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Key Features and Results Benefits XLSTAT-ADA’s functions Canonical correlation analysis Studies the correlation between two sets of variables Extracts a set of canonical variables that are as closely correlated with both tables as possible and orthogonal to each other. Symmetrical method Canonical correlation analysis Recording of data on men in a training center, Two sets of data: The physiological data: • Weight • Waist • Pulse The exercises the men did: • Chin-ups • Sit-ups • Jumps Canonical correlation analysis Men doing sit-ups or chin-ups have usually a smaller waist. In general people training more have a smaller waist and weight. Jumping seems to have an impact on the weight but not as much on the waist. Redundancy analysis Redundancy Analysis is an alternative to Canonical Correlation Analysis. Non-symmetric method. The components extracted from X are such that they are as closely correlated with the variables of Y as possible. Then, the components of Y are extracted so that they are as closely correlated with the components extracted from X as possible. Redundancy analysis Same example as Canonical correlation analysis: Recording of data on men in a training center, Two sets of data: The physiological data: • Weight • Waist • Pulse The exercises the men did: • Chin-ups • Sit-ups • Jumps Redundancy analysis Same relationships are observed: • Men doing more sit-ups or chin-ups have usually a smaller waist. • In general people training more have a smaller waist and weight. • Jumping seems to have an impact on the weight but not as much on the waist. The larger the waist, the lower the pulse Note that the first factor is explaining more variance than in canonical correlation analysis (93,30) Redundancy analysis It is possible to project the observations in the same graphic. It is easy to visualize which men are doing more exercises and the one being fitter. Canonical Correspondence Analysis Canonical Correspondence Analysis (CCA) was developed to allow ecologists to relate the abundance of species to environmental variables. Principles of Canonical Correspondence q Analysis p species n sites T1 Contingency table descriptive variables n sites T2 CCA simultaneous representation of the sites, the objects, and the variables describing the sites. Canonical Correspondence Analysis Canonical Correspondence Analysis can be divided into two parts: • A constrained analysis in a space which number of dimensions is equal to q = analysis of the relation between the two tables T1 and T2. • An unconstrained part = analysis of the residuals. XLSTAT-ADA offers as well: • Partial CCA • PLS-CCA Canonical Correspondence Analysis Contingency table: • the counts of 10 species of insects • on 12 different sites in a tropical region. A second table includes 3 quantitative variables that describe the 12 sites: • altitude, • humidity, • and distance to the lake. Canonical Correspondence Analysis Some insects: insects 2, 4 and 5 prefer the humid sites, such as sites 7 to 12, while some prefer dry climates such as insects 1, 6, 8 and 10. Insect 9 prefers a climate with higher altitude Principal coordinate analysis Principal Coordinate Analysis is aimed at graphically representing a resemblance matrix between p elements. The algorithm can be divided into three steps: Principal coordinate analysis Principal Coordinate Analysis is aimed at graphically representing a resemblance matrix between p elements. The algorithm can be divided into three steps: 1. Computation of a distance matrix for the p elements p p x11 x12 x1p 0 d12 0 d1p 0 n 0 p 0 dp1 dp2 xn1 xn2 xnp 0 Principal coordinate analysis Principal Coordinate Analysis is aimed at graphically representing a resemblance matrix between p elements. The algorithm can be divided into three steps: 2. Centering of the matrix by rows and columns p p p x11 x12 x1p 0 d12 0 -r1-c1 d1p d1p-r1-cp 0 n 0 p 0 dp1 dp2 xn1 xn2 xnp p 0 dij-ri-cj dp1-rp-c1 -rp-cp Principal coordinate analysis Principal Coordinate Analysis is aimed at graphically representing a resemblance matrix between p elements. The algorithm can be divided into three steps: 3. Eigen-decomposition of the centered distance matrix p x11 x12 p x1p p 0 d12 0 -r1-c1 d1p t d1p-r1-cp t 0 n 0 p 0 dp1 dp2 xn1 xn2 xnp p 0 dij-ri-cj dp1-rp-c1 p -rp-cp p Principal coordinate analysis Principal Coordinate Analysis is aimed at graphically representing a resemblance matrix between p elements. The algorithm can be divided into three steps: 1. 2. 3. Computation of a distance matrix for the p elements Centering of the matrix by rows and columns Eigen-decomposition of the centered distance matrix The rescaled eigenvectors correspond to the principal coordinates that can be used to display the p objects in a space with 1, 2, p-1 dimensions. Principal coordinate analysis P1 P2 P3 P4 P5 5 products are graded by 10 individuals Ind1 2 1 4 5 3 Ind2 3 1 2 5 4 Note that product 4 is preferable. Ind3 1 2 4 3 5 Ind4 3 2 4 5 1 Ind5 3 2 4 5 1 Ind6 2 1 3 5 4 Ind7 1 3 4 2 5 Ind8 3 1 2 4 5 Ind9 3 1 2 5 4 Ind10 1 4 5 2 1 Average 2,2 1,8 3,4 4,1 3,3 Principal coordinate analysis The results is a map of the proximity of the 5 products. P1 and P3 are the most similar products. Generalized Procrustes Analysis (GPA) GPA is a pretreatment used to: • reduce the scale effects • and obtain a consensual configuration on data where products have been graded by several judges. GPA compares the proximity between the terms that are used by different experts to describe products. Generalized Procrustes Analysis (GPA) 10 experts graded 4 cheeses for 3 sensory attributes: • Acidity • Strangeness • Hardness Generalized Procrustes Analysis (GPA) The products do not have the exact same grade by each expert Generalized Procrustes Analysis (GPA) A consensus can be found for the position of each product Cheese 1 and 2 are the strangest Cheese 3 is the Hardest Generalized Procrustes Analysis (GPA) Strangeness is not graded in the same way by the different experts Acidity and Hardness are quite reproducible Multiple Factor Analysis (MFA) MFA is a generalization of PCA (Principal Component Analysis) and MCA (Multiple Correspondence Analysis). MFA makes it possible to: • Analyze several tables of variables simultaneously, • Obtain results that allow studying the relationship between the observations, the variables and tables. Multiple Factor Analysis (MFA) 36 experts have graded 21 wines analysed on several criteria: • Olfactory (5 variables) • Visual (3 variables) • Taste (9 variables) • Quality (2 variables) Multiple Factor Analysis (MFA) MFA groups the information on one chart Multiple Factor Analysis (MFA) MFA groups the information on one chart Multiple Factor Analysis (MFA) Wine 13 is in the direction of the two quality variables and is therefore the wine of preference. Multiple Factor Analysis (MFA) The olfactory criteria are often increasing the distance between the wines. Penalty analysis Identify potential directions for the improvement of products, on the basis of surveys performed on consumers or experts. Two types of data are used: • Preference data (or liking scores) for a product or for a characteristic of a product • Data collected on a JAR (Just About Right) scale Penalty analysis A type of potato chips is evaluated: By 150 consumers On a JAR scale (1 to 5) for 4 attributes: • Saltiness, • Sweetness, • Acidity, • Crunchiness. And on an overall liking (1 to 10) score scale Penalty analysis Mean of Liking for JAR – Mean of Liking for too little and too much Semantic differential charts The semantic differential method is a visualization method to plot the differences between individuals' connotations for a given word. This method can be used for: • Analyzing experts’ agreement on the perceptions of a product described by a series of criteria on similar scales • Analyzing customer satisfaction surveys and segmentation • Profiling products Semantic differential charts 1 yoghurt 5 experts 6 attributes: • Color • Fruitiness • Sweetness • Unctuousness • Taste • Smell Semantic differential charts TURF analysis TURF = Total Unduplicated Reach and Frequency method Highlight a line of products from a complete range of products in order to have the highest market share. XLSTAT offers three algorithms to find the best combination of products TURF analysis 27 possible dishes 185 customers "Would you buy this product?" (1: No, not at all to 5: Yes, quite sure). The goal is to obtain a product line of 5 dishes maximizing the reach TURF analysis Product characterization Find which descriptors are discriminating well a set of products and which the most important characteristics of each product are. Check the influence on the scores of attributes of: • Session • Product • Judge • Judge*Product All computations are based on the analysis of variance (ANOVA) model. Product characterization 29 assessors 6 chocolate drinks 14 characteristics: • Cocoa and milk taste and flavor • Other flavors: Vanilla, Caramel • Tastes: bitterness, astringency, acidity, sweetness • Texture: granular, crunchy, sticky, melting Product characterization DOE for sensory data analysis Designing an experiment is a fundamental step to ensure that the collected data will be statistically usable in the best possible way. DOE for sensory data analysis Prepare a sensory evaluation where judges (experts and/or consumers) evaluate a set of products taking into account: • Number of judges to involve • Maximum number of products that a judge can evaluate during each session • Which products will be evaluated by each of the consumers in each session, and in what order (carry-over) Complete plans or incomplete block designs, balanced or not. Search optimal designs with A- or Defficiency DOE for sensory data analysis 60 judges 8 products Saturation: 3 products / judge DOE for sensory data analysis DOE for sensory data analysis Let XLSTAT-ADA complete your advanced analytical needs [email protected]