to a team’s success or failure, the skill level is affected by many personal and environmental factors. A physics-informed AI statistics has become extremely important. In this article, a complex non-linear process is considered by taking into account the average points per game of each player, playing time, shooting percentage, and others. This physics-informed statistics is to construct a multiple linear regression model with physics-informed neural networks. Based on the official data provided by the American Basketball League, and combined with specific methods of R program analysis, the regression model affecting the player’s average points per game is verified, and the key factors affecting the player’s average points per game are finally elucidated. The paper provides a novel window for coaches to make meaningful in-game adjustments to team members.

The Application of SPSS in Statistical Analysis Project-A Study of the Inheritance of Chinese Traditional Shadow Play in Schools

Chinese traditional shadow play has been selected into the List of Intangible Cultural Heritage in 2011.Yet,reflecting abundant national cultural values,such traditional art form is degenerating and fading out from people’s sight.As the earliest statistical analysis software,Statistical Package for the Social Science(SPSS)is comprehensive in analyzing and managing statistical data.This study explores the application of SPSS in minimizing the workload of researchers while raising the validity of data in supporting the analysis of the survey data which reflected the inheritance and development of Chinese traditional shadow play in schools.

STATISTICAL ANALYSIS AND NUMERICAL SIMULATION OF POYANG LAKE'S INFLUENCE ON TROPICAL CYCLONES

Based on the Tropical Cyclone(TC briefly thereafter)Yearbook 1980-2009,this paper first analyzes the number and intensity change of the TCs which passed directly over or by the side of Poyang Lake(the distance of TC center is less than 1°longitude or 1°latitude from the Lake)among all the landfalling TCs in China during the past 30 years.Two cases are examined in detail in this paper.One is severe typhoon Rananim with a speed of 3.26 m/s and a change of 1 hPa in intensity when it was passing the Lake.The other is super typhoon Saomai with a faster moving speed of 6.50 m/s and a larger change in intensity of 6 hPa.Through numerical simulation experiments,this paper analyzes how the change of underlying surface from water to land contributes to the differences in intensity,speed and mesoscale convection of the two TCs when they passed the Lake.Results show that the moisture and dynamic condition above the Lake were favorable for the maintenance of the intensity when Rananim was passing through Poyang Lake,despite the moisture supply from the ocean was cut off.As a result,there was strong convection around the lake which led to a rainfall spinning counter-clockwise as it was affected by the TC movement.However,little impact was seen in the Saomai case.These results indicate that for the TCs coming ashore on Poyang Lake with a slow speed,the large water body is conducive to the sustaining of the intensity and strengthening of the convection around the TC center and the subsequent heavy rainfall.On the contrary,a fast-moving TC is less likely to be influenced by the underlying surface in terms of intensity and speed.

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.

Potential hydraulic connectivity of coal mine aquifers based on statistical analysis of hydrogeochemistry

Mining activities interfere with the natural groundwater chemical environment,which may lead to hydrogeochemical changes of aquifers and mine water inrush disasters.This study analyzed the hydrochemical compositions of 80 water samples in three aquifers and developed a water source identification model to explore the control factors and potential hydraulic connection of groundwater chemistry in a coal mine.The results showed that the hydrochemical types of the three aquifers were different.The main hydrochemical compositions of the loose-layer,coal-bearing,and limestone aquifers were HCO_(3)·Cl-Na,SO_(4)·HCO_(3)-Na,and SO_(4)-Na·Ca,respectively.The correlation,Unmix,and factor an-alyses showed that the hydrochemical composition of groundwater was controlled by the dissolution of soluble minerals(such as calcite,dolomite,gypsum,and halite)and the weathering of silicate minerals.The factor score plot combined with Q-mode cluster analysis demon-strated no remarkable hydraulic connection among the three aquifers in the study area.The water source identification model effectively identified the source of inrush water.Moreover,the mixing ratio model rationally quantified the contributions of the three aquifers to inrush water.

Corrected Statistical Energy Analysis Model in a Non-Reverberant Acoustic Space

Statistical Energy Analysis(SEA)is a well-known method to analyze the flow of acoustic and vibration energy in a complex structure.This study investigates the application of the corrected SEA model in a non-reverberant acoustic space where the direct field component from the sound source dominates the total sound field rather than a diffuse field in a reverberant space which the classical SEA model assumption is based on.A corrected SEA model is proposed where the direct field component in the energy is removed and the power injected in the subsystem considers only the remaining power after the loss at first reflection.Measurement was conducted in a box divided into two rooms separated by a partition with an opening where the condition of reverberant and non-reverberant can conveniently be controlled.In the case of a non-reverberant space where acoustic material was installed inside the wall of the experimental box,the signals are corrected by eliminating the direct field component in the measured impulse response.Using the corrected SEA model,comparison of the coupling loss factor(CLF)and damping loss factor(DLF)with the theory shows good agreement.

STATISTICAL ANALYSIS ON THE INFLUENCE OF THE LANDFALLING STRONG TROPICAL CYCLONES IN THE CATASTROPHIC MIGRATIONS OF NILAPARVATA LUGENS(STL) IN CHINA

In order to clarify the statistical pattern by which landfalling strong tropical cyclones(LSTCs)influenced the catastrophic migrations of rice brown planthopper(BPH),Nilaparvata lugens(stl)in China,the data of the LSTCs in China and the lighting catches of BPH that covered the main Chinese rice-growing regions from 1979 to 2008 were collected and analyzed in this work with the assistance of ArcGIS9.3,a software of geographic information system.The results were as follows:(1)In China,there were 220 strong tropical cyclones that passed the main rice-growing regions and 466 great events of BPH’s immigration in the 30 years from 1979 to 2008.73 of them resulted in the occurrence of BPH’s catastrphic migration(CM)events directly and 147 of them produced indirect effect on the migrations.(2)The number of the LSTCs was variable in different years during 1979 to 2008 and their influence was not the same in the BPH’s northward and southward migrations in the years.In the 30 years,the LSTCs brought more obvious influence on the migrations in 1980,1981,2005,2006 and 2007.The influence was the most obvious in2007 and all of the 7 LSTCs produced remarkable impact on the CMs of BPH’s populations.The effect of the LSTCs on the northward immigration of BPH’s populations was the most serious in 2006 and the influence on the southward immigration was the most remarkable in 2005.(3)In these years,the most of LSTCs occurred in July,August and September and great events of BPH's immigration occurred most frequently in the same months.The LSTCs played a more important role on the CM of BPH’s populations in the three months than in other months.(4)The analysis on the spatial distribution of the LSTCs and BPH’s immigration events for the different provinces showed that the BPH’s migrations in the main rice-growing regions of the Southeastern China were influenced by the LSTCs and the impact was different with the change of their spatial probability distribution during their passages.The most serious influence of the LSTCs on the BPH’s migrations occurred in Guangdong and Fujian provinces.(5)The statistical results indicated that a suitable insect source is an indispensable condition of the CMs of BPH when a LSTC influenced a rice-growing region.

基于SPSS的城市区域地下水变异Factor Analysis过程

对需要大量运算的统计问题,运用SPSS软件可以快速得到演算结果,从而彻底消除重复而单调的过程,研究人员可更多地专注于统计模型的建立。作者建立了城市建设引发城市区域的地下水缓慢变异的模型,调用SPSS的Factor Analysis过程,对城市区域地下水场变异起重要的组分进行提取,以起重要作用的K、Na、Ca、Mg、Fe、Mn组分最少组合来作为评价地下水变异的指标体系。对南宁市区地下水中特征点进行初步定量分析表明,城市区域地下水年变异水平是城市的建设与发展作用的结果,随时间增长变异水平呈增长之势。从历史背景下研究城市区域地下水缓慢变异程度及趋势,对城市地下水演化规律的认识有重要的指导意义。