A new method for non-parametric multivariate analysis of variance

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The nonparametric multivariate analysis of variance (NPMANOVA) testing procedure has been proven to be a valuable tool for comparing groups. In the present paper, we propose a kernel extension of this technique in order to effectively confront high-dimensionality, a recurrent problem in many fields of science. The new method is called kernel multivariate analysis of variance (KMANOVA). The basic idea is to take advantage of the kernel framework: we propose to project the data from the original data space to a Hilbert space generated by a given kernel function and then perform the NPMANOVA method in the reproducing kernel Hilbert space (RKHS). Dispersion of the embedded points can be measured by the distance induced by the inner product in the RKHS but also by many other distances best suited in high-dimensional settings. For this purpose, we study two promising distances: a Manhattan-type distance and a distance based on an orthogonal projection of the embedded points in the direction of the group centroids. We show that the NPMANOVA method and the KMANOVA method with the induced distance are essentially equivalent. We also show that the KMANOVA method with the other two distances performs considerably better than the NPMANOVA method. We illustrate the advantages of our approach in the context of genetic association studies and demonstrate its usefulness on Alzheimer’s disease data. We also provide a software implementation of the method that is available on GitHub https://github.com/8699vicente/Kmanova.

ObjectivesJob exposure matrices (JEMs) can be constructed from expert-rated assessments, direct measurement and self-reports. This paper describes the construction of a general population JEM based on self-reported physical exposures, its...

The paper discusses the symmetric balanced incomplete block designs (SBIBD’s) and further verifies whether treatment adjustment in SBIBD is necessary using analysis of variance (ANOVA) method. Fortunately, the data collected for the analysis were in the same group of the balanced incomplete-block designs (BIBD’s), that is, symmetric balance incomplete block design (SBIBD).The ANOVA method is applied differently on the two sets of data arising from the symmetric balanced incomplete block designs (SBIBDs). In this work, the basic interest is to verify empirically whether treatment adjustment is necessary in SBIBDs with data from National Root Crop Research Institute (N.R.C.R.I), Umudike, AbiaState. To achieve this, we considered treatment (not adjusted), treatment (adjusted), and block (adjusted) in the ANOVA method. The study discovered that if ANOVA method is applied on the symmetric balanced incomplete block design (SBIBD) when a treatment is not significant, it turns out to be significant when the same treatment is adjusted. It obvious from the experiments that were carried out that the adjustment of the treatment in SBIBD’s is very necessary when the ANOVA method is applied. Apart from the improvement in the level of significance of the result, the error is also greatly reduced when treatment is adjusted.

Relationship of medical status, medications, and salivary flow rates in adults of different ages

Forest fires are influenced by several factors, including forest location, species type, age and density, date of fire occurrence, temperatures, and wind speeds, among others. This study investigates the quantitative effects of these factors on the degree of forest fire disaster using nonparametric statistical methods to provide a theoretical basis and data support for forest fire management. Data on forest fire damage from 1969 to 2013 was analyzed. The results indicate that different forest locations and types, fire occurrence dates, temperatures, and wind speeds were statistically significant. The eastern regions of the study area experienced the highest fire occurrence, accounting for 85.0% of the total number of fires as well as the largest average forested area burned. April, May, and October had more frequent fires than other months, accounting for 78.9%, while September had the most extensive forested area burned (63.08 ha) and burnt area (106.34 ha). Hardwood mixed forest and oak forest had more frequent fires, accounting for 31.9% and 26.0%, respectively. Hardwood-conifer mixed forest had the most forested area burned (50.18 ha) and burnt area (65.09 ha). Temperatures, wind speeds, and their interaction had significant impacts on forested area burned and area burnt.

A microcosm experiment was carried out in order to test the effect of the herbicide metolachlor on river periphytic diatoms and to find potential diatom bioindicators of contamination. Effects were investigated at different biological organization levels (biofilm, diatom community, population and individual levels). The colonization of glass substrates by natural biofilm in artificial streams did not vary quantitatively between control and contaminated conditions (5 and 30 μg.L− 1 ). However, non-parametric multivariate analysis of variance revealed a significant difference between contaminated and control diatom communities with regard to species composition. The difference was due to the greater development of probably tolerant species in the presence of the herbicide (e.g. , Planothidium frequentissimum, Planothidium lanceolatum, Amphora montana, Surirella brebissonii and Nitzschia gracilis ). An increase in the occurrence of abnormal forms was observed in relation to metolachlor concentration. In particular, up to 8% of the frustules of the species Surirella angusta exhibited prominent deformities. Monospecific acute toxicity tests were then performed on two species to estimate toxicity parameters based on growth inhibition. These tests also confirmed the teratogenic effect of the herbicide on S. angusta . This study shows that low concentrations of metolachlor in natural streams may significantly alter diatom community structure and that abnormal diatom forms should be taken into account in water contamination assessment.

In spite of their ecological and economic importance, reef fishes from the coast of Oaxaca, Mexico are rarely studied, therefore precluding their management and conservation. In order to identify the set of habitat characteristics/environmental conditions that predict major shifts in fish assemblages in space and time, a stationary census (5′, φ = 5 m) was conducted on a semi-monthly basis from 2006 to 2009 at patch reefs along the coast. Habitat configuration was gathered using 25 m long point-intersect transects (data every 25 cm), recording all underlying coral species and substrate characteristics (rocks, sand, algal mats, rubble or dead corals). Recorded were 65 452 fishes grouped in 11 orders, 36 families, 65 genera and 89 species. Labridae (nine species), Pomacentridae (eight species) and Serranidae (seven species) were the most frequent families. Abundance is severely skewed among species; four species Thalassoma lucasanum, Chromis atrilobata, Apogon pacificus and Stegastes acapulcoensis comprise nearly 59% of the fish abundance, 11 species contribute 30%, whereas most of the species (75) can be considered as rare since they contribute <1% each to the total. Species richness and family-level assemblage composition are similar to those recorded elsewhere in the eastern Pacific. Non-parametric multivariate analysis of variance demonstrated that changes of diversity metrics might be associated with environmental differences on the scale of hundreds of meters to kilometers, as well as coupled with major changes on oceanographic variables throughout time, exerting meaningful changes on reef-related fish assemblages.

The Taguchi and analysis of variance (ANOVA) methods were applied to investigate the effects of the structural and operational parameters on the heat transfer performance of a vertical sinter cooling packed bed. The analysed parameters were the gas flow rate, the air inlet temperature, the sinter inlet temperature, the cooling bed diameter and the cooling bed height, all of which contain three levels. The purpose was to improve the heat transfer performance of a vertical sinter cooling bed. A numerical analysis model was established to assess the heat transfer performance with respect to the varying parameters and their different levels. This mathematical model was validated by using data from practical industrial processes. The Taguchi method for the L27 (35) orthogonal design experiment was selected to evaluate the impacts of the design parameters on the heat transfer performance and to acquire the optimum combination of parameters. The analysis of variance was applied to assess the impact weights and the order of significance of the design parameters. The results show that the sinter inlet temperature and cooling bed diameter have great influences and impact the exergy of the wasted heat recovery by 61.65% and 23.31%, respectively. However, the gas flow rate and the air inlet temperature have small effects on the response. Furthermore, the air and sinter inlet temperatures have the most significant impacts on the efficiency of heat transfer by 68.83% and 23.31%, respectively. The optimal parameter combination (A1B1C3D3E3) was obtained, and the optimal results were validated by confirmation tests.

This research is about the roundness characteristics of the turning process parameters on St 42 material using the Taguchi and ANOVA (Analysis of Variance) methods. A cylindrical product requires a good roundness value to ensure its quality. One of the factors that determine the quality of these products is the machining process parameters. In this study, optimization of the turning process parameters using the Taguchi and ANOVA methods was carried out on the roundness characteristics of the workpiece. The workpiece used is Steel St 42. The lathe used is the Krisbow Precision Gear Head Machine 410X1000MM. After data analysis using the Taguchi method, the parameters with the optimum roundness value of 7.385 µm were 510 rpm spindle rotation, 1mm depth of cut, and coolant opening valve. The results of the ANOVA analysis show the percent contribution of each parameter, respectively, as follows: spindle rotation 26.97%, depth of cut 24.82%, and coolant 38.63%.

This paper aims to present the analysis of a part manufactured in three shifts, which has a specific characteristic dimension, using DFSS (Design for Six Sigma) ANOVA (Analysis of Variance) method. In every shift, the significant characteristic, “SC”, dimension should be produced within the given tolerance. The question that arises is: “Does the shift have any influence on the “SC” dimension realization?” By using the one way ANOVA method, one can observe the variation between the means of each of the three shifts. Afterwards, specific action can be undertaken to adjust, if necessary, the differences between the shifts.

In this study, the effect of various parameters on the power coefficient (CP) performance of a vertical axis wind turbine (VAWT) was optimized using the Taguchi method. The optimization was conducted with the Taguchi method, employing three control factors: blade-spoke connection (BSC), turbine blade pitch angle (β), and turbine blade pitch direction (φ). Subsequently, the analysis of variance (ANOVA) method as employed to determine the contribution ratio of each control factor. Regression analysis (RA) was applied to develop an empirical equation predicting the CP of the VAWT, incorporating the control factors. The results indicated an optimal parameter configuration of BSC = 0.5c, β = 2°, and φ = (-), which maximizes the system performance. The performance of the optimal model was observed to exceed that of the conventional VAWT (B1) by 5.82%. Using the ANOVA method, the contribution of parameters on the CP performance of the VAWT was ranked as follows: φ &amp;gt; BSC &amp;gt; β. The φ parameter has the most significant effect at 82.07%, whereas the β parameter exhibits the least effect of 1.17%. Moreover, the predictive accuracy of the developed regression model was validated, yielding R2 values of 0.9221 for the training data and 0.9908 for the test data.

Assessment of six soil ecosystem services by coupling simulation modelling and field measurement of soil properties

Flood events consist of flood peaks and flood volumes that are mutually correlated and need to be described by multivariate analysis methods, of which the copula functions are most desirable. Until now, the multivariate flood frequency analysis methods based on copulas does not consider the historical floods or paleological information. This may underestimate or overestimate the flood quantiles or conditional probabilities corresponding to high return periods, especially when the length of gauged record data series is relatively short. In this paper, a modified inference functions for margins (MIFM) method is proposed and used to estimate the parameters of both marginal distribution and joint distribution with incorporation of historical information. The conditional probabilities of flood volumes given that the peak discharge exceeding various values were derived. The Three Gorges reservoir (TGR) in China was selected as a case study. The bivariate flood quantiles were obtained based on bivariate return period and compared with current univariate design values. It is shown that the proposed method provides an alternative way for multivariate frequency analysis with historical information.

The multivariate statistical analysis methods, using both multiple linear regression(MLR) and partial least square(PLS), have been applied to predict the reactor properties and the product quality of a direct esterification reactor for polyethylene terephthalate(PET) synthesis. On the basis of the set of data including the flow rate of water vapor, the flow rate of EG vapor, the concentration of acid end groups of a product and other operating conditions such as temperature, pressure, reaction times and feed monomer mole ratio, two multi-variable analysis methods have been applied. Their regression and prediction abilities also have been compared. The prediction results are critically compared with the actual plant data and the other mathematical model based results in reliability. This paper shows that PLS method approach can be used for the reasonably accurate prediction of a product quality of a direct esterification reactor in PET synthesis process.