XLSTAT: Analysis of Projective Mapping Data in Excel

 

Dataset for Example

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.

We will use the example:

1. To study and visualize the relationships between smoothies. We will construct a product map representing the global point of view of the subjects.

2. To study the agreements between the subjects, in order to determine if their answers are similar and if atypical subjects exist.

 

Setting Up

• Open XLSTAT.

• Click on the Sensory/ Rapid tasks menu and select the Projective mapping data analysis feature.

• 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.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

After showing descriptive statistics and eigenvalues, the 2D map reveals product proximities. "Casino_PBC" and "Innocent_PBC" are perceived as similar, differing from "Casino_SRB", while "Innocent_SB" and "Immedia_MP" are positioned oppositely.

The RV matrix shows subject similarity. Subject 1 is closely aligned with subject 2 but differs significantly from subject 4, who also shows low similarity with many others.

Scaling factors show how much each subject used the available space. Higher factors mean lower usage. Here, subjects 3 and 8 used the sheet space the least, clustering their product placements closely.

It is useful to assess each subject's proximity to the overall consensus. The bar chart shows subjects 2 and 4 as atypical, unlike subjects 18 and 23 who align closely with the consensus.

The graph shows residuals by product, highlighting smoothies placed similarly by subjects (e.g., "Innocent_PBC") versus those placed more variably (e.g., "Carrefour_SB").

The subject homogeneity index (ranging from 1/m to 1) measures consensus among subjects—the closer to 1, the more homogeneous the responses. Here, homogeneity is medium, suggesting clustering (e.g., with CLUSTATIS) may help identify groups with similar views.