Un mesurage pour les nombres recueillis [0,1] avec un curseur, au cours de présentations par couple de stimuli

Mathématiques et sciences humaines. Mathematics and social sciences

Maurin, Michel¹ 

关键词: measurement theory;    bounded continuum;    cross-ratio;    design of experiment;    homographic function;    odd;    stimuli’s couple;   

DOI  :  10.4000/msh.12132

学科分类：数学（综合）

来源: College de France * Ecole des Hautes Etudes en Sciences Sociales (E H E S S)

【 摘 要 】

Many methods for recording subject's responses in surveys are available. One of them is to mark a sign on a horizontal segment of a straight line drawn in the questionnaire, as a graphical valuation. It is like the use of an individual cursor on [0,1]. In this way, the response is a number, but a number subject to important boundary effects close to the two endpoints of the continuum of possible responses, and indeed the usual and common numerical operations on numbers are not valid here. The object of this paper is to propose a measurement scale for these numbers included in the general framework of measurement theory, with a representation theorem, a uniqueness theorem, and meaningfulness of statistical statements. The stimuli are presented in pairs (two by two), and the technical tools used here are the cross-ratio and a group of homographic functions. Finally one observes that simple transforms of responses on [0,1] are measured on more usual and familiar scales of measurement (ratio and difference scales). This leads to a number of possible, common and meaningful statistical processings that can be applied to these transformed cursor-[0,1]'s responses.

【 授权许可】

Unknown