Fitts’s Law - Modeling Target Movement Time in HCI. according to Fitts' Law, a quantitative measure of the difficulty of performing a skill involving both speed and accuracy requirements manual aiming skills motor skills that involve arm, hand, and/or finger movement to a target; e.g., putting a key into a keyhole, threading a needle with thread, and typing on a computer keyboard It is possible for criterion-referenced tests to have many questions with p-values close to 1.0. Fitts’ law is a factual model used to represent the speed accuracy trade off features of human muscle movement, with analogy method to Shannon’s channel capacity theorem. That is why some statisticians also call the difficulty index “the easiness index” when they are performing an item analysis on data sets that have to do with education. 7 0 obj The formula looks like this: the number of students who answer a question correctly (c) divided by the total number of students in the class who answered the question (s). stream endstream endobj x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �1Up�W� stream As mentioned earlier, Index of Difficulty describes the number of bits of information transmitted within the context of human motor system. Fitts’ Law Index of Difficulty Evaluated and Extended for Screen Size Variations, User Interfaces, Rita Matrai, IntechOpen, DOI: 10.5772/9496. x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �1Wp�W� movement time. endobj to Fitts’ law, movement time scales linearly with a single quantity, the index of difficulty (ID), which quantifies task difficulty through the quotient of target width and distance. Determining the validity of individual question items on a test is vital, especially for standardized tests, the results of which can dictate the amount of money a school will receive in federal funding or even if students will be accepted to college. From this formula we can see that the task gets harder, the farther away the target is … endobj Different types of tests aim for different levels of easiness. In the scenario with students answering questions on a test, higher p-values, or p-values closer to 1.0, correspond with a greater proportion of students answering that question correctly. /Contents 22 0 R>> Item discrimination is measured in a range between -1.0 and 1.0. 14 0 obj <> 11 0 obj We tested a hypothesis that the classical relation between movement time and index of difficulty (ID) in quick pointing action (Fitts' Law) reflects processes at the level of motor planning. endobj � ��� /Length 5725 >> As expected, movement time for hard tasks is longer than for easy tasks. <> (Fitts, 1954; Fitts & Peterson, 1964). /Contents 20 0 R>> t = a + b ID (1) ID = log2(A/W+1) (2) In Eqs. � ��� [V)֕H)]���t�,��1̧�t7���������w�(��Zw�?.�w�w�l��:���u���YkH�Ŧ�Yzl���Ҟ�D���o����I�0��~�P����{�_�7�����6�`P�v?��@����VHp�����SQ�h��T!�z��y����>���5h���a/�Խ@t)�_����\2�{;`�C���|��M�@Z����7[��b�ETZI[EU@^k��g������k����{v}���Ȯ��8L����!YO'�:|�̖0)�ZL e��{�7_�g��=���we�2z���h�Ak��߽/L� 3{��m�C�b��"p��7 �M�9��>V�|v��26�C>M���'L>,*���������}��d�� w_-�a��vo�1(�o��%��c�2���w>��$+:�A��y�u0##l�-��`4��=0��`�v��҆�Y. 4 0 obj Fitts’ law remains silent, however, on how ID affects the dynamic and kinematic patterns Now that we’ve seen Fitts’ Law applied in a simple setting, let’s see the nuts and bolts of the law. P-values are found by using the difficulty index formula, and they are reported in a range between 0.0 and 1.0. P-values are found by using the difficulty index formula, and they are reported in a range between 0.0 and 1.0. They do this by running statistical analyses of individual test questions. endobj /Contents 24 0 R>> The term Log 2 (2A/W) is referred to as the index of difficulty (abbreviated ID), which seems to define the difficulty of the various combinations of A and W. Therefore, Fitts' Law says that MT is linearly related to the Log 2 (2 A / W ), or simply, that MT is linearly related to the index of difficulty (ID). <> � ��� The first thing to note about Fitts' Law is that it is an equation that calculates something called the Index of Difficulty. Test takers with mastery of the material should be more likely to answer a question correctly, whereas students without mastery of the material should get the question wrong. Fitts defined the term Index of Difficulty (ID, shown in Figure 3), as a measure of the task difficulty as follows: (3) Mackenzie (MacKenzie 1992), suggested a more stable model for the Fitts Law, which works better -also more like the Shannon’s original formula- for the small values of ID as follows: (2a) (3a) Negative discrimination indicates that students who are scoring highly on the rest of the test are answering that question wrong. If tests do not measure the standards they intend to measure, then their results are not valid, and they cannot be used to judge schools, teachers or individual students. Subtract the number of students in the lower-scoring group who answered the question correctly (lc) from the number of students in the higher-scoring group who answered the question correctly (hc). Norm-referenced tests, for example, will have questions with varying levels of easiness because they are trying to create a wider spread in scores and categorize test takers into norms. <> This process is also called item analysis. /Contents 8 0 R>> <> Fitts’ law is centered around a mathematical equation that is used to illustrate the time it takes to reach a target object. 26 0 obj 1 0 obj <> 6 0 obj 22 0 obj A movement model based on Fitts' law is an equation predicting movement time ( ) from a task's index of difficulty ( ). Item discrimination evaluates how well an individual question sorts students who have mastered the material from students who have not. W is the width of the target. <> endobj Corners -As the mouse cursor stops at the edge of the screen, corners can be considered to have an "infinite" width. <> You have a class of 20 students, so after you arrange them by score in a table, you should have 10 on each side of the dividing line. 3 0 obj <> A java application that tests Fitts Law’s Index of difficulty formula most commonly used in Human Computer Interaction and known as Shannon’s formula. endobj <> endstream <>>>] endobj /Contents 18 0 R>> The only difference is that p-value is left as a decimal point and is not converted to a percentage value out of 100. endobj Review, 1979). 19 0 obj Determining item discrimination is more complicated and involves more steps than finding an item’s difficulty. 219 stream You might be surprised to learn that curriculum writers have to test the validity of their assessments. x��\ێGr�8_�OF�w����5��%�v���-a�~(�5�^5{��f�ϰ��'>��UY�M �%ꮮ�Kdĉ���J��WBҿ����\}��$~x%�W�T�Q���z#>�����Iܼ������*O+a��.��%'n�\}ש Fw*��Ο�f��A����W�"���.��^jyk0��bke��^_-�>a���@^J�]�� ��������R7�ۍr�{*��I������}��0.��m��G�gw���R����������{��1�� ��[�p~��~Z��0��:�rV�[���r;�,��~`���]�����Нꝁ�lU�"my�Abt]N����,�ϐqA���y{�Vwܜ��&ev� �pa�o�%���gg��s�q��? the whole, Equation 3, known as the Shannon formulation, is prefenwd because it provides a slightly better fit with observations, exactly mimics the information theorem underlying Fitts’ law, and always gives a positive rating for the index of task difficulty. endobj � ��� Two statistical methods used in item analysis are the item difficulty index and the item discrimination index. Example: Out of the 20 students who answered question five, only four answered correctly. stream <> Hidehiko Okada and Takayuki Akiba (May 1st 2010). 15 0 obj Because the resulting p-value is closer to 0.0, we know that this is a difficult question. Criterion-referenced tests, on the other hand, are trying to measure mastery. endobj endstream The discrimination index is another way that test writers can evaluate the validity of their tests. endobj As … endstream stream endobj W/2 stream endobj endstream stream <> Essentially, a standardized test that has not been statistically analyzed before it is given is useless. Questions that do a good job of sorting those students who have mastered the material from students who have not are called “highly discriminating.” Such tests can be very beneficial, especially in areas where mastery is key, such as in medical certification. 13 0 obj The user needs much less precision because they can simply fling the mouse in the direction of a corner and the limitations of the screen restrict where the pointer ends up. A Note on the Validity of the Shannon Formulation for Fitts’ Index of Difficulty. endobj Fitts's law (often cited as Fitts' law) is a model of human movement in human-computer interaction and ergonomics which predicts that the time required to rapidly move to a target area is a function of the distance to and the size of the target. 25 0 obj Review, 1988) posit that Fitts’s Law is the result of the choice of the duration of the initial submovement, and that the submovement duration choice adheres to the linear speed accuracy trade-off principles outlined by Schmidt et al. endobj Open Journal of Applied Sciences Vol.3 No.6，October 16, 2013 DOI: 10.4236/ojapps.2013.36046 4,299 Downloads 6,203 Views Citations x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �14Rp�W� A central thesis in Fitts' work is that throughput is independent of movement amplitude and target width, as … If six students in the higher-scoring group answered the question correctly, and six students in the lower-scoring group also answered the question correctly, you should already know without doing the math that the item is not very discriminatory. (Psych. endobj Specifically, Specifically, ID = log 2 (2 A / W ) 12 0 obj 1. Then, divide the resulting number by the number of students on each side of your dividing line, which should be half of the class (t). The critical variable is the ID, which depends on the amplitude ( A ) of the movement (i.e., the distance separating the targets) and the width ( W ) of the targets. /Contents 6 0 R>> stream /Contents 16 0 R>> According to Fitts, a movement tasks' difficulty (ID, the "index of difficulty") can be quantified using information theory by the metric "bits". On the other hand, Meyer et al. stream 9 0 obj endstream <> This is a unitless numberthat is used to describe how difficultit is for users to point at something. Fitts' law is a well established empirical formula, known for encapsulating the "speed-accuracy trade-off". endobj <> /Group <> endobj The prediction equation for the line in … x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �14Pp�W� endobj First, create a table of your students along with their test scores. Fitts’ law states that it takes more time to hit a target if the target is further away and it also takes more time if the target is smaller. However, we can still measure with the formula. The equation for the standard normal distribution f(x) is 2 2 2 1 ( ) x f x e π (8) The area beneath f(x) from -z to +z gives the probability of a hit within that range. The item difficulty index measures how easy a question is by determining the proportion of students who got it right. Because it has no units, it can be a little tricky to … Fitts' Law states that _____ is linearly related to index of difficulty (ID). � �]� 18 0 obj endstream <> Figure 3 shows the general idea. Fitts Law Fitts law is a descriptive model of human movement. Index of difficulty (ID) is defined by Fitts’ law. /Contents 12 0 R>> <> MT = a + b log 2 (A / W + 1) Where MT is the dependent variable a and b are regression coefficients A is the distance or amplitude to move The index of difficulty (ID) of the task is the numerator and the mean movement time (MT) is the denominator: (17.3) With ID in bits and MT in seconds, TP has units bits per second or bits/s. a theory of task-difficulty in which the movement time (MT) for a hand-position task was given as: MT = K log (~2) A 2! Ian Scott MacKenzie. Fitts’ law relates movement time (MT) to the index of difficulty following the equation: , where α and β are empirical constants depending upon the individual and the task, and . (Psych. /Contents 26 0 R>> /Contents 14 0 R>> This formula predicts linear increases in MT with increases in the index of difficulty (ID), defined as Log2(2D/W). 8 0 obj Fitts’s law is expressed mathematically by the following formula: where MT denotes movement time, ID the index of difficulty of the movement and a and b are empirical constants. The item difficulty index is often called the p-value because it is a measure of proportion – for example, the proportion of students who answer a particular question correctly on a test. The key statement of Fitts’s Law is that the time required to move a pointing device to a target is a function of the distance to the target and its size. 17 0 obj endstream endobj x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �14Tp�W� <> The opposite is also true. x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �1Tp�W� endobj index of difficulty. Movement time prediction. 24 0 obj Fitts’ Law predicts that the time to point at an object using a device is a function of the distance from the target object & the object’s size. � ��� endstream <> The item difficulty index is a common and very useful analytical tool for statistical analysis, especially when it comes to determining the validity of test questions in an educational setting. Fitts' law also states that the target acquisition time increases drastically if the target gets tiny. Although the number could be higher, this question would still be a decent indicator of whether or not the student understood the material. Rebecca Renner is a teacher and college professor from Florida. endobj %PDF-1.4 In other words, easier test questions will have greater p-values. <> The formulation of Fitts's index of difficulty most frequently used in the human–computer interaction community is called the Shannon formulation: x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �1Rp�W� Fitts’s law holds that the time, T, to complete a speeded movement to a target is a linear function of an index of difficulty, ID, characterizing the movement: T D a C b ID. � ��� <> For highly discriminating questions, students who answer correctly are those who have done well on the rest of the test. x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �Tp�W� � �T� In a third column, indicate whether the student answered the question you are measuring correctly by placing a 1 (for correct answers) or a 0 (for incorrect answers) in the corresponding box. Fitts's law is a model of speed-accuracy tradeoffs used in human–computer interaction and ergonomics.It predicts time required to acquire a target on screen as a function of the distance to the target and the size of the target. This is partly w… <> She loves teaching about literature, and she writes about books for Book Riot, Real Simple, Electric Literature and more. 10 0 obj /Contents 10 0 R>> ; �,G���i�u���& ��^l5�Β���I�S����@�Q��v? THEORY. Available from: � ��� The formula for this problem should look like this: This item is not a good measure of mastery because its discrimination index is zero. <>/Group <> Students who answer highly discriminating questions incorrectly tend to do poorly on the rest of the test as well. GitHub - unaizafaiz/FittsLaw: A java application that tests Fitts Law’s Index of difficulty formula most commonly used in Human Computer Interaction and known as Shannon’s formula. stream � �f� endstream In the scenario with students answering questions on a test, higher p-values, or p-values closer to 1.0, correspond with a greater proportion of students answering that question correctly. Test writers should reevaluate questions that result in negative discrimination because they do not help to show mastery. Both statements are in accordance with common sense. � ��� x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �1Sp�W� Rebecca Renner - Updated December 11, 2018, Copyright 2020 Leaf Group Ltd. / Leaf Group Education, Explore state by state cost analysis of US colleges in an interactive article, University of Wisconsin-Oshkosh: Item Analysis, Cogent Education: Using Reliability and Item Analysis to Evaluate a Teacher-Developed Test in Educational Measurement and Evaluation. Named the Index of difficulty, D is the distance from the starting point to the center of the target. 21 0 obj 27 0 obj 16 0 obj x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �1Vp�W� Fitts’ original formula was based on Shannon’s theorem (Shannon, stream Divide the table in half between high and low scorers, with an equal number of students on each side of the dividing line. Effects of Gain and Index of Difficulty on Mouse Movement Time and Fitts’ Law Abstract: The mouse, being the major means of inputting and controlling data on a computer, should beset right for best performance. There are several different formulas that calculate item discrimination, but the one that is most commonly used is called the point-biserial correlation, which compares a test taker’s score on an individual item with their score on the test overall. 5 0 obj If, however, six students in the higher-scoring group answer correctly, and only two students in the lower-scoring group answer correctly, the item is a much better measure of mastery. x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �Pp�W� This could mean that there is a problem with the question, such as bias or even a typo in the answer key. <> MT ID Figure 3. 2.066 2 b 1 MTe a A W z (7) Having obtained the z-score from Fitts’ law parameters, we use ±z to calculate the probability of a selection occurring within that range. x�3R��2�35W(�*T0P�R0T(�Y@���@QC= P A�J��� �1Qp�W� The mathematical formula behind Fitts’ law, as shown in the image at the top of this article, is T (Time) = a + b log 2 (2 D (Distance)/ W (Width) . (1) The index of difficulty depends on the target distance, D, from the starting point to the center of the target, and the target width, W. The definition of ID has evolved � � � 23 0 obj The second major contribution of Fitts’ law are the measures to assess Index of Difficulty, Throughput, and predicted Movement Time. Now, arrange your students from highest scorers to lowest scorers, with the highest scorers at the top. The item discrimination index measures how well a test question can help examiners differentiate between test takers who have attained mastery of the material and those who have not. 20 0 obj <> The law (in the Shannon formulation [MacKenzie and Buxton 1992]) states that where A is the task's amplitude or distance, W is the target's width, and the resulting ID is the aforementioned Index of Difficulty. The answer will equal a value between 0.0 and 1.0, with harder questions resulting in values closer to 0.0 and easier questions resulting in values closer to 1.0. endstream <> It is well-known as Fitts law that the time for a user to point a target can be modelled as a linear function of index of difficulty (ID), where ID is formulated as a function of the target size and distance (Fitts, 1954; MacKenzie, 1992). When teachers and curriculum writers are developing tests to give to students, they can’t just write a test and assume it will measure the standards they wish to assess. endobj The generic formulation of Fitts’ Law for this assignment in the form of a linear regression is as follows: MT= a+ b ID where MTis the movement time, and IDis the index of di culty of the movement task. endobj /Contents 4 0 R>> stream stream Fitts' Law states that movement time is linearly related to _____. The difficulty index formula is fairly easy to remember because it is the same as determining the percentage of students who answered the question correctly. In layman’s terms: **the closer and larger a target, the faster it is to click on that target**. endstream How well an individual question sorts students who answered question five, four. The item discrimination is more complicated and involves more steps than finding an item ’ s.... For criterion-referenced tests to have many questions with p-values close to 1.0 transmitted... Indicates that students who answer correctly are those who have done well on the rest of the test well... Item analysis are the item difficulty index and the item discrimination index, only four answered correctly measures how a! Highest scorers at the top difficulty, D is the distance from the starting point to the center of test... And is not converted to a percentage value out of the test as well it to. 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Renner is a descriptive model of human movement easy a question is by determining the proportion of students each! As a decimal point and is not converted to a percentage value out of.... That test writers should reevaluate questions that result in negative discrimination indicates that students who not. Or not the student understood the material known for encapsulating the `` speed-accuracy trade-off '' of tests... Levels of easiness increases in the answer key Book Riot, Real,... As mentioned earlier, index of difficulty ( ID ), defined as log2 ( )..., defined as log2 ( 2D/W ) and the item difficulty index measures how easy a is! Curriculum writers have to test the validity of their tests discrimination indicates that students who correctly... Analyzed before it is given is useless '' width fitts ' Law is a established. Who are scoring highly on the rest of the screen, corners be. 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A target object still be a little tricky index of difficulty formula fitts' law … Hidehiko Okada Takayuki! Of bits of information transmitted within the context of human motor system and college professor from Florida the are!

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