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Benefits

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.

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Benefits

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  1. Key Features and Results Benefits

  2. XLSTAT-ADA’s functions

  3. 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

  4. 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

  5. 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.

  6. 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.

  7. 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

  8. 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)

  9. 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.

  10. 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 Analysis p species T1 n sites q descriptive variables Contingency table T2 n sites • CCA  simultaneous representation of the sites, the objects, and the variables describing the sites.

  11. 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

  12. 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.

  13. 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

  14. 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:

  15. 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: • Computation of a distance matrix for the p elements p p x11 x12 x1p xn1 xn2 xnp 0 d12 d1p 0 0 0 0 dp1 dp2 0 n p

  16. 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: • Centering of the matrix by rows and columns p p p x11 x12 x1p xn1 xn2 xnp -r1-c1 d1p-r1-cp dij-ri-cj dp1-rp-c1 -rp-cp 0 d12 d1p 0 0 0 0 dp1 dp2 0 n p p

  17. 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: • Eigen-decomposition of the centered distance matrix p p t p p x11 x12 x1p xn1 xn2 xnp -r1-c1 d1p-r1-cp dij-ri-cj dp1-rp-c1 -rp-cp 0 d12 d1p 0 0 0 0 dp1 dp2 0 t n p p p p

  18. 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: • 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. • Computation of a distance matrix for the p elements • Centering of the matrix by rows and columns • Eigen-decomposition of the centered distance matrix

  19. Principal coordinate analysis • 5 products are graded by 10 individuals Note that product 4 is preferable.

  20. Principal coordinate analysis • The results is a map of the proximity of the 5 products. • P1 and P3 are the most similar products.

  21. 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.

  22. Generalized Procrustes Analysis (GPA) • 10 experts graded 4 cheeses for 3 sensory attributes: • Acidity • Strangeness • Hardness

  23. Generalized Procrustes Analysis (GPA) • The products do not have the exact same grade by each expert

  24. 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

  25. Generalized Procrustes Analysis (GPA) • Strangeness is not graded in the same way by the different experts • Acidity and Hardness are quite reproducible

  26. 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.

  27. 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)

  28. Multiple Factor Analysis (MFA) • MFA groups the information on one chart

  29. Multiple Factor Analysis (MFA) • MFA groups the information on one chart

  30. Multiple Factor Analysis (MFA) • Wine 13 is in the direction of the two quality variables and is therefore the wine of preference.

  31. Multiple Factor Analysis (MFA) • The olfactory criteria are often increasing the distance between the wines.

  32. 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

  33. 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

  34. Penalty analysis Mean of Liking for JAR – Mean of Liking for too little and too much

  35. 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

  36. Semantic differential charts • 1 yoghurt • 5 experts • 6 attributes: • Color • Fruitiness • Sweetness • Unctuousness • Taste • Smell

  37. Semantic differential charts

  38. 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

  39. 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

  40. TURF analysis

  41. Product characterization • Find which descriptors are discriminating well a set of productsand which the most important characteristics of each product are. • Check the influence on the scores of attributes of: • Product • Judge • Session • Judge*Product • All computations are based on the analysis of variance (ANOVA) model.

  42. 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

  43. Product characterization

  44. 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. 

  45. 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 D-efficiency

  46. DOE for sensory data analysis • 60 judges • 8 products • Saturation: 3 products / judge

  47. DOE for sensory data analysis

  48. DOE for sensory data analysis

  49. Let XLSTAT-ADA completeyouradvancedanalyticalneeds info@xlstat.com

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