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On the Measurement of Movement Difficulty in the Standard Approach to Fitts' Law  [PDF]
Yves Guiard, Halla B. Olafsdottir
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0024389
Abstract: Fitts' law is an empirical rule of thumb which predicts the time it takes people, under time pressure, to reach with some pointer a target of width W located at a distance D. It has been traditionally assumed that the predictor of movement time must be some mathematical transform of the quotient of D/W, called the index of difficulty (ID) of the movement task. We ask about the scale of measurement involved in this independent variable. We show that because there is no such thing as a zero-difficulty movement, the IDs of the literature run on non-ratio scales of measurement. One notable consequence is that, contrary to a widespread belief, the value of the y-intercept of Fitts' law is uninterpretable. To improve the traditional Fitts paradigm, we suggest grounding difficulty on relative target tolerance W/D, which has a physical zero, unlike relative target distance D/W. If no one can explain what is meant by a zero-difficulty movement task, everyone can understand what is meant by a target layout whose relative tolerance W/D is zero, and hence whose relative intolerance 1–W/D is 1 or 100%. We use the data of Fitts' famous tapping experiment to illustrate these points. Beyond the scale of measurement issue, there is reason to doubt that task difficulty is the right object to try to measure in basic research on Fitts' law, target layout manipulations having never provided users of the traditional Fitts paradigm with satisfactory control over the variations of the speed and accuracy of movements. We advocate the trade-off paradigm, a recently proposed alternative, which is immune to this criticism.
VALIDITY, RELIABILITY AND DIFFICULTY INDICES FOR INSTRUCTOR-BUILT EXAM QUESTIONS  [PDF]
Gholamreza JANDAGHI,Fatemeh SHATERIAN
Journal of Applied Quantitative Methods , 2008,
Abstract: The purpose of the research is to determine college Instructor’s skill rate in designing exam questions in chemistry subject. The statistical population was all of chemistry exam sheets for two semesters in one academic year from which a sample of 364 exam sheets was drawn using multistage cluster sampling. Two experts assessed the sheets and by using appropriate indexes and z-test and chi-squared test the analysis of the data was done. We found that the designed exams have suitable coefficients of validity and reliability. The level of difficulty of exams was high. No significant relationship was found between male and female instructors in terms of the coefficient of validity and reliability but a significant difference between the difficulty level in male and female instructors was found(P<.001). It means that female instructors had designed more difficult questions. We did not find any significant relationship between the instructors’ gender and the coefficient of discrimination of the exams.
Is Fitts’ Law Continuous in Discrete Aiming?  [PDF]
Rita Sleimen-Malkoun, Jean-Jacques Temprado, Raoul Huys, Viktor Jirsa, Eric Berton
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0041190
Abstract: The lawful continuous linear relation between movement time and task difficulty (i.e., index of difficulty; ID) in a goal-directed rapid aiming task (Fitts’ law) has been recently challenged in reciprocal performance. Specifically, a discontinuity was observed at critical ID and was attributed to a transition between two distinct dynamic regimes that occurs with increasing difficulty. In the present paper, we show that such a discontinuity is also present in discrete aiming when ID is manipulated via target width (experiment 1) but not via target distance (experiment 2). Fitts’ law’s discontinuity appears, therefore, to be a suitable indicator of the underlying functional adaptations of the neuro-muscular-skeletal system to task properties/requirements, independently of reciprocal or discrete nature of the task. These findings open new perspectives to the study of dynamic regimes involved in discrete aiming and sensori-motor mechanisms underlying the speed-accuracy trade-off.
Assessment of Validity, Reliability and Difficulty Indices for Teacher-built Physics Exam Questions in First Year High School  [PDF]
G Jandaghi
Arts and Social Sciences Journal , 2011,
Abstract: The purpose of the research is to determine high school teachers’ skill rate in designing exam questions in physics subject. The statistical population was all of physics exam shits for two semesters in one school year from which a sample of 364 exam shits was drawn using multistage cluster sampling. Two experts assessed the shits and by using appropriate indices and z-test and chi-squared test the analysis of the data was done. We found that the designed exams have suitable coefficients of validity and reliability. The level of difficulty of exams was high. No significant relationship was found between male and female teachers in terms of the coefficient of validity and reliability but a significant difference between the difficulty level in male and female teachers was found (P<0.001). It means that female teachers had designed questions that are more difficult. We did not find any significant relationship between the teachers’ gender and the coefficient of discrimination of the exams.
Rate of validity, reliability and difficulty indices for teacher-designed exam questions in first year high school
Gholamreza Jandaghi,Fatemeh Shaterian
International Journal of Human Sciences , 2008,
Abstract: The purpose of the research is to determine high school teachers’ skill rate in designing exam questions in mathematics subject. The statistical population was all of mathematics exam shits for two semesters in one school year from which a sample of 364 exam shits was drawn using multistage cluster sampling. Two experts assessed the shits and by using appropriate indices and z-test and chi-squared test the analysis of the data was done. We found that the designed exams have suitable coefficients of validity and reliability. The level of difficulty of exams was high. No significant relationship was found between male and female teachers in terms of the coefficient of validity and reliability but a significant difference between the difficulty level in male and female teachers was found (P<.001). It means that female teachers had designed more difficult questions. We did not find any significant relationship between the teachers’ gender and the coefficient of discrimination of the exams.
Cortical Correlates of Fitts’ Law  [PDF]
Peter J. Ifft,Mikhail A. Lebedev,Miguel A. L. Nicolelis
Frontiers in Integrative Neuroscience , 2011, DOI: 10.3389/fnint.2011.00085
Abstract: Fitts’ law describes the fundamental trade-off between movement accuracy and speed: it states that the duration of reaching movements is a function of target size (TS) and distance. While Fitts’ law has been extensively studied in ergonomics and has guided the design of human–computer interfaces, there have been few studies on its neuronal correlates. To elucidate sensorimotor cortical activity underlying Fitts’ law, we implanted two monkeys with multielectrode arrays in the primary motor (M1) and primary somatosensory (S1) cortices. The monkeys performed reaches with a joystick-controlled cursor toward targets of different size. The reaction time (RT), movement time, and movement velocity changed with TS, and M1 and S1 activity reflected these changes. Moreover, modifications of cortical activity could not be explained by changes of movement parameters alone, but required TS as an additional parameter. Neuronal representation of TS was especially prominent during the early RT period where it influenced the slope of the firing rate rise preceding movement initiation. During the movement period, cortical activity was correlated with movement velocity. Neural decoders were applied to simultaneously decode TS and motor parameters from cortical modulations. We suggest that sensorimotor cortex activity reflects the characteristics of both the movement and the target. Classifiers that extract these parameters from cortical ensembles could improve neuroprosthetic control.
Beyond the Shannon-Khinchin Formulation: The Composability Axiom and the Universal Group Entropy  [PDF]
Piergiulio Tempesta
Physics , 2014,
Abstract: The notion of entropy is ubiquitous both in natural and social sciences. In the last two decades, a considerable effort has been devoted to the study of new entropic forms, which generalize the standard Boltzmann-Gibbs (BG) entropy and are widely applicable in thermodynamics, quantum mechanics and information theory. In [23], by extending previous ideas of Shannon [38], [39], Khinchin proposed an axiomatic definition of the BG entropy, based on four requirements, nowadays known as the Shannon-Khinchin (SK) axioms. The purpose of this paper is twofold. First, we show that there exists an intrinsic group-theoretical structure behind the notion of entropy. It comes from the requirement of composability of an entropy with respect to the union of two statistically independent subsystems, that we propose in an axiomatic formulation. Second, we show that there exists a simple universal class of admissible entropies. This class contains many well known examples of entropies and infinitely many new ones, a priori multi-parametric. Due to its specific relation with the universal formal group, the new family of entropies introduced in this work will be called the universal-group entropy. A new example of multi-parametric entropy is explicitly constructed.
Performance is not Related to Perception of Target Width in Fitts’ Law  [cached]
Zelaznik Howard N.,Croxall Roxanne,Vanhooser Jake
BIO Web of Conferences , 2011, DOI: 10.1051/bioconf/20110100100
Abstract: We report a new experiment in a series of studies in which research participants perform a Fitts’ Law repetitive task, and then are required to judge the width of the target that was utilized. The first two experiments previously reported showed no relation between perception and performance. However in those two experiments subjects were never provided with feedback on their performance. In the current study, we provided participants with their performance score. Providing their performance score did not produce a relation between target width perception and performance. We posit that sports studies that have shown this relation are the results of intimate knowledge of what it means to perform well. Our inexperienced Fitts’ Law participants lacked such an understanding.
Age-related dedifferentiation of cognitive and motor slowing: insight from the comparison of Hick–Hyman and Fitts’ laws  [PDF]
Rita Sleimen-Malkoun,Jean-Jacques Temprado,Eric Berton
Frontiers in Aging Neuroscience , 2013, DOI: 10.3389/fnagi.2013.00062
Abstract: The present study aimed to determine whether the general slowing hypothesis (GSH) could be extended to the motor domain by comparing cognitive and motor age-related slowing. To achieve this objective, we compared the slopes of Hick–Hyman’s law and Fitts’ law, in young and older adults. The general hypothesis was that, due to the dedifferentiation of cognitive and motor neural resources during aging, the slopes of Hick–Hyman’s law and Fitts’ law should become closer, if not similar, in older adults. Ten young adults (mean age = 26 ± 3 years) and 14 older adults (mean age = 78 ± 7 years) participated in the experiment. They had to perform a discrete rapid-aiming task and a reaction time (RT) task. In the aiming task, five index of difficulty (ID) levels were used (from three to seven bits by increments of 1.0 bit). Task difficulty was scaled via the manipulation of target distance from home position. In the RT task, five IDs were selected: 0, 1, 2, 3, and 4 bits, with incompatible S–R associations. RT and movement times were recorded. Efficiency and Brinley regression functions were calculated. Age-related slowing ratios were estimated. Response times increased in both tasks in older adults. The slopes of Hick–Hyman’s law and Fitts’ law were steeper in older adults than in young participants. In young participants, the slope of Hick–Hyman’s law was smaller than that of Fitts’ law. In older adults, no difference was found. Slowing ratios observed in both tasks were equivalent. The present results extended the GSH to the motor domain. They suggested that, due to dedifferentiation of cognitive and motor neural resources, decrease in processing speed acts as a common cause to behavioral slowing in both cognitive and motor tasks.
Re-Formulation of Mean King’s Problem Using Shannon’s Entropy  [PDF]
Masakazu Yoshida, Hideki Imai
Journal of Quantum Information Science (JQIS) , 2013, DOI: 10.4236/jqis.2013.31002
Abstract:

Mean King’s problem is formulated as a retrodiction problem among noncommutative observables. In this paper, we reformulate Mean King’s problem using Shannon’s entropy as a first step of introducing quantum uncertainty relation with delayed classical information. As a result, we give informational and statistical meanings to the estimation on Mean King problem. As its application, we give an alternative proof of nonexistence of solutions of Mean King’s problem for qubit system without using entanglement.

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