Benefits Key Features and Results. XLSTAT-ADA’s functions.

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.

Note that the first factor is explaining more variance than in canonical correlation analysis (93,30)

The larger the waist, the lower the pulse

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.

CCA simultaneous representation of the sites, the objects, and the variables describing the sites.

Principles of Canonical Correspondence Analysis

T1n

sites

pspecies

T2n

sites

qdescriptive variables

Contingency table

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.


1. Computation of a distance matrix for the p elements

p

n

x11 x12 x1p

xn1 xn2 xnp

p

p

0 d12 d1p

0 0 0 0dp1 dp2 0




2. Centering of the matrix by rows and columns

p

n

p

p

x11 x12 x1p

xn1 xn2 xnp

0 d12 d1p

0 0 0 0dp1 dp2 0

p

p

-r1-c1 d1p-r1-cp dij-ri-cj dp1-rp-c1 -rp-cp




3. Eigen-decomposition of the centered distance matrix

p

n

p

p

x11 x12 x1p

xn1 xn2 xnp

0 d12 d1p

0 0 0 0dp1 dp2 0

p p

pt

t

p

p

-r1-c1 d1p-r1-cp dij-ri-cj dp1-rp-c1 -rp-cp




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.

1. Computation of a distance matrix for the p elements2. Centering of the matrix by rows and columns3. Eigen-decomposition of the centered distance

matrix

Principal coordinate analysis

5 products are graded by 10 individualsNote that product 4 is preferable.

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


The products do not have the exact same grade by each expert


A consensus can be found for the position of each product

Cheese 1 and 2 are the strangest

Cheese 3 is the Hardest


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.

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)

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


Wine 13 is in the direction of the two quality variables and is therefore the wine of preference.


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 analysisA type of potato chips is evaluated:

By 150 consumersOn 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.

All computations are based on the analysis of variance (ANOVA) model.

Check the influence on the scores of attributes of:

• Product• Judge

• Session• Judge*Product

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 D-efficiency

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

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Benefits Key Features and Results. XLSTAT-ADA’s functions.

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