Using Excel to Explore the Effects of Assumption Violations on One-Way Analysis of Variance (ANOVA) Statistical Procedures

To understand any statistical tool requires not only an understanding of the relevant computational procedures but also an awareness of the assumptions upon which the procedures are based, and the effects of violations of these assumptions. In our earlier articles (Laverty, Miket, & Kelly [1]) and (Laverty & Kelly, [2] [3]) we used Microsoft Excel to simulate both a Hidden Markov model and heteroskedastic models showing different realizations of these models and the performance of the techniques for identifying the underlying hidden states using simulated data. The advantage of using Excel is that the simulations are regenerated when the spreadsheet is recalculated allowing the user to observe the performance of the statistical technique under different realizations of the data. In this article we will show how to use Excel to generate data from a one-way ANOVA (Analysis of Variance) model and how the statistical methods behave both when the fundamental assumptions of the model hold and when these assumptions are violated. The purpose of this article is to provide tools for individuals to gain an intuitive understanding of these violations using this readily available program.

ONE-WAY MULTIVARIATE REPEATED MEASUREMENTS ANALYSIS OF VARIANCE MODEL

The one-way multivariate repeated measurements analysis of variance (1-way MRM ANOVA) model for complete data and the sphericity test are studied.

Analysis on Chinese Regional Differences in International Tourism Foreign Exchange Earnings with Method of One-way Variance Analysis

Based on data over 31 provinces and cities in China from2006 to 2013,this thesis first divides those 31 provinces and cities into four economic regions including northeastern region,central region,eastern region and western region.Based on data over 31 provinces and cities in China from 2006 to 2013,those 31 provinces and cities were devided into four economic regions in this thesis,including northeastern region,central region,eastern region and western region.Then,it takes international tourism foreign exchange earnings as the dependent variable,the four economic regions as the factor to measure the difference of international tourism foreign exchange earnings in different regions,and finds out the main reasons of it.Through the one-way variance analysis on international tourism foreign exchange earnings,we can know that international tourism foreign exchange earnings have differences in different regions apparently.Besides,significant differences can be found between northeastern and central regions as well as eastern and western regions,while it is not the same case between the central and western regions.

Using Contrasts in One-Way Analysis of Variance with Control Groups and an Application

In this study, it was shown that, same comparisons can be made by using contrast coefficients instead of Dunnett＇s test in the experiments with control groups. It was also shown that, in situations with an ordinal scale and equal spacing quantitative grouping, a trend investigation could be done by contrast coefficients. For this purpose, a small part of the data from a TUBITAK project in the Soil Science Department, Agriculture Faculty, Kahramanmaras Sutcu Imam University, was used with permission. The soils were absorbed to natural zeolite in concentration of 0, 2.5, 5 and 10 mg/kg, and after two years, the available Zinc （Zn） amounts in the soil were analyzed. As a result, in both Dunnett＇s test and contrast methods, the Zn amounts in control and 2.5 mg/kg concentration groups were found similar （P 〉 0.01）; but were different （P 〈 0.01） between control and 5 mg/kg concentration groups, and control and 10 mg/kg concentration groups. Furthermore, when orthogonal polynomial contrast coefficients were investigated, linear effects were found significant （P 〈 0.01） and cubic effects were obtained significant （P 〈 0.05）, but quadratic effect was obtained insignificant （P 〉 0.05）.

An Analysis-of-Variance (ANOVA) Approach for Sib-pair Linkage Analysis of Complex Ordinal Human Diseases

Sib-pair linkage analysis of complex human diseases has become a method of choice in modern human genetic studies, especially for the diseases with a late age at onset. The traditional parametric methods for sib pair data need to take the categorical nature of a disease phenotype into account and to explicitly model the non-linear relationship between the discrete phenotype and genetic determinants, or to force their relationship to be linear. The first approach is desirable theoretically, but explicitly modeling the sophisticated genetic architecture of a complex disease can be prohibitively complex and computational demand is high. The second approach, typically a linear regression, relies on a large sample theory and is not appropriate. In this paper, we propose to apply Analysis of Variance (ANOVA) to sib pair linkage analysis of complex human diseases. This approach has avoided building the complicated relationship between the phenotype (the affection group or status of a sib pair) and the underlying genetic determinant (identical-by-decent (IBD) values etc). We have explored its statistical efficiency and properties in sibpair linkage analysis of ordinal complex human diseases via simulation. The simulation suggests that it is a powerful approach for locating genes that presumably control phenotypic expression of complex human diseases.

Optimizing SUS 304 wire drawing process by grey relational analysis utilizing Taguchi method

In the stainless steel 304 （SUS 304） wire drawing process, optimizing the die life and wire tensile strength, which are the larger-the-better quality characteristics （QCH） types, is of main interest. Three control factors, involving reduction ratio, lubricant temperature, and drawing speed, were investigated utilizing L9（34） orthogonal array （OA）. The grey relational analysis was conducted for the normalized signal-to-noise （S/N） ratios. The ordinal value of the grey grade was then used to decide optimal factor levels. The anticipated improvements in die life and wire tensile strength were estimated 25.31 h and 22.50 kg/mm2, respectively. To decide the significant factor which had effect on each QCH and predict the average value of each QCH, analysis of variance （ANOVA） was performed for S/N ratio and QCH. Confirmation experiments were then conducted, where a good overlap was noticed between the predicted and confirnation intervals for each QCH. The Hotelling T2 and the sample generalized variance control charts were finally utilized in controlling and monitoring future production. In conclusion, the grey relational analysis utilizing Taguchi method is an effective approach for optimizing the die life and wire tensile strength for SUS wire drawing process. 2008 University of Science and Technology Beijing. All rights reserved.

Regression analysis of major parameters affecting the intensity of coal and gas outbursts in laboratory

Estimating the intensity of outbursts of coal and gas is important as the intensity and frequency of outbursts of coal and gas tend to increase in deep mining. Fully understanding the major factors contributing to coal and gas outbursts is significant in the evaluation of the intensity of the outburst. In this paper, we discuss the correlation between these major factors and the intensity of the outburst using Analysis of Variance(ANOVA) and Contingency Table Analysis(CTA). Regression analysis is used to evaluate the impact of these major factors on the intensity of outbursts based on physical experiments. Based on the evaluation, two simple models in terms of multiple linear and nonlinear regression were constructed for the prediction of the intensity of the outburst. The results show that the gas pressure and initial moisture in the coal mass could be the most significant factors compared to the weakest factor-porosity. The P values from Fisher's exact test in CTA are: moisture(0.019), geostress(0.290), porosity(0.650), and gas pressure(0.031). P values from ANOVA are moisture(0.094), geostress(0.077), porosity(0.420), and gas pressure(0.051). Furthermore, the multiple nonlinear regression model(RMSE: 3.870) is more accurate than the linear regression model(RMSE: 4.091).

Optimization of Tribological Performance of Al-6061T6-15% SiCp-15% Al₂O₃Hybrid Metal Matrix Composites Using Taguchi Method &Grey Relational Analysis

In this investigation, optimization of tribological performance parameters of Al-6061T6 alloy reinforced with SiC (15% by weight) and Al2O3 (15% by weight) particulates having particle size of 37 μm each has been presented. The wear and frictional properties of the hybrid metal matrix composites have been studied by performing dry sliding wear test using pin-on-disc wear tester. A L27 orthogonal array is selected for the analysis of the data. From the test results it is observed that sliding distance has the significant contribution in controlling the friction and wear behaviour of hybrid composites. A confirmation test is also carried out to verify the accuracy of the results obtained through the optimization. In addition an optical micrograph test is also performed on the wear tracks to study the wear mechanism.

Major-minor element analysis in some plant seeds consumed as feed in Turkey

In this study, samples (clover, oats, bean, green lentil, spinach, corn, red lentil and rice) taken from some seeds consumed as food by people and from plant seeds used as provender are examined. Element analysis (Al, B, Ba, Bi, Ca, Cd, Co, Cr, Cu, Fe, K, La, Mg, Mn, Na, Ni, Pb, Sn, Sr, Sb, Si, Ti, U, Zn and Zr) in these samples was measured by using ICP-OES. Ca, K and Mg as major elements in all samples are determined. As results of the element analysis, meaningful relations between the elements in seeds have been researched by making statistical comparisons using one way analysis of variance (ANOVA).

An analysis of tourist’s perceptions toward tourism development:Study of cold desert destination,India

Tourism impacts on society are complex and mixed.However,they are vital to diverse societies,clusters,and individuals dependent upon their morals,attitudes,and resources existing for tourism development.Increasing tourism also brings many problems.Hence,tourist experience is fundamental for destination image and devel-opment.This research examines tourist perceptions and attitudes toward tourism impacts in Chitkul,Kalpa,and Nako in Kinnaur.Random sampling has been used to measure tourist responses on a range of indicators related to tourism development.Likert scale responses were analyzed using factor analysis,ANOVA,Mann-Whitney U-test,Kolmogorov test,and descriptive statistics.The results confirmed that tourists do not perceive any type of pollu-tion or societal barriers.They observed that natural magnetism and the socio-cultural milieu of the destination is what attracts tourists.However,tourists are not satisfied with‘networking services’,‘organization efforts’,‘sup-plementary conveniences’,and‘carriage concerns’at selected destinations in Kinnaur.Moreover,Chitkul emerged as the top tourist destination in Kinnaur.Since the destination would emerge as a hub of tourist activities shortly considering the congestion and exploitation of nearby tourist destinations at Kulu-Manali-Rohtang in Beas Valley.Hence,the assessment of tourist perceptions can be used as an indicator of tourism destination competitiveness and can assist in developing appropriate tourism policies and infrastructure upgrades.

Numerical Investigation of Laser Surface Hardening of AISI 4340 Using 3D FEM Model for Thermal Analysis of Different Laser Scanning Patterns

Laser surface hardening is becoming one of the most successful heat treatment processes for improving wear and fatigue properties of steel parts. In this process, the heating system parameters and the material properties have important effects on the achieved hardened surface characteristics. The control of these variables using predictive modeling strategies leads to the desired surface properties without following the fastidious trial and error method. However, when the dimensions of the surface to be treated are larger than the cross section of the laser beam, various laser scanning patterns can be used. Due to their effects on the hardened surface properties, the attributes of the selected scanning patterns become significant variables in the process. This paper presents numerical and experimental investigations of four scanning patterns for laser surface hardening of AISI 4340 steel. The investigations are based on exhaustive modelling and simulation efforts carried out using a 3D finite element thermal analysis and structured experimental study according to Taguchi method. The temperature distribution and the hardness profile attributes are used to evaluate the effects of heating parameters and patterns design parameters on the hardened surface characteristics. This is very useful for integrating the scanning patterns’ features in an efficient predictive modeling approach. A structured experimental design combined to improved statistical analysis tools is used to assess the 3D model performance. The experiments are performed on a 3 kW Nd:Yag laser system. The modeling results exhibit a great agreement between the predicted and measured values for the hardened surface characteristics. The model evaluation reveals also its ability to provide not only accurate and robust predictions of the temperature distribution and the hardness profile as well an in-depth analysis of the effects of the process parameters.

An Efficiency Analysis of MBA Programs in China’s Business Schools

Based on the data of the best MBA ranking in China selected by Manager Magazine,DEA and Malmquist index were used to evaluate the efficiency of MBA programs of top 25 business schools in China.The results show that the overall MBA programs have a high value on technical efficiency due to the high pure technical efficiency and scale efficiency.As the technical regress deepened,the total factor productivity of MBA program presents a dropped tendency.The results of ANOVA show that the location,type and international certification have no significant effect on the efficiency.According to the cross analysis of technical efficiency and total factor productivity,different business schools should adopt different development strategies.

基于K-Means-NCS-ANOVA的八大民窑颜色聚类与应用偏好研究

中华陶瓷文化源远流长,颜色作为陶瓷的一种装饰,可以表达不同的设计理念、情感意识、地域特征和服务对象。为了更好地传承陶瓷艺术文化,本研究提出了一种基于K-means-NCS-ANOVA的颜色分类研究方法。首先,采用K-means颜色聚类、NCS颜色体系提取宋代八大民窑的颜色特征,分析八大瓷窑的区域特征及设计理念;基于上述分析结果制作问卷调查;并利用描述性分析、单因素方差分析(One-Way ANOVA),探究现代设计师对八大民窑颜色的应用偏好。由实验结果可知,设计师性别、专业、工龄也会对八大民窑颜色的应用偏好产生影响;景德镇窑的颜色最受现代设计师欢迎,而耀州窑、磁州窑、定窑的颜色已经不太符合现代审美。本研究采用现代人工智能技术识别八大民窑特征,调研现代设计师对八大民窑颜色的使用偏好,为文物识别、陶瓷文化传承及人才培养提供理论和技术支持。

基于ANOVA模型的延边地区制造业偏离-份额分析

通过建立基于ANOVA的偏离-份额分析对延边地区制造业竞争力进行数据分析,可重新回顾进入新时期之后延边地区制造业相对于全国范围制造业的竞争力强弱,判断制造业各产业部门较国家制造业产业部门的竞争力优势水平,进而完善和改进延边地区经济发展战略。由分析结果可知,延边地区制造业总体竞争力与国内水平相比较弱,27个产业研究对象中有21个产业部门的竞争力较全国制造业对应产业部门处于竞争劣势。虽然医药制造业、纺织业等主要产业的竞争力较为突出,但是这些行业在整个延边制造业中所占的比重极小,不足以改变整个延边制造业的整体竞争力水平,导致了延边地区制造业整体增长缓慢。

基于ANOVA方差的生态旅游者对景区管理模式的态度分析

根据环境认知差异对生态旅游者进行分类,可以探究不同类型的生态旅游者对景区管理模式的态度差异。以我国黄山、张家界、云台山以及庐山风景区为样本,对生态旅游者的态度分四组进行问卷调查,然后使用ANOVA方差分析法对不同类型的生态旅游者对景区管理模式的态度进行计量分析。研究表明,不同类型的生态旅游者对景区生态管理方式的态度确实存在明显差别:1组生态旅游者更注重旅游的生态体验,他们对当前景区管理方式在一定程度上持反对态度;2组和3组对当前景区管理方式的态度并不明显;4组为生态忧患型的生态旅游者,对于当前景区管理方式基本持肯定态度。

Study on the Effect of Variation of Flow in Sequencing Batch Reactor Using PCA and ANOVA

Wastewater treatment using Sequencing Batch Reactor (SBR) technology is one of the state-of-the art wastewater management systems. In this technology equalization, biological treatment and secondary clarification are performed in a single reactor in a time control sequence. SBR system is idler for the areas where the available land is limited, since it operates in less space and very cost effective even on small scales. The control of the operational parameters during the process of biological wastewater treatment is often complicated due to the dynamic change in the composition and characteristics of the raw wastewater, flow rates and other parameters influencing the complex nature of the treatment process and the process in SBR has a unique cyclic batch operation. The performance of the SBR was studied using pilot and real plant at Puducherry. The parameters considered in this study are flow, Mixed Liquor Suspended Solids (MLSS), pH, temperature, influent and effluent of Total Suspended Solids (TSS), Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand (COD). As a part of the study, the effect of constant flow and varying flow on the organic loading of the influent TSS, BOD and COD and their influence on the organic load of the effluent parameters were examined to identify the level of significance of the parameters in relation to the flow. The impact of flow on other parameters was also examined. The experimental data obtained from pilot and real plants were analyzed using multi variate statistical analyses like correlation analysis, Principal Component Analysis (PCA) and Analysis of variance (ANOVA). The statistical analysis revealed that constant flow had no significant role and the influent parameters alone had the critical role, whereas varying flow as well as the influent parameters had the significant role on the performance of SBR.

An innovative classification system for ranking the biological effects of marine aromatic hydrocarbons based on fish embryotoxicity

Petroleum hydrocarbon pollution is a global concern,particularly in coastal environments.Polycyclic aromatic hydrocarbons(PAHs) are regarded as the most toxic components of petroleum hydrocarbons.In this study,the biomonitoring and ranking effects of petroleum hydrocarbons and PAHs on the marine fish model Oryzias melastigma embryos were determined in the Jiulong River Estuary(JRE) and its adjacent waters in China.The results showed that the levels of petroleum hydrocarbons from almost all sites met the primary standard for marine seawater quality,and the concentrations of the 16 priority PAHs in the surface seawater were lower compared with those in other coastal areas worldwide.A new fish expert system based on the embryotoxicity of O.melastigma(OME-FES) was developed and applied in the field to evaluate the biological effects of petroleum hydrocarbons and PAHs.The selected physiological index and molecular indicators in OME-FES were appropriate biomarkers for indicating the harmful effects of petroleum hydrocarbons and PAHs.The outcome of OME-FES revealed that the biological effect levels of the sampling sites ranged from level Ⅰ(no stress) to level Ⅲ(medium stress),which is further corroborated by the findings of nested analysis of variance(ANOVA) models.Our results suggest that the OME-FES is an effective tool for evaluating and ranking the biological effects of marine petroleum hydrocarbons and PAHs.This method may also be applied to evaluate other marine pollutants based on its framework.

Spatio-temporal variation and relationship between agricultural efficiency and irrigation intensity in a semi-arid region of India

A surging population in Karnataka State,a semi-arid region in India,poses a threat to both food security and livelihood sustainability,necessitating a concentrated effort to bolster agricultural efficiency and achieve United Naton’s Sustainable Development Goal 2(zero hunger).Therefore,in order to address the pressing issue of food scarcity in Karnataka,this study meticulously examined the spatio-temporal variation of agricultural efficiency and irrigation intensity in Karnataka,uncovering its significant dependence of agricultural efficiency on irrigation intensity.Specifically,this study used a one-way analysis of variance(ANOVA)to ascertain significant differences in the means of agricultural efficiency and irrigation intensity during 2004-2005 and 2018-2019.This study showed that the maximum improvement in agricultural efficiency index was recorded in Belgaum(40.24),Gulbarga(24.77),and Yadgir districts(22.92)between 2004-2005 and 2018-2019,which indicated the progressing trend and better scope for agriculture extension.On the contrary,some districts expressed threat(a decline of above 20.00 of agricultural efficiency index)and needed special care for the improvement of agricultural efficiency in four northern districts(Bagalkot,Bidar,Raichur,and Bijapur),three southern districts(Chitradurga,Chikballapur and Hassan),and two southern districts(Koppal and Gadag)in Karnataka.During 2004-2005,irrigation intensity varied from 3.19%to 56.39%,with the lowest irrigation intensity in Kodagu District and the highest irrigation intensity in Shimoga District.During 2018-2019,irrigation intensity changed from 0.77%to 72.77%,with the lowest irrigation intensity in Kodagu District and the highest in Dakshin Kannad District.Moreover,the research scrutinized the complex relationship between agricultural efficiency and irrigation intensity,with the correlation coefficient increased from 0.162 during 2004-2005 to 0.255 during 2018-2019.It implies that in both periods,a low positive correlation existed between these two variables.Over time,several factors(high-yield seeds and chemical fertilizers)other than irrigation intensity gradually became essential for agricultural efficiency.This research offers a wealth of valuable insights for regional planners and policy-makers contending with comparable challenges in various regions of India and other developing countries.

玻璃文物成分分析与鉴别的数学模型

针对2022年全国大学生数学建模竞赛C题“玻璃文物的成分分析与鉴别问题”中的4个问题分别进行建模分析,根据玻璃文物的化学成分含量、纹饰及颜色等数据,基于单因素方差分析,探究玻璃文物的表面风化与玻璃类型、纹饰及颜色的关系,建立ARIMA模型,预测风化前玻璃文物的化学成分含量;通过主成分分析提取玻璃文物的分类特征,结合聚类算法进行亚类划分;通过基于欧氏距离的聚类算法鉴别未知玻璃文物的类别,分析玻璃文物分类结果的敏感性;通过K-Means++聚类算法分析不同类别玻璃文物的关联关系,对不同类别玻璃文物关联关系的差异性进行判断,给出结论。

Strain rate analyses during elliptical vibration cutting of Inconel 718 using finite element analysis,Taguchi method,and ANOVA

The high strain rate in metal cutting significantly affects the mechanical properties of the work piece by altering its properties.This study outlines the material strain rates during elliptical vibration cutting.The finite element analysis,Taguchi method,and analysis of variance(ANOVA)were employed to analyze the effects and contributions of cutting and vibration process parameters(feed rate,rake angle,tangential amplitude,and frequency of vibration)on the variation of strain rates during machining of Inconel 718.Taguchi signal-to-noise analysis on an L18(2^1×3^3)orthogonal array was used to determine the optimum parametric combination for the maximum strain rate,and ANOVA was applied to evaluate the significance of control parameter factors on the strain rate.The results of the finite element analysis under different conditions illustrated that the feed rate and rake angle were negatively related to the strain rate,whereas the tangential amplitude and frequency had a positive response.Furthermore,ANOVA results indicated that the effect of the feed rate,tool rake angle,vibration frequency,and tangential amplitude on the strain rate were all statistically significant,with a reliability level of 95%.Of these,the dominant parameter affecting the strain rate was the feed rate,with a percentage contribution of 40.36%.The estimation of the optimum strain rate and confirmation tests proved that the Taguchi method could successfully optimize the working conditions to obtain the desired maximum strain rate.