It is customary to train participants in the magnitude estimation process before attempting to apply it to the evaluation of tasks in a usability study. About 20 years later, McGee (2003, 2004) published favorable papers describing his applications of UME to the measurement of usability. Cordes (1984a,b) had participants draw lines to represent the relative ease of completing tasks in a usability study. There have been a few published attempts to apply magnitude estimation methods to the study of the perception of usability. In a usability testing context, the goal of UME is to get a measurement of usability that enables ratio measurement, so a task (or product) with a perceived difficulty of 100 is perceived as twice as difficult as a task (or product) with a perceived difficulty of 50. In magnitude estimation, participants judge the intensity of a stimulus against a baseline stimulus (e.g., how bright a stimulus light is as a ratio of the perceived brightness of a reference light-five times as bright, half as bright, etc.). In his work, Fechner developed a variety of experimental methods, one of which was magnitude estimation. Psychophysics had its start in the early- to mid-19th century with the work of Weber (on just noticeable differences) and Fechner (sensory thresholds), culminating in Fechner’s Law ( Massaro, 1975): S = k(log 10 I)-that there is a logarithmic relationship between the intensity of a physical stimulus ( I) and its perceived sensation ( S), replaced in most psychophysics work about 100 years later by Stevens’ Power Law: S = kI n, which provided a better fit for most relationships ( Mussen et al., 1977). Magnitude estimation has a rich history in psychophysics, the branch of psychology that attempts to develop mathematical relationships between the physical dimensions of a stimulus and its perception. Lewis, in Quantifying the User Experience (Second Edition), 2016 Description of UME The lesson to be absorbed is that a magnitude estimate provides some limited information about the subject's assessment of the stimulus, but is never to be taken at its face value. So this second suggestion employs the same mathematical theory as the first, but now directed toward the relationships between different experimental paradigms, including the classical psychophysical methods listed above. Inverse variance is Fisher's ( 1922) measure of information and is closely related to d′ 2. An ‘analysis of variance’ of sensory judgment provides a second vehicle of enquiry. That precision varies inversely with the square of the log stimulus range and also depends on the randomness of the stimulus presentation schedule. The inverse variance in units of log stimulus magnitude measures the precision of the judgments. Magnitude estimation and category judgment may be meaningfully analyzed using a multistimulus elaboration of the normal signal detection model, with a separate normal distribution for each stimulus value (the Law of Categorical Judgment, Case IC Torgerson 1958). Laming, in International Encyclopedia of the Social & Behavioral Sciences, 2001 3.2 The Precision of Sensory Judgment
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