# Analysis of projective mapping data with Excel

This tutorial explains how to perform and interpret a projective mapping data analysis in Excel using the XLSTAT software.

## Projective mapping dataset

The data comes from a projective mapping/Napping performed in Rennes by AGROCAMPUS OUEST. 24 subjects have placed 8 smoothies on a paper sheet. A person finding two products similar will place them close to each other on the paper sheet, and the products perceived differently will be placed far away from each other. The projective mapping (or Napping) thus gives a notion of distance between the products.

For data analysis, the coordinates of each paper sheet are collected. The original file can be obtained with the R package SensoMineR.

## Goal of this tutorial

The aim of this tutorial is:

- To study and visualize the relationships between smoothies. We will construct a product map representing the global point of view of the subjects.
- To study the agreements between the subjects, in order to determine if their answers are similar and if atypical subjects exist.

## Setting up a projective mapping data analysis in XLSTAT

Select the **XLSTAT** / **Advanced features** / **Sensory data analysis** / **projective mapping data analysis** command.

The **projective mapping data analysis** dialog box appears.

In the **General** tab, select the projective mapping data (all the coordinates of the subjects concatenated vertically). The product labels (smoothies) can also be selected.

Two methods are proposed for data analysis: the STATIS method and the Multiple Factor Analysis (MFA). We choose here to use the **STATIS** method.

In the **Options** tab, limit the number of axes to 5 and to choose to build the map on the first two axes. If you want to use other axes than F1 and F2, uncheck this last option.
The computations start when you click the **OK** button.

## Interpreting the results of a projective mapping data analysis in Excel using XLSTAT

After having displayed some descriptive statistics along with some eigenvalues, we can visualize the main goal of projective mapping data analysis: represent the products on a 2-dimensional map, and thus identify proximities between them. We can see that the "Casino_PBC" and "Innocent_PBC" smoothies are perceived as close but differ from "Casino_SRB". On the other hand, "Innocent_SB" and "Immedia_MP" smoothies are opposite.
If we are interested in two particular subjects, it is useful to observe the **RV matrix** which gives the RV coefficient between each subject (this coefficient is between 0 and 1 and increases with the proximity of the subjects). Here, subject 1 has a very similar opinion to subject 2, but very different from subject 4 (who has low RV values with many other subjects here).
The **scaling factors** for each subject indicate how the subjects used the space of the paper sheet relatively to the others. The higher a subject's factor, the more the method had to amplify the spaces between products to counteract low sheet usage. Here, we see that subjects 3 and 8 have used very little of the sheet space in comparison to the others (they concentrated their products more or less in the same place).
It is also interesting to **evaluate the proximity of a subject to all the others**, i.e. to the global point of view reflected by the consensus. To do this, we look at the bar chart representing the similarity of a subject with the consensus, and we see that subjects 2 and 4 are rather atypical, unlike 18 or 23.
The following graph gives the **residuals** by product, which indicates which smoothies were placed (in relation to the others) more or less similarly by the subjects, like the "Innocent_PBC" smoothie, or rather differently, like the "Carrefour_SB" smoothie.
Finally, the subject **homogeneity index** (between 1/m and 1, m being the number of subjects) allows us to evaluate whether the subjects have responded in a consensual way. The closer the index is to 1, the more homogeneous the subjects are. Here, we see that the homogeneity is medium. A clustering of the subjects might be necessary to determine classes of subjects with the same point of view. In order to perform this, you can use the CLUSTATIS method.

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