Constructing meaningful numerical response when evaluating (dis)comfort perception in a univariate case

Abstract

In many ergonomic studies, one is interested by the responses of subjects in relation to their environment. The experimental situations are described by geometrical or physical variables, while the subject's responses are recorded frequently by ordered category scales. The critical issue is how to obtain a numerical value for categorical responses. Here, we present a new way of obtaining a numerisation of categorical responses within the general framework of measurement theory. It focuses on the existence of a numerical representation, which can be demonstrated by theorems. Then, the meaningfulness of later numerical statements can be investigated, and a relevant embedding of data can be obtained in numerical and vectorial spaces. This is the case for ordered category scales with the Adams and Messick ‘successive intervals’ method. The method is illustrated by five examples in a univariate situation. The proposed method is also compared with three usual numerical scales in ergonomics.

Keywords:

• rating scale
• category scale
• (dis)comfort evaluation
• successive intervals method
• measurement theory

Notes

1. However Arts and Sciences are much more associated with the Rousseau Discours than opposed such as in our discussion.

2. The system is over-determined as long as (I − 1) (J − 3) > 0, with 2I + J − 1 unknown values and I(J − 1) + 2 relations.