Napping (method of data collection)

The Napping is a method of data collection related to the perception of a set of stimuli, such as food products. It is mainly used in sensory analysis but its potential field of application goes far beyond this area.

Context

We are interested in how a set of products is perceived. Classically, a panel of tasters is asked to evaluate each product using a score sheet with several descriptors, such as sourness, bitterness, etc. For each descriptor and each product, each taster scores, on a scale ranging for example from 0 to 10, the intensity of the descriptor as he perceives it in the product. This method is fundamental in sensory analysis. But it says nothing about the importance of the descriptors in the perception of the products studied. The Napping was conceived in this perspective.

Description of the protocol

We present to the tasters all the products, say wines to fix ideas. We then asked each taster to position all wines on a sheet of paper (hence the origin of the word Napping, from the French word nappe which means tablecloth) so that the distances on the paper reflect the perceived distances. It must be clear to the panelists that there is no right or wrong answer, that we are looking for a personal perception and that all the tasters have not necessarily the same view of the products. Indeed, for example, some may grant great importance to olfactory aspects, others to taste aspects, etc.

In practice, the data entry is done using a screen on which the taster reproduces the position of wines on the tablecloth.

Data

The data set of one taster is the horizontal (X) and vertical (Y) coordinates of each product. This data set is called nappe. If there are $I$ products, these data can be gathered into a table with $I$ rows (products) and two columns (X and Y). If there are $J$ tasters, the whole data set is in a table with $I$ rows and $2J$ columns (Figure 1).

File:Figure 1 of the article napping.png

Figure 1. Structure of napping data.

Statistical analysis

To analyze this type of data, the multiple factor analysis (MFA ) fits perfectly. In this analysis, each taster is a group of two variables. To keep the distances on tablecloths, variables must not be reduced. The MFA provides several graphs whose two main ones are the following.

• A representation of the "average" products, that is to say as close as possible to the set of the representations provided by the tasters (the "nappes"). The first dimension of this average representation is somewhat the dimension common to the greatest number of "nappes".
• A representation of tasters indicating the importance that each of them has granted to the dimensions of the average representation. One recognizes the INDSCAL model. According to this view, the MFA provides an estimate of its parameters.

Small example

Data

Eight Bordeaux wines were selected according to an experimental design to study the relative importance of the Appellation (Graves or Médoc), the variety (Cabernet Sauvignon or Merlot) and ageing (vats or barrels) on the overall perception of this type of wine. The wine labels start with the order number followed by three letters reminding the categories of the factors of the design (Table 1).

Table 1. Small example. Description of the eight wines.

	Label	Appellation	Variety	Ageing
$1$	1GCf	Graves	Cabernet	barrels
$2$	2MCf	Médoc	Cabernet	barrels
$3$	3GMf	Graves	Merlot	barrels
$4$	4MMf	Médoc	Merlot	barrels
$5$	5GCc	Graves	Cabernet	vats
$6$	6MCc	Médoc	Cabernet	vats
$7$	7GMc	Graves	Merlot	vats
$7$	8MMc	Médoc	Merlot	vats

To obtain data on overall perception of these wines, we gathered a panel of three persons (= judges) who were asked to use the approach of napping. The data are in Figure 2.

File:Figure 2 of the article napping.png

Small Example: data table and nappes

The general problem of this study mainly revolves around the question: what is the relationship between the overall perception of these wines and the three factors of the design used to select wines?

Methodology

These data were subjected to MFA in which:

• Each of the three "nappes" is an active group,
• Each of the three experimental factors is an additional group.

Results

The MFA provided, among numerous results, the graphs of Figures 3 and 4.

File:Figure 3 of the article napping.png

Small example. MFA. Representation of the wines and of the categories

Figure 3 is interpreted as usually in factorial analysis. Two wines are close each other if they are close on the nappes. A category is at the barycenter of the wines which possesses it. Figure 3 leads to the following interpretations.

• The first axis contrasts wines {1, 2, 3, 4} to the others. These wines have been aged in barrels (see their labels) which is not the case for the others. This opposition is an opposition between ageing. It is clearly visible on each of the three "nappes".
• The second axis opposes wines 3, 4, 7 and 8 to the others. These wines were made with Merlot, the other with Cabernet. There is therefore an opposition between varieties. It can be seen on the "nappes" of judges 1 and 2.

File:Figure 4 of the article napping.png

Small example. MFA. Relationship square. Representation of the judges and of the qualitative variables.

The relationship square (Figure 4) must be interpreted in reference to figure 3 left. Interpretation of judges: the coordinate of judge $j$ on axis $s$ is high if the dimension $s$ on figure 3 left correspond to a important dimension of nappe $j$. Interpretation of qualitative variable : the coordinate of variable $k$ on axis $s$ is the squared correlation ratio between the variable $k$ and axis $s$ of the representation of wines (figure 3 left). Figure 4 shows the following results.

• The first dimension of the average configuration of wines (opposition between wines {1, 2, 3, 4} and wines {5, 6, 7, 8}) is important for the three judges (their coordinate is maximum along this axis); the most important factor in the perception of these wines is the way of ageing.
• The second dimension is related only to judges 1 and 2 (a little more strongly for judge1 which has a slightly higher coordinate than the judge 2 along the second axis) and is much less important than the first one (in fact, the direct examination of the "nappes" first shows the opposition between ageing ways). This dimension is also closely linked to the variety but is not identical with it.
• There is no connection between the appellation and the two main dimensions of variability of the images of these wines.

The representation of qualitative variables defining wines brings little here compared to Figure 3 because the variables are few and have only two categories. It is not the case in practice of napping where this graph provides a visualization all the more valuable than variables are numerous and include many categories.

Conclusion

These data illustrate the interest of napping. Data are collected giving a great freedom of expression to the tasters. But they contain in themselves the latent variables of perception of wines by the judges. Proper statistical analysis allows to identify these latent variables (here, first the ageing and then the variety).

Extension: the sorted napping

The napping belongs to holistic methods so called because they require judges to consider each product as a whole (unlike the usual descriptive methods that analyze each product descriptor by descriptor). Another holistic method is the free sorting in which judges are asked to gather the product into groups.

We can combine napping and free sorting by asking panelists, at the end of napping, to gather products which they consider particularly close. This procedure is called the sorted napping. Data from sorted napping are complex in that they contain both quantitative variables (coordinates on the "nappes") and qualitative variables (partition from free sorting). The well fitted statistical treatment is Hierarchical MFA (HMFA). A description of HMFA with an application to sorted napping data is in Pagès 2013.

History

The napping was introduced by Jérôme Pagès in 2003 in French and in 2005 in English.

The first study using napping was performed with Pascale Deneulin (with wines from Loire valley), then student at Agrocampus Rennes The sorted napping has been introduced in 2010 These methods have been widely used by Lucie Perrin in her work on Loire wines.

The napping is still the subject of research and gives rise to theses or articles.

Software

The R package SensoMineR contains all the necessary functions for the analysis of data from the napping, the free sorting and the sorted napping. This software also contains functions for all common problems of sensory analysis. It is based on the R package FactoMineR, which contains functions for the most useful methods of data analysis.

External links

• FactoMineR, a R package devoted to exploratory data analysis.
• SensoMineR, a R package devoted to statistical analysis of sensory data.

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