Multivariate statistical analysis of highway accident and highway conditions. Final report.

Transportation Department, Office of University Research, Washington, D.C.

Toward prediction of class II mouse major histocompatibility complex peptide binding affinity:in silico bioinformatic evaluation using partial least squares, a robust multivariate statistical technique

The accurate identification of T-cell epitopes remains a principal goal of bioinformatics within immunology. As the immunogenicity of peptide epitopes is dependent on their binding to major histocompatibility complex (MHC) molecules, the prediction of binding affinity is a prerequisite to the reliable prediction of epitopes. The iterative self-consistent (ISC) partial-least-squares (PLS)-based additive method is a recently developed bioinformatic approach for predicting class II peptide−MHC binding affinity. The ISC−PLS method overcomes many of the conceptual difficulties inherent in the prediction of class II peptide−MHC affinity, such as the binding of a mixed population of peptide lengths due to the open-ended class II binding site. The method has applications in both the accurate prediction of class II epitopes and the manipulation of affinity for heteroclitic and competitor peptides. The method is applied here to six class II mouse alleles (I-Ab, I-Ad, I-Ak, I-As, I-Ed, and I-Ek) and included peptides up to 25 amino acids in length. A series of regression equations highlighting the quantitative contributions of individual amino acids at each peptide position was established. The initial model for each allele exhibited only moderate predictivity. Once the set of selected peptide subsequences had converged, the final models exhibited a satisfactory predictive power. Convergence was reached between the 4th and 17th iterations, and the leave-one-out cross-validation statistical terms - q2, SEP, and NC - ranged between 0.732 and 0.925, 0.418 and 0.816, and 1 and 6, respectively. The non-cross-validated statistical terms r2 and SEE ranged between 0.98 and 0.995 and 0.089 and 0.180, respectively. The peptides used in this study are available from the AntiJen database (http://www.jenner.ac.uk/AntiJen). The PLS method is available commercially in the SYBYL molecular modeling software package. The resulting models, which can be used for accurate T-cell epitope prediction, will be made freely available online (http://www.jenner.ac.uk/MHCPred).

Multivariate statistical analysis on the kaolinite/chlorite ratios from 20 South Atlantic sediment cores

Multivariate statistical analysis on the kaolinite/chlorite ratios from 20 South Atlantic sediment cores allowed for the extraction of two processes controlling the fluctuations of the kaolinite/chlorite ratio during the last 130,000 yrs, (1) the relative strength of North Atlantic Deep Water (NADW) inflow into the South Atlantic Ocean and (2) the influx of aeolian sediments from the south African continent. The NADW fluctuation can be traced in the entire deep South Atlantic while the dust signal is restricted to the vicinity of South Africa. Our data indicate that NADW formation underwent significant changes in response to glacial/interglacial climate changes with enhanced export to the Southern Hemisphere during interglacials. The most pronounced phases with Enhanced South African Dust Export (ESADE) occurred during cold Marine Isotope Stage (MIS) 5d and across the Late Glacial/Holocene transition from 16 ka to 4 ka (MIS 2 to 1). This particular pattern is attributed to the interaction of Antarctic Sea Ice extent, the position of the westerlies and the South African monsoon system.

Multivariate statistical modeling of an anode backing furnace - Modélisation statistique multivariée du four à cuisson des anodes utilisées dans la fabrication d'aluminium primaire

La stratégie actuelle de contrôle de la qualité de l’anode est inadéquate pour détecter les anodes défectueuses avant qu’elles ne soient installées dans les cuves d’électrolyse. Des travaux antérieurs ont porté sur la modélisation du procédé de fabrication des anodes afin de prédire leurs propriétés directement après la cuisson en utilisant des méthodes statistiques multivariées. La stratégie de carottage des anodes utilisée à l’usine partenaire fait en sorte que ce modèle ne peut être utilisé que pour prédire les propriétés des anodes cuites aux positions les plus chaudes et les plus froides du four à cuire. Le travail actuel propose une stratégie pour considérer l’histoire thermique des anodes cuites à n’importe quelle position et permettre de prédire leurs propriétés. Il est montré qu’en combinant des variables binaires pour définir l’alvéole et la position de cuisson avec les données routinières mesurées sur le four à cuire, les profils de température des anodes cuites à différentes positions peuvent être prédits. Également, ces données ont été incluses dans le modèle pour la prédiction des propriétés des anodes. Les résultats de prédiction ont été validés en effectuant du carottage supplémentaire et les performances du modèle sont concluantes pour la densité apparente et réelle, la force de compression, la réactivité à l’air et le Lc et ce peu importe la position de cuisson.

Characterization of aromatic profiles in brazilian tropical wines determined by gas chromatography and multivariate statistical analysis.

2011

Preharvest factors affecting quality and antioxidant levels on Abate Fétel pears: study of superficial scald with a multivariate statistical approach and neural networks

There are only a few insights concerning the influence that agronomic and management variability may have on superficial scald (SS) in pears. Abate Fétel pears were picked during three seasons (2018, 2019 and 2020) from thirty commercial orchards in the Emilia Romagna region, Italy. Using a multivariate statistical approach, high heterogeneity between farms for SS development after cold storage with regular atmosphere was demonstrated. Indeed, some factors seem to affect SS in all growing seasons: high yields, soil texture, improper irrigation and Nitrogen management, use of plant growth regulators, late harvest, precipitations, Calcium and cow manure, presence of nets, orchard age, training system and rootstock. Afterwards, we explored the spatio/temporal variability of fruit attributes in two pear orchards. Environmental and physiological spatial variables were recorded by a portable RTK GPS. High spatial variability of the SS index was observed. Through a geostatistical approach, some characteristics, including soil electrical conductivity and fruit size, have been shown to be negatively correlated with SS. Moreover, regression tree analyses were applied suggesting the presence of threshold values of antioxidant capacity, total phenolic content, and acidity against SS. High pulp firmness and IAD values before storage, denoting a more immature fruit, appeared to be correlated with low SS. Finally, a convolution neural networks (CNN) was tested to detect SS and the starch pattern index (SPI) in pears for portable device applications. Preliminary statistics showed that the model for SS had low accuracy but good precision, and the CNN for SPI denoted good performances compared to the Ctifl and Laimburg scales. The major conclusion is that Abate Fétel pears can potentially be stored in different cold rooms, according to their origin and quality features, ensuring the best fruit quality for the final consumers. These results might lead to a substantial improvement in the Italian pear industry.

Evaluation of natural and synthetic compounds according to their antioxidant activity using a multivariate approach

The antioxidant activity of natural and synthetic compounds was evaluated using five in vitro methods: ferric reducing/antioxidant power (FRAP), 2,2-diphenyl-1-picrylhydradzyl (DPPH), oxygen radical absorption capacity (ORAL), oxidation of an aqueous dispersion of linoleic acid accelerated by azo-initiators (LAOX), and oxidation of a meat homogenate submitted to a thermal treatment (TBARS). All results were expressed as Trolox equivalents. The application of multivariate statistical techniques suggested that the phenolic compounds (caffeic acid, carnosic acid, genistein and resveratrol), beyond their high antioxidant activity measured by the DPPH, FRAP and TBARS methods, showed the highest ability to react with the radicals in the ORAC methodology, compared to the other compounds evaluated in this study (ascorbic acid, erythorbate, tocopherol, BHT, Trolox, tryptophan, citric acid, EDTA, glutathione, lecithin, methionine and tyrosine). This property was significantly correlated with the number of phenolic rings and catecholic structure present in the molecule. Based on a multivariate analysis, it is possible to select compounds from different clusters and explore their antioxidant activity interactions in food products.

Exploring the knowledge contained in neuroimages: Statistical discriminant analysis and automatic segmentation of the most significant changes

Objective: The aim of this article is to propose an integrated framework for extracting and describing patterns of disorders from medical images using a combination of linear discriminant analysis and active contour models. Methods: A multivariate statistical methodology was first used to identify the most discriminating hyperplane separating two groups of images (from healthy controls and patients with schizophrenia) contained in the input data. After this, the present work makes explicit the differences found by the multivariate statistical method by subtracting the discriminant models of controls and patients, weighted by the pooled variance between the two groups. A variational level-set technique was used to segment clusters of these differences. We obtain a label of each anatomical change using the Talairach atlas. Results: In this work all the data was analysed simultaneously rather than assuming a priori regions of interest. As a consequence of this, by using active contour models, we were able to obtain regions of interest that were emergent from the data. The results were evaluated using, as gold standard, well-known facts about the neuroanatomical changes related to schizophrenia. Most of the items in the gold standard was covered in our result set. Conclusions: We argue that such investigation provides a suitable framework for characterising the high complexity of magnetic resonance images in schizophrenia as the results obtained indicate a high sensitivity rate with respect to the gold standard. (C) 2010 Elsevier B.V. All rights reserved.

DESARROLLO DE APLICACIONES ESTADÍSTICAS PARA LA AGRICULTURA DE PRECISIÓN. STATISTICAL APPLICATIONS FOR PRECISION AGRICULTURE

A partir de las últimas décadas se ha impulsado el desarrollo y la utilización de los Sistemas de Información Geográficos (SIG) y los Sistemas de Posicionamiento Satelital (GPS) orientados a mejorar la eficiencia productiva de distintos sistemas de cultivos extensivos en términos agronómicos, económicos y ambientales. Estas nuevas tecnologías permiten medir variabilidad espacial de propiedades del sitio como conductividad eléctrica aparente y otros atributos del terreno así como el efecto de las mismas sobre la distribución espacial de los rendimientos. Luego, es posible aplicar el manejo sitio-específico en los lotes para mejorar la eficiencia en el uso de los insumos agroquímicos, la protección del medio ambiente y la sustentabilidad de la vida rural. En la actualidad, existe una oferta amplia de recursos tecnológicos propios de la agricultura de precisión para capturar variación espacial a través de los sitios dentro del terreno. El óptimo uso del gran volumen de datos derivado de maquinarias de agricultura de precisión depende fuertemente de las capacidades para explorar la información relativa a las complejas interacciones que subyacen los resultados productivos. La covariación espacial de las propiedades del sitio y el rendimiento de los cultivos ha sido estudiada a través de modelos geoestadísticos clásicos que se basan en la teoría de variables regionalizadas. Nuevos desarrollos de modelos estadísticos contemporáneos, entre los que se destacan los modelos lineales mixtos, constituyen herramientas prometedoras para el tratamiento de datos correlacionados espacialmente. Más aún, debido a la naturaleza multivariada de las múltiples variables registradas en cada sitio, las técnicas de análisis multivariado podrían aportar valiosa información para la visualización y explotación de datos georreferenciados. La comprensión de las bases agronómicas de las complejas interacciones que se producen a la escala de lotes en producción, es hoy posible con el uso de éstas nuevas tecnologías. Los objetivos del presente proyecto son: (l) desarrollar estrategias metodológicas basadas en la complementación de técnicas de análisis multivariados y geoestadísticas, para la clasificación de sitios intralotes y el estudio de interdependencias entre variables de sitio y rendimiento; (ll) proponer modelos mixtos alternativos, basados en funciones de correlación espacial de los términos de error que permitan explorar patrones de correlación espacial de los rendimientos intralotes y las propiedades del suelo en los sitios delimitados. From the last decades the use and development of Geographical Information Systems (GIS) and Satellite Positioning Systems (GPS) is highly promoted in cropping systems. Such technologies allow measuring spatial variability of site properties including electrical conductivity and others soil features as well as their impact on the spatial variability of yields. Therefore, site-specific management could be applied to improve the efficiency in the use of agrochemicals, the environmental protection, and the sustainability of the rural life. Currently, there is a wide offer of technological resources to capture spatial variation across sites within field. However, the optimum use of data coming from the precision agriculture machineries strongly depends on the capabilities to explore the information about the complex interactions underlying the productive outputs. The covariation between spatial soil properties and yields from georeferenced data has been treated in a graphical manner or with standard geostatistical approaches. New statistical modeling capabilities from the Mixed Linear Model framework are promising to deal with correlated data such those produced by the precision agriculture. Moreover, rescuing the multivariate nature of the multiple data collected at each site, several multivariate statistical approaches could be crucial tools for data analysis with georeferenced data. Understanding the basis of complex interactions at the scale of production field is now within reach the use of these new techniques. Our main objectives are: (1) to develop new statistical strategies, based on the complementarities of geostatistics and multivariate methods, useful to classify sites within field grown with grain crops and analyze the interrelationships of several soil and yield variables, (2) to propose mixed linear models to predict yield according spatial soil variability and to build contour maps to promote a more sustainable agriculture.

Multivariate Analysis for Animal Selection in Experimental Research

Background: Several researchers seek methods for the selection of homogeneous groups of animals in experimental studies, a fact justified because homogeneity is an indispensable prerequisite for casualization of treatments. The lack of robust methods that comply with statistical and biological principles is the reason why researchers use empirical or subjective methods, influencing their results. Objective: To develop a multivariate statistical model for the selection of a homogeneous group of animals for experimental research and to elaborate a computational package to use it. Methods: The set of echocardiographic data of 115 male Wistar rats with supravalvular aortic stenosis (AoS) was used as an example of model development. Initially, the data were standardized, and became dimensionless. Then, the variance matrix of the set was submitted to principal components analysis (PCA), aiming at reducing the parametric space and at retaining the relevant variability. That technique established a new Cartesian system into which the animals were allocated, and finally the confidence region (ellipsoid) was built for the profile of the animals’ homogeneous responses. The animals located inside the ellipsoid were considered as belonging to the homogeneous batch; those outside the ellipsoid were considered spurious. Results: The PCA established eight descriptive axes that represented the accumulated variance of the data set in 88.71%. The allocation of the animals in the new system and the construction of the confidence region revealed six spurious animals as compared to the homogeneous batch of 109 animals. Conclusion: The biometric criterion presented proved to be effective, because it considers the animal as a whole, analyzing jointly all parameters measured, in addition to having a small discard rate.

Monitoring of crystallization processes by using infrared spectroscopy and multivariate methods

Väitöstutkimuksessa on tarkasteltuinfrapunaspektroskopian ja monimuuttujaisten aineistonkäsittelymenetelmien soveltamista kiteytysprosessin monitoroinnissa ja kidemäisen tuotteen analysoinnissa. Parhaillaan kiteytysprosessitutkimuksessa maailmanlaajuisesti tutkitaan intensiivisesti erilaisten mittausmenetelmien soveltamista kiteytysprosessin ilmiöidenjatkuvaan mittaamiseen niin nestefaasista kuin syntyvistä kiteistäkin. Lisäksi tuotteen karakterisointi on välttämätöntä tuotteen laadun varmistamiseksi. Erityisesti lääkeaineiden valmistuksessa kiinnostusta tämäntyyppiseen tutkimukseen edistää Yhdysvaltain elintarvike- ja lääkeaineviraston (FDA) prosessianalyyttisiintekniikoihin (PAT) liittyvä ohjeistus, jossa määritellään laajasti vaatimukset lääkeaineiden valmistuksessa ja tuotteen karakterisoinnissa tarvittaville mittauksille turvallisten valmistusprosessien takaamiseksi. Jäähdytyskiteytyson erityisesti lääketeollisuudessa paljon käytetty erotusmenetelmä kiinteän raakatuotteen puhdistuksessa. Menetelmässä puhdistettava kiinteä raaka-aine liuotetaan sopivaan liuottimeen suhteellisen korkeassa lämpötilassa. Puhdistettavan aineen liukoisuus käytettävään liuottimeen laskee lämpötilan laskiessa, joten systeemiä jäähdytettäessä liuenneen aineen konsentraatio prosessissa ylittää liukoisuuskonsentraation. Tällaiseen ylikylläiseen systeemiin pyrkii muodostumaan uusia kiteitä tai olemassa olevat kiteet kasvavat. Ylikylläisyys on yksi tärkeimmistä kidetuotteen laatuun vaikuttavista tekijöistä. Jäähdytyskiteytyksessä syntyvän tuotteen ominaisuuksiin voidaan vaikuttaa mm. liuottimen valinnalla, jäähdytyprofiililla ja sekoituksella. Lisäksi kiteytysprosessin käynnistymisvaihe eli ensimmäisten kiteiden muodostumishetki vaikuttaa tuotteen ominaisuuksiin. Kidemäisen tuotteen laatu määritellään kiteiden keskimääräisen koon, koko- ja muotojakaumansekä puhtauden perusteella. Lääketeollisuudessa on usein vaatimuksena, että tuote edustaa tiettyä polymorfimuotoa, mikä tarkoittaa molekyylien kykyä järjestäytyä kidehilassa usealla eri tavalla. Edellä mainitut ominaisuudet vaikuttavat tuotteen jatkokäsiteltävyyteen, kuten mm. suodattuvuuteen, jauhautuvuuteen ja tabletoitavuuteen. Lisäksi polymorfiamuodolla on vaikutusta moniin tuotteen käytettävyysominaisuuksiin, kuten esim. lääkeaineen liukenemisnopeuteen elimistössä. Väitöstyössä on tutkittu sulfatiatsolin jäähdytyskiteytystä käyttäen useita eri liuotinseoksia ja jäähdytysprofiileja sekä tarkasteltu näiden tekijöiden vaikutustatuotteen laatuominaisuuksiin. Infrapunaspektroskopia on laajalti kemian alan tutkimuksissa sovellettava menetelmä. Siinä mitataan tutkittavan näytteenmolekyylien värähtelyjen aiheuttamia spektrimuutoksia IR alueella. Tutkimuksessa prosessinaikaiset mittaukset toteutettiin in-situ reaktoriin sijoitettavalla uppoanturilla käyttäen vaimennettuun kokonaisheijastukseen (ATR) perustuvaa Fourier muunnettua infrapuna (FTIR) spektroskopiaa. Jauhemaiset näytteet mitattiin off-line diffuusioheijastukseen (DRIFT) perustuvalla FTIR spektroskopialla. Monimuuttujamenetelmillä (kemometria) voidaan useita satoja, jopa tuhansia muuttujia käsittävä spektridata jalostaa kvalitatiiviseksi (laadulliseksi) tai kvantitatiiviseksi (määrälliseksi) prosessia kuvaavaksi informaatioksi. Väitöstyössä tarkasteltiin laajasti erilaisten monimuuttujamenetelmien soveltamista mahdollisimman monipuolisen prosessia kuvaavan informaation saamiseksi mitatusta spektriaineistosta. Väitöstyön tuloksena on ehdotettu kalibrointirutiini liuenneen aineen konsentraation ja edelleen ylikylläisyystason mittaamiseksi kiteytysprosessin aikana. Kalibrointirutiinin kehittämiseen kuuluivat aineiston hyvyyden tarkastelumenetelmät, aineiston esikäsittelymenetelmät, varsinainen kalibrointimallinnus sekä mallin validointi. Näin saadaan reaaliaikaista informaatiota kiteytysprosessin ajavasta voimasta, mikä edelleen parantaa kyseisen prosessin tuntemusta ja hallittavuutta. Ylikylläisyystason vaikutuksia syntyvän kidetuotteen laatuun seurattiin usein kiteytyskokein. Työssä on esitetty myös monimuuttujaiseen tilastolliseen prosessinseurantaan perustuva menetelmä, jolla voidaan ennustaa spontaania primääristä ytimenmuodostumishetkeä mitatusta spektriaineistosta sekä mahdollisesti päätellä ydintymisessä syntyvä polymorfimuoto. Ehdotettua menetelmää hyödyntäen voidaan paitsi ennakoida kideytimien muodostumista myös havaita mahdolliset häiriötilanteet kiteytysprosessin alkuhetkillä. Syntyvää polymorfimuotoa ennustamalla voidaan havaita ei-toivotun polymorfin ydintyminen,ja mahdollisesti muuttaa kiteytyksen ohjausta halutun polymorfimuodon saavuttamiseksi. Monimuuttujamenetelmiä sovellettiin myös kiteytyspanosten välisen vaihtelun määrittämiseen mitatusta spektriaineistosta. Tämäntyyppisestä analyysistä saatua informaatiota voidaan hyödyntää kiteytysprosessien suunnittelussa ja optimoinnissa. Väitöstyössä testattiin IR spektroskopian ja erilaisten monimuuttujamenetelmien soveltuvuutta kidetuotteen polymorfikoostumuksen nopeaan määritykseen. Jauhemaisten näytteiden luokittelu eri polymorfeja sisältäviin näytteisiin voitiin tehdä käyttäen tarkoitukseen soveltuvia monimuuttujaisia luokittelumenetelmiä. Tämä tarjoaa nopean menetelmän jauhemaisen näytteen polymorfikoostumuksen karkeaan arviointiin, eli siihen mitä yksittäistä polymorfia kyseinen näyte pääasiassa sisältää. Varsinainen kvantitatiivinen analyysi, eli sen selvittäminen paljonko esim. painoprosentteina näyte sisältää eri polymorfeja, vaatii kaikki polymorfit kattavan fysikaalisen kalibrointisarjan, mikä voi olla puhtaiden polymorfien huonon saatavuuden takia hankalaa.

Multivariate relationships between groundwater chemistry and toxicity in an urban aquifer

Multivariate statistical methods were used to investigate file Causes of toxicity and controls on groundwater chemistry from 274 boreholes in an Urban area (London) of the United Kingdom. The groundwater was alkaline to neutral, and chemistry was dominated by calcium, sodium, and Sulfate. Contaminants included fuels, solvents, and organic compounds derived from landfill material. The presence of organic material in the aquifer caused decreases in dissolved oxygen, sulfate and nitrate concentrations. and increases in ferrous iron and ammoniacal nitrogen concentrations. Pearson correlations between toxicity results and the concentration of individual analytes indicated that concentrations of ammoinacal nitrogen, dissolved oxygen, ferrous iron, and hydrocarbons were important where present. However, principal component and regression analysis suggested no significant correlation between toxicity and chemistry over the whole area. Multidimensional Scaling was used to investigate differences in sites caused by historical use, landfill gas status, or position within the sample area. Significant differences were observed between sites with different historical land use and those with different gas status. Examination of the principal component matrix revealed that these differences are related to changes in the importance of reduced chemical species.

MODELING THE EVOLUTION OF COMPLEX NETWORKS THROUGH THE PATH-STAR TRANSFORMATION AND OPTIMAL MULTIVARIATE METHODS

The topology of real-world complex networks, such as in transportation and communication, is always changing with time. Such changes can arise not only as a natural consequence of their growth, but also due to major modi. cations in their intrinsic organization. For instance, the network of transportation routes between cities and towns ( hence locations) of a given country undergo a major change with the progressive implementation of commercial air transportation. While the locations could be originally interconnected through highways ( paths, giving rise to geographical networks), transportation between those sites progressively shifted or was complemented by air transportation, with scale free characteristics. In the present work we introduce the path-star transformation ( in its uniform and preferential versions) as a means to model such network transformations where paths give rise to stars of connectivity. It is also shown, through optimal multivariate statistical methods (i.e. canonical projections and maximum likelihood classification) that while the US highways network adheres closely to a geographical network model, its path-star transformation yields a network whose topological properties closely resembles those of the respective airport transportation network.

Discrimination of geomorphic surfaces with multivariate analysis of soil attributes in sandstone - basalt lithosequence

O conceito de superfície geomórfica permite uma interligação entre os diferentes ramos da ciência do solo, tais como geologia, geomorfologia e pedologia. Esta associação favorece a compreensão da distribuição espacial dos solos na paisagem, e torna possível compreender o comportamento dos atributos do solo, que estão principalmente relacionadas com a estratigrafia e formas do relevo. Assim, este estudo visa à aplicação da estatística multivariada para categorizar superfícies geomórficas em uma litossequência arenito-basalto, de modo a fornecer uma base para a avaliação do solo em áreas afins. A área de estudo está localizada no município de Pereira Barreto, São Paulo, Brasil. A área escolhida possui 530 hectares, onde foram localizadas e mapeadas três superfícies geomórficas (I, II e III). Na área, 134 amostras foram coletadas nas profundidades de 0,0-0,2 m e 0,8-1,0 m, foram determinados os conteúdos de areia, silte e argila, pH em CaCl2, conteúdo de MO, P, Ca, Mg, K, Al e H+Al. Com base nos resultados, foram realizadas a análise univariada e multivariada de variância, clusters e principal componente, a fim de comparar as três superfícies geomórficas. A análise estatística univariada dos atributos do solo não foi eficiente na identificação das três superfícies geomórficas. Utilizando-se os atributos físicos e químicos do solo, as técnicas estatísticas multivariada permitiram à separação dos três grupos de corpos naturais do solo que foram equivalentes as três superfícies geomórficas mapeadas. Estes resultados são interessantes, pois demonstram a viabilidade da utilização de classificação numérica das superfícies geomórficas para ajudar no mapeamento de solo.

Multivariate analysis of stable isotope data in the traceability process for birds

A análise isotópica tem se mostrado uma ferramenta de suma importância ao processo de rastreabilidade, no entanto, existem divergências nas análises estatísticas dos resultados, uma vez que os dados são dependentes e advindos de vários elementos químicos tais como Carbono, Hidrogênio, Oxigênio, Nitrogênio e Enxofre (CHON'S). Com o intuito de estabelecer a análise propícia para os dados de rastreabilidade em aves pela técnica de isótopos estáveis e avaliar a necessidade da análise conjunta das variáveis, foram usados dados de carbono-13 e de nitrogênio-15 de ovos (albúmen + gema) de poedeiras e músculo peitoral de frangos de corte, os quais foram submetidos à análise estatística univariada (Anova e complementada pelo teste de Tukey) e multivariada (Manova e Discriminante). Os dados foram analisados no software Minitab 16, e os resultados, consolidados na teoria, confirmam a necessidade de análise multivariada, mostrando também que a análise discriminante esclarece as dúvidas apresentadas nos resultados de outros métodos de análise comparados nesta pesquisa.