Multivariate Statistical Methods Applied to Sizing and Fit Testing

1998 ◽  
Vol 42 (10) ◽  
pp. 732-735 ◽  
Author(s):  
Stacie E. Taylor
Keyword(s):  
Statistical Methods ◽  
Principal Component ◽  
Distance Matrix ◽  
Multivariate Regression Analysis ◽  
Important Variable ◽  
Matrix Analysis ◽  
Multivariate Statistical Methods ◽  
Euclidean Distance Matrix ◽  
Multivariate Statistical ◽  
Fit Testing

The difficulty of developing accurate sizing charts for clothing or equipment is often underestimated. Typically, designers intend for the item to fit a specific range of people. However, accommodation ofthat range is not always achieved. Fit testing is an important part of the design process that allows collection of data where the item is actually tried on and used by people, instead of mannequins. Multivariate statistical procedures are the proper analytic techniques for investigating this fit test data. Multivariate methods are used because univariate tests can cause designers to correct a “problem” fit area, leading to possibly more problems, instead of identifying important variable combinations which may be the true fit problem. Some of these multivariate statistical methods include principal component analysis (PCA), discriminant analysis (DA), Euclidean distance matrix analysis (EDMA), multivariate analysis of variance (MANOVA), and multivariate regression analysis (MRA). This paper discusses why and when to use these techniques and illustrates some of them with case studies.

Multivariate Techniques of Use in Biological Research

1969 ◽  
Vol 5 (1) ◽  
pp. 67-77 ◽  
Author(s):  
S. C. Pearce
Keyword(s):  
Principal Component Analysis ◽  
Statistical Methods ◽  
Matrix Algebra ◽  
Principal Component ◽  
Component Analysis ◽  
Canonical Analysis ◽  
Biological Research ◽  
Multivariate Techniques ◽  
Multivariate Statistical Methods ◽  
Multivariate Statistical

SUMMARYMultivariate statistical methods are used increasingly in biological research to investigate the responses of organisms considered as a whole, whereas established statistical methods are usually concerned with measured characteristics considered one at a time. Multivariate techniques are mostly explained in terms of matrix algebra, which is a way of dealing with groups of numbers rather than individual ones. A brief description is given of some elementary results of matrix algebra and a method is presented whereby hypotheses can be generated about interrelations within an organism. Two techniques, principal component analysis and canonical analysis, are described in greater detail. It is emphasized that hypotheses need to be tested even though they have been generated by objective statistical means.

Evaluation of colon cancer elements contents in serum using statistical methods

2007 ◽  
Vol 61 (5) ◽  
Author(s):  
D. Milde ◽  
J. Macháček ◽  
V. Stužka
Keyword(s):  
Statistical Methods ◽  
Tnm Classification ◽  
Principal Component ◽  
Absorption Spectrometry ◽  
Acid Mixture ◽  
Multivariate Statistical Methods ◽  
Serum Samples ◽  
Multivariate Statistical ◽  
Colorectal Cancer Patients

AbstractClassification of normal and different cancer groups (TNM classification) with univariate and multivariate statistical methods according to the contents of Cu, Fe, Mn, Se, and Zn in blood serum is discussed. All serum samples were digested by acid mixture in a microwave mineralization unit prior to the analysis by atomic absorption spectrometry. Results show that univariate methods can distinguish normal and cancer groups. Level of selenium evaluated as arithmetic mean with its standard deviation in colorectal cancer patients was (42.61 ± 23.76) µg L−1. Retransformed mean was used to evaluate levels of managanese (11.99 ± 1.71) µg L−1, copper (1.05 ± 0.06) mg L−1, zinc (2.14 ± 0.21) mg L−1, and iron (1.82 ± 0.22) mg L−1. Conclusions of multivariate statistical procedures (principal component analysis, hierarchical, and k-means clustering) do not correlate very well with the division of serum samples according to the TNM classification.

scholarly journals Geochemical classification of groundwater using multivariate statistical analysis in Latvia

2016 ◽  
Vol 47 (4) ◽  
pp. 799-813 ◽  
Author(s):  
Inga Retike ◽  
Andis Kalvans ◽  
Konrads Popovs ◽  
Janis Bikse ◽  
Alise Babre ◽  
...  
Keyword(s):  
Trace Elements ◽  
Statistical Methods ◽  
Principal Component ◽  
Hierarchical Cluster ◽  
Ion Chemistry ◽  
Multivariate Statistical Methods ◽  
Multivariate Statistical ◽  
Gypsum Dissolution ◽  
Major Ion

Multivariate statistical methods – principal component analysis (PCA) and hierarchical cluster analysis (HCA) – are applied to identify geochemically distinct groundwater groups in the territory of Latvia. The main processes observed to be responsible for groundwater chemical composition are carbonate and gypsum dissolution, fresh and saltwater mixing and ion exchange. On the basis of major ion concentrations, eight clusters (C1–C8) are identified. C6 is interpreted as recharge water not in equilibrium with most sediment forming minerals. Water table aquifers affected by diffuse agricultural influences are found in C3. Groundwater in C4 reflects brine or seawater admixture and gypsum dissolution in C5. C7 and C2 belong to typical bicarbonate groundwater resulting from calcite and dolomite weathering. Extremely low Cl− and SO42− are observed in C8 and described as pre-industrial groundwater or a solely carbonate weathering result. Finally, C1 seems to be a poorly defined subgroup resulting from mixing between other groups. This research demonstrates the validity of applying multivariate statistical methods (PCA and HCA) on major ion chemistry to distribute characteristic trace elements in each cluster even when incomplete records of trace elements are present.

scholarly journals Use of multivariate statistical methods for classification of olive oil

2021 ◽  
Vol 6 (1) ◽  
pp. 035-043
Author(s):  
Moacyr Cunha Filho ◽  
Renisson Neponuceno Araujo Filho ◽  
Ana Luiza Xavier Cunha ◽  
Victor Casimiro Piscoya ◽  
Guilherme Rocha Moreira ◽  
...  
Keyword(s):  
Olive Oil ◽  
Statistical Methods ◽  
Virgin Olive Oil ◽  
Principal Component ◽  
Extra Virgin Olive Oil ◽  
Fuzzy Cluster ◽  
Multivariate Statistical Methods ◽  
Multivariate Statistical ◽  
Fuzzy Clustering Method ◽  
Silhouette Index

Multivariate statistical methods can contribute significantly to classification studies of extra virgin and common olive oil groups. Therefore, nuclear magnetic resonance (NMR) was used to discriminate olive oil samples, multivariate statistical techniques Principal Component Analysis - PCA, Fuzzy Cluster, Silhouette Validation Method to describe and classify. The groups' distinction into organic and common was observed by applying the non-hierarchical Fuzzy grouping with a distinction between the two groups with a 65% confidence interval. The validation was performed by the silhouette index that presented S (i) of 0.73, which showed that the adopted grouping presented adequate strength and distinction criterion. However, PCA only analyzed the behaviors of data from extra virgin olive oil. Thus, the Fuzzy clustering method was the most suitable for classifying extra virgin olive oil.

scholarly journals The usefulness of robust multivariate methods: A case study with the menu items of a fast food restaurant chain

2020 ◽  
Vol 42 ◽  
pp. e17
Author(s):  
Paulo Jorge Canas Rodrigues ◽  
Rafael Almeida ◽  
Kézia Mustafa
Keyword(s):  
Principal Component Analysis ◽  
Cluster Analysis ◽  
Statistical Methods ◽  
Fast Food ◽  
Principal Component ◽  
Component Analysis ◽  
Fast Food Restaurant ◽  
Multivariate Statistical Methods ◽  
Multivariate Statistical ◽  
Robust Statistical Methods

Multivariate statistical methods have been playing an important role in statistics and data analysis for a very long time. Nowadays, with the increase in the amounts of data collected every day in many disciplines, and with the raise of data science, machine learning and applied statistics, that role is even more important. Two of the most widely used multivariate statistical methods are cluster analysis and principal component analysis. These, similarly to many other models and algorithms, are adequate when the data satisfies certain assumptions. However, when the distribution of the data is not normal and/or it shows heavy tails and outlying observations, the classic models and algorithms might produce erroneous conclusions. Robust statistical methods such as algorithms for robust cluster analysis and for robust principal component analysis are of great usefulness when analyzing contaminated data with outlying observations. In this paper we consider a data set containing the products available in a fast food restaurant chain together with their respective nutritional information, and discuss the usefulness of robust statistical methods for classification, clustering and data visualization.

It is better an approximate answer to the right question than the exact answer to the wrong question : the case of the psychometric analysis of the ASQ:SE

2020 ◽  
Author(s):  
Luis Anunciacao ◽  
janet squires ◽  
J. Landeira-Fernandez
Keyword(s):  
Internal Structure ◽  
Statistical Methods ◽  
Principal Component ◽  
Psychological Theory ◽  
Published Data ◽  
Multivariate Statistical ◽  
Exact Answer ◽  
Wide Range ◽  
Ages And Stages Questionnaire ◽  
The Right

One of the main activities in psychometrics is to analyze the internal structure of a test. Multivariate statistical methods, including Exploratory Factor analysis (EFA) and Principal Component Analysis (PCA) are frequently used to do this, but the growth of Network Analysis (NA) places this method as a promising candidate. The results obtained by these methods are of valuable interest, as they not only produce evidence to explore if the test is measuring its intended construct, but also to deal with the substantive theory that motivated the test development. However, these different statistical methods come up with different answers, providing the basis for different analytical and theoretical strategies when one needs to choose a solution. In this study, we took advantage of a large volume of published data (n = 22,331) obtained by the Ages and Stages Questionnaire Social-Emotional (ASQ:SE), and formed a subset of 500 children to present and discuss alternative psychometric solutions to its internal structure, and also to its subjacent theory. The analyses were based on a polychoric matrix, the number of factors to retain followed several well-known rules of thumb, and a wide range of exploratory methods was fitted to the data, including EFA, PCA, and NA. The statistical outcomes were divergent, varying from 1 to 6 domains, allowing a flexible interpretation of the results. We argue that the use of statistical methods in the absence of a well-grounded psychological theory has limited applications, despite its appeal. All data and codes are available at https://osf.io/z6gwv/.

Methods for Studying Morphological Integration and Modularity

2010 ◽  
Vol 16 ◽  
pp. 213-243 ◽  
Author(s):  
Anjali Goswami ◽  
P. David Polly
Keyword(s):  
Distance Matrix ◽  
Japanese Macaques ◽  
Morphological Integration ◽  
Matrix Analysis ◽  
Euclidean Distance Matrix ◽  
Phenotypic Data ◽  
Graphical Modelling ◽  
Landmark Data ◽  
Competing Models ◽  
Matrix Correlation

Morphological integration and modularity are closely related concepts about how different traits of an organism are correlated. Integration is the overall pattern of intercorrelation; modularity is the partitioning of integration into evolutionarily or developmentally independent blocks of traits. Modularity and integration are usually studied using quantitative phenotypic data, which can be obtained either from extant or fossil organisms. Many methods are now available to study integration and modularity, all of which involve the analysis of patterns found in trait correlation or covariance matrices. We review matrix correlation, random skewers, fluctuating asymmetry, cluster analysis, Euclidean distance matrix analysis (EDMA), graphical modelling, two-block partial least squares, RV coefficients, and theoretical matrix modelling and discuss their similarities and differences. We also review different coefficients that are used to measure correlations. We apply all the methods to cranial landmark data from and ontogenetic series of Japanese macaques,Macaca fuscatato illustrate the methods and their individual strengths and weaknesses. We conclude that the exploratory approaches (cluster analyses of various sorts) were less informative and less consistent with one another than were the results of model testing or comparative approaches. Nevertheless, we found that competing models of modularity and integration are often similar enough that they are not statistically distinguishable; we expect, therefore, that several models will often be significantly correlated with observed data.

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