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Results for criterions: Keyword: Odd Modify search criterions 1 match Title A measurement for numbers recorded on [0,1] with a cursor during the presentation of pairs of stimuli Author MAURIN Michel Keywords Bounded continuum, Cross-ratio, Design of experiment, Homographic function, Measurement theory, Odd, Stimuli's couple Topic None Abstract 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. Number 196, Winter 2011 Language   French Read the article Users rights : The entire journal is licensed under a Creative Commons license