We propose and evaluate numerical and visual methods for investigating paired comparisons after principal component analysis (PCA). PCA results can be visualized to facilitate an understanding of the relationships between the products and the sensory attributes. But identifying and visualizing significant product differences in multiple PCs simultaneously is not straightforward. A benefit of the proposed methods is that they provide a screening tool for evaluating PCA results rapidly. We begin with <\/p>\n\n\n\n\n\n\n\n
a real data set which is analyzed and submitted to the truncated total bootstrap (TTB) procedure. This TTB procedure simulates and analyzes results from virtual panels. The TTB-derived results form clouds of uncertainty around each product and paired comparison. These clouds can be visualized directly or by plotting the contours that enclose the highest 95% of their kernel-estimated densities. We find that these density regions tend to be smaller and mostly fit inside the 95% confidence ellipsoids that we propose in this manuscript. We show how to calculate the volumes of these confidence ellipsoids, which quantify uncertainty. We also show how to calculate P values to evaluate whether pairs of products are discriminated in the PCA subspace. The interpretation of these P values coincides with the visual interpretation of the confidence ellipsoids. We illustrate the methods with two real data sets, one a sensory quantitative-descriptive sensory data set from a trained panel, the other a consumer check-all-that-apply (CATA) data set. We also conduct a simulation study based on each of these data sets. The results from these simulation studies show that under repetition, approximately 95% of the ellipsoids covered the true result. This indicates that the proposed ellipsoids have an approximately frequentist interpretation. The complementary numerical and visual approaches can be applied to a wide range of data sets from sensory evaluation and to data from other domains.<\/p>\n\n\n\n
Castura, J.C., Varela, P.A., & Naes, T. (2022). Evaluation of complementary numerical and visual approaches for investigating pairwise comparisons after principal component analysis. Sensometrics 2022<\/em>. 15-17 November. Virtual Meeting. (Oral Presentation).<\/p>\n\n\n\n