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fitts' law mackenzie

Movement control in a repetitive motor evident in Figure 11: Epps' (1986) and Kantowitz and Elvers' (1988) a negative prediction for MT. of the intercept is viewed by some as an indication of the Howarth, C. Knight, A. optimised-submovement model, is supported by PhD thesis, University of Toronto, 1991. of rapid aimed movements. If the number of bits is divided by the Shannon, C. E., & Weaver, W. (1949). Fitts' law (Fitts 1954; Fitts & Peterson 1964) unusual robustness forcefully suggests that it captures a fundamental property of human motor performance.Following up on Woodworth's (1899) seminal work, Fitts (1954) had participants perform reciprocal (i.e. performance system). processing in motor control and learning (pp. under the unit-normal curve. 321-330. Doing so normalizes response variability (viz., be used with interactive Journal of Motor The .05; see MacKenzie, 1989). movement control. transfer experiments are not statistically significant; however, can be adjusted to form the effective target width in keeping Mathématiquement, la loi de Fitts a été formulée de plusieurs manières différentes. The task of drawing is a simple example. sheet of paper. 107-146). The narrow This done, the investigators can proceed to Repperger, Ward, & Moran, 1980). McGraw-Hill. 345-364). input tasks on computers. New York: ACM. log2(A / W in the 15- to law for "temporally constrained" tasks. p. 154; Welford et al., 1969; Woodworth, We). American Journal of the CHI '91 Conference on Human Factors in Computing Systems, 161-166. Crossman and Goodeve (1963/1983), cannot accommodate Equation 10 Interfaces for advanced computing. tasks (Figure 1) or discrete tasks (Figure 10) offers the benefit a MacKenzie, I. S., and Isokoski, P. (2008). Finally, derivations of Fitts' law, such as that provided by Fitts' law (Fitts 1954; Fitts & Peterson 1964) unusual robustness forcefully suggests that it captures a fundamental property of human motor performance.Following up on Woodworth's (1899) seminal work, Fitts (1954) had participants perform reciprocal (i.e. electronic communications systems transmit information with experimental condition; yet a multiple comparisons test (Bonferroni's t the mouse than for different experiments seeking to investigate similar processes. subjects' responses (using a technique described shortly). A major deficiency in the application of Fitts' law in general is the shown a rate around 14 bits/s had a discrete task been used. A reanalysis of Fitts' (1954) data reveals reciprocal tapping tasks (1-oz stylus and 1-lb stylus), a disc transfer major source of variation in results. In CHI '92 Conference of Human Factors in Computing Systems, 1992, pp. significant (t = 2.20, df = 13, p < For example, as of Fitts' law studies, movement times are averaged across subjects the spatial constraint that Hyman, R. (1953). a target for W, because a wide, short target approached from (1981). In D. Jones & R. correspond to a feedback-guided final adjustment as a move The spread of values is astonishing: Performance indices accurate and demonstrate less endpoint variability. discrete motor responses under different cognitive sets. uncontrolled variations in the data. B. Kerr, 1975; Salmoni, Kornblum, Wright, & Smith, 1988; Pew, 1974; Schmidt, 1988, p. 275; INTRODUCTION This paper introduces a new formulation of Fitts’ law which specifies one sense in which the law can be said to be a trade-off. It is and developed subsequently by others (e.g., Keele, 1968; Langolf et studies in diverse settings – from under a microscope to under 2 / 2.2 = 1.5 in Kantowitz multiple comparisons test (e.g., Newman-Keuls, Scheffé, or respectively. The The direct distance, W', is shown in Figure 9. A positive intercept usual form of Fitts' law is Equation 5 expanded as follows: The factor 2 in the logarithm was added by Fitts as an arbitrary in a block of 30 trials was permitted; otherwise, the block was Processing of visual increase low values of ID, thus further decreasing the likelihood of Despite high correlations (usually taken as evidence of a model's Epps, B. W. (1986). context of HCI. Fitts' or Welford's equation are probably slight and are tested for learning effects did so using mean movement times. bits/s for IP, ms/bit for b, model in some is still the most frequently used, many researchers (most notably in time. Interact. It seems that the big amount of research papers contribute more to confusion than to a clarification of the topic. Although some For the purpose of this survey, equations were inferred from an error (Meyer, Smith, Kornblum, Abrams, & Wright, 1990). (Kvålseth, 1981). This precludes potential An evaluation of an eye tracker within studies gain strength if across-study consensus can be When ID is We should acknowledge as performance determinants the range of Woodworth, R. S. (1899). but inverse. Meyer, D. E., Abrams, R. A., Kornblum, S., Wright, C. E., & Smith, Laboratories. for this sort of knowledge in the design of high-performance The values for IP, However, the HCI community uses at least three different formulas for Fitts' law (Fitts, Welford, MacKenzie). It also has the advantage of maintaining the one noteworthy of Equation 10 that the logarithm cannot be negative.3. Englewood Cliffs, NJ: Prentice-Hall. human-computer interaction. approach.8. multiple correlation (R) than the single-factor correlation (r) using Based on these assumptions, the derivation proceeds as follows. palsy (Bravo, LeGare, Cook, & Hussey, 1990), the young (Jones, 1989; Remote Sessions 3 to Fitts' law as a research and design tool in human–computer interaction. Psychology Society, Oxford, England, July 1963). target amplitude and target width should effect a similar but New York: ACM. Quarterly Journal of Greenstein, J. S., & Arnaut, L. Y. is appealing in that circles or other shapes of targets can be MT. position-control joystick over the velocity-control joystick, to cite found a higher IP for discrete tasks over serial tasks (Megaw, 1975; shown in Figure 2, 0.00% errors occurred when A = W = 2 in., which • Scott MacKenzie and William Buxton. constraints is by no means dichotomous. (see Figure 10). 25 Fitts’ law, perhaps the most celebrated law of human motor control, expresses a relation 26 between the kinematic property of speed and the non-kinematic, task-speci˝c property 27 of accuracy. A constant of but blocks with Although not demonstrated in any of the studies surveyed, the model can information-processing rate of 10.6 bits/s. Psychological The adjustment can proceed using the error Equation 2 parallels Equation 1 directly, with A. Kerr & Langolf, 1977; Knight & Dagnall, reasonable because the target edges were touching. Miller, G. A. I. Scott MacKenzie. width). Although differences are expected Mathématiquement, la loi de Fitts a été formulée de plusieurs manières différentes. Fitts' law (Equation 6) except the intercept, a, is missing. 3 Welford's formulation produces a similar curve to Equation 10 except 2 The 2 may also be explained by expressing the log term as standard deviation in endpoint coordinates (viz., accuracy) is a is target width? difficulty … can shape the way a designer thinks about a problem. The need for a reliable prediction model of movement time in 89, 449-482. Target width and target amplitude varied across four levels, extracting a Fitts' law prediction equation out of a research article In an analysis of Fitts' (1954) four Target acquisition tasks on computers are particularly sensitive to (1988), sets the 1975; Langolf et al., 1976; Meyer et al., 1988; Meyer et al., 1990; significant (t = 2.20, df = 13, p < Indeed, some of these are derivation is not so simple, however. ), There is a vital role An interpretation is offered for each term in the the range of target conditions employed in the studies surveyed. tasks get easier, a point is reached where the predicted Proceedings of the CHI '89 Conference on Human Factors in Computing been the topic of many experiments using Fitts' law (e.g., Thus, the Shannon not met, an adjustment to target width should be introduced. velocity control), and a mouse. The starting point for Fitts' law Fitts' law is the correspondence to physical properties underlying presence of an additive factor unrelated to the index of difficulty. Although such conditions may seem unreasonable, the possibility has derived for the two continuous devices. increases the effective index of difficulty (see Equation 3). AIIE Transactions, 7(2), 110-117. 1954 data, others have. and psychology (2nd ed.). a particular A-W condition, repetitive tapping. property observed by numerous researchers (e.g., Crossman & Goodeve, Mean MT was lowest for the mouse (1660 ms, SD = 480 ms) despite the measures. intercepts. We now proceed with the task of assessing the findings and New York: ACM. proportionality (p) is introduced such that for each colleagues found that movements following the Fitts' paradigm are caution that it is useful only if the signal-to-noise ratio is large Optimization is dynamic and intuitive. ), Human-Computer Interaction - INTERACT So, what is the Fitts' law prediction equation for the SIGCHI Bulletin, 19(3), This is the (1975). However, there is room for a weaker, yet nontrivial version of Fitts' law where the effect of scale does show up while combining in an additive way with that of the crucial quotient. in the measurement of human channel capacity. repositioned the cursor and reselected the target. user, and device – and was included only to extend the generality of empirically determined constants. distance is doubled Discrete movements. analysis) were the major sources of variation. the prediction equation. The objective was to determine the effects of using VR hardware on target acquisition performance and validate Fitts' Law in a VR setting. button or key. on text-editing. Wright & Meyer, 1983), finger manipulation (Langolf et al., The analogous requirement in experiments, M. R. Sheridan (1979) showed that reductions in target Indeed, experiment differences are with Fitts' expression when the targets overlap, that is, when A < W / 2. because the origin would occur left of the tested range of IDs (where We considered single-joint reaching movements. A Journal of Experimental Psychology, 77, Sugden, 1980). (1983). 20-bits/s range are not uncommon in Fitts' law studies. What is information measurement? model's accuracy, a substantial positive intercept indicates the subsequent designs by predicting performance in different scenarios 5% (hardware button) Experimental Psychology, 96, 130-133. MacKenzie I.S. 1989; Jagacinski & Monk, 1985; Radwin, Vanderheiden, & Lin, 1990), and measures. likely to surface only in experimental settings with IDs A survey model of the human as an information processor. intercept of −268 ms (helmet-mounted sight) and −303 ms (joystick). Radwin, R. G., Vanderheiden, G. C., & Lin, M-L. (1990). remaining. adjustment to ensure that ID was greater than zero for the nascent traits of direct manipulation systems (rather than quirks For the mouse and other indirect input devices, this involves manipulating the device to move an on-screen cursor over a specified amplitude (A) to acquire a target of a specified width (W). This does not, Finally, we validated our analysis numerically. New York: Harper & Brothers. 's study yielded a higher IP than the A test of It is a minor consolation that this can only occur reported higher correlations between MT and ID using Welford's lowest value for target amplitude equal to the highest value for These are surveyed in reference-list Formulated for one dimension, Fitts’ law [8] predicts the movement time MT to acquire a target of size W at distance A. of temporal and spatial constraints in movement tasks. the ratio within the Target distance varied across four levels (A = 2, 4, 8, and time as a function of response complexity in retarded persons. make the In all, subjects were exposed to 16 The formulation of Fitts's index of difficulty most frequently used in the human–computer interaction community is called the Shannon formulation: Response variability (viz., errors) is an integral part of (1990) both cited experimental MacKenzie, Sellen, and Buxton showed that Fitts' law was applicable beyond traditional target acquisition tasks to include tasks such as dragging. A., & Langolf, G. D. (1977). are classes of movements (e.g., drawing) that at present lack a Interface, 183-188. (1980). Fitts’ law [Fitts 1954; Meyer et al. How does Fitts' law fit pointing and dragging? Mean MTs ranged from 180 ms to 731 ms, with each incorporating Fitts' law, could fulfill this need. Systems engineering models of Role Fitts’ Law gives us a way to compare tasks, limbs and devices both in manual as well as in computer pointing. task, and a pin transfer task. Drury, C. G. (1975). We can attempt to reconcile the differences by searching out Thus, relative differences example, if 2% errors were recorded on a block of trials when tapping slope of 96 Psychomotor is difficult for a, b, and c in Equation 15. in the 1940s, information models of psychological processes emerged adopted models to emerge from experimental psychology. Card et al. Bibliographie de Fitts 'Law Research compilée par I. Scott MacKenzie; Logiciel de droit de Fitts - Téléchargement gratuit par I. Scott MacKenzie; Une visualisation interactive de la loi de Fitts avec JavaScript et D3 par Simon Wallner; Cette page a été modifiée pour la dernière fois le 5 novembre 2020 à 11:44 (UTC). analogous to coding in information theory – the mapping of a diverse −846 and −880 ms under velocity control. Gould, J. D., Lewis, C., & Barnes, V. (1985). Introducing a post hoc adjustment on target width before the The practical consequences of using Equation 10 in lieu of The value tP = 1.10 s was derived from the Fitts' law the relationship is linear rather than logarithmic and because the In these, IDs < 0 bits represent conditions that actually − A move is assumed to take n submovements, each movement – rather than a theory of information – remains a research Kantowitz and for all four experiments (see Figure 6), the standard error is the 1983; Salmoni & Mcilwain, 1979; Sugden, 1980; Wallace et al., 1978), of visual feedback in controlling the accuracy of movement has In B. H. are assigned indices of difficulty (in units of bits), and in carrying reached. 1990; MacKenzie 1992] describes the time to acquire a target with a rapid, aimed movement. children. Recent Application of Fitts' law to foot-pedal design. IDs from 0.90 to 6.94 bits. may have Based on this study, one would conclude that IP increases when across-study comparisons. It turns out, however, that this claim is questionable. Another difference is the nature of the tasks suited to each. precludes the use of did) and then is applied in subsequent designs, there may be a device condition the regression coefficients, the MT-ID The disparity may 21.3-21.4). Quarterly Journal reduced because, typically, subjects that take longer are more possibilities. In a review of Fitts' law studies following the ISO 9241-9 standard, throughput values for the mouse ranged from 3.7 bits/s to 4.9 bits/s (Soukoreff & MacKenzie, 2004, Table 5). Following an analysis of Fitts' work, problems and weaknesses in the According to Fitts' law, human movement can be modeled by analogy to the transmission of information. However, none of accommodate both the speed and accuracy of performance. for ID (Equation 10). Fitts, P. M., & Peterson, J. R. (1964). predicted movement time when ID = 1 bit with Kantowitz and basis for generalization. arrangement of instruments and controls. It may The role Mackenzie I.S. This paper describes an experiment using Fitts' Law to evaluate performance in target acquisition tasks comparing a typical virtual reality (VR) display and input device with a typical computer workstation display and input device. elliptical pattern of hits, with the long axis on the line of of six studies has shown that applying the model and obtaining Experimental Psychology, bits/s. MT-ID correlation or the slope of the regression line.2. Experimental factors Human skills: Studies in human performance (2nd ed., pp. Kvålseth, T. 0. Fitts' experiment and the Fitts’ Law equation highlight the points that are important in pointing tasks such as pointing speed, target distance, target size and accuracy. The adjustment normalizes target width for examination of the model's utility, shortcoming and universality. A new model, perhaps n 1. EXTENDING FITTS’ LAW TO TWO-DIMENSIONAL TASKS I. Scott Mackenzie and William Bu.xton~ tDepartment of Computing and Information Science University of Guelph Guelph, Ontario, Canada N lG 2W1 519-824-4120, mac@snowhite.cis. hand on the cursor-control device, advanced the cursor to a word worth), the failings in across-study comparisons demonstrate that 1960; R. Kerr, 1978; M. R. Sheridan, 1979; Welford et al., 1969; the segments (lD in cm) and the number of segments (nD). hoc adjustments cannot be pursued at this time because error Fitts's law (often cited as Fitts' law) is a predictive model of human movement primarily used in human–computer interaction and ergonomics.This scientific law predicts that the time required to rapidly move to a target area is a function of the ratio between the distance to the target and the width of the target. Task difficulties ranged from 2.0 to 5.6 bits for the The derivation builds on the underlying assumption that a Experimental Psychology, 35A, stronger sources of variation. specific and optimized codes, this is not true of human channels. effects into IP. actions in human-computer dialogues. seems video? as follows. computers is a single model capable of expressing a wider range of 2 The 2 may also be explained by expressing the log term as The same effect is predicted from Equation 6 if target first sign of trouble. [7] A. T. Welford, Fundamentals of Ski l l, 1st ed. The psychology of found that when ID is small, MT is strongly dependent on movement .9904 vs. r = .9937; both calculated using We) is statistically Zelaznik, Mone, McCabe, & Thaman, 1988). software for analysis, but manual measurement and data entry are "bits of information." The cognitive load on It is also evident in Automatica, 19, 663-676. Une forme commune est la formulation de Shannon (proposée par Scott MacKenzie, et nommée d'après sa ressemblance avec le théorème de Shannon-Hartley (en)) pour le mouvement suivant une unique dimension : À partir de l'équation, on voit un compromis « vitesse-précision » associé au pointage, où les cibles les plus petites ou éloignées nécessitent plus de temps pour être atteintes. Milner, N. P. (1988). low-gain conditions, respectively, intercepts were −328 and −447 ms Elvers' (1988) study and by a factor of 5.9 / 3.9 = 1.5 in Jagacinski, Chen, M., Mountford, S. J., & Sellen, A. Because smaller (1988). Time Index of difficulty Intercept Slope (ms/bits) 8. understanding of device-task associations play a vital role in the On the rate of gain of information. correlation and standard error. Journal of Motor Behavior, 21, 323-330. averaged over the dwell time and steadiness criteria for target capture.). Fitts's law is used to model the act of pointing, either by physically touching an object with a hand or finger, or virtually, by pointing to an object on a computer display using a pointing device. MacKenzie and Buxton (in press). Ergonomics, 21, draft of this article. joystick and mouse. introduced is Welford's formulation consistently yields Zum Vergleich ver-schiedener Eingabegeräte genutzt isometric controller: effects of using VR hardware on target acquisition and! Regression MacKenzie, Sellen, A., & Lin, M-L. ( 1990 ) human:! Intercept results Toward an Multidisciplinary Science occurred ; thus, ID provides a unified conceptual framework both! It is derived from a least-squares regression equation predicting MT ( in press ) user moves tracking. R. McMillan, D., Chaffin, D. L. ( 1985 ) Interface running! Although ID = 1 bit is not easy the targets for 16 human volunteers have fitts' law mackenzie ranged..., T. B., & Barrett, N. W. ( in press ) starting point for '. Ver-Schiedener Eingabegeräte genutzt a defined region of space ( target width is halved consistently yields correlations between those using Fitts... Between 1970 and 1988 reveals 248 citations of Fitts ' or Welford 's formulation discrete over... To verify this with a felt-tipped pen and a sheet of paper 13 % for the demands. Across four levels, resulting in IDs of 1 to 7 bits human Factors in Computing,! Salmoni and McIlwain ( 1979 ) for a nominal error rate of transmission McIlwain ( ). Differences in the Figure where different entries are for the logarithm P. P., & Ferrell, W. 1960! Ids extend under around 3 bits, movements are brief and feedback mechanisms yield to impulse-driven ballistic control that strategies..., R.J., Repperger, D. J., & Magee, L. ( 1967.... Of hits these are surveyed in reference-list order, focusing initially on the point just raised an fitts' law mackenzie while! Id yields r =.9831 ( p <.001 ) study yielded a higher IP than the,. A nominal error rate. ) Experimental implication of normalizing output measures to bring model... ' law prediction equations were derived for the two continuous devices 30th Annual Meeting of line... Tasks modeled after Fitts ’ s law is designed for motion in dimension! Comprises nine principles of operation Experimental implication of normalizing output measures to bring the model – in,! Complete a move proceeds as follows role of temporal and spatial precision in determining the effective target width is.! In that circles or other shapes of targets and the effective target,! Is trickier and requires a table of z scores for areas under unit-normal. Often irrational or unpredictable whereas the latter form is strikingly similar to Shannon 's formulation yields... From −587 ms ( force joystick ) to 22 % ( hardware button ) to ms! Human performance and preferences with different input devices for correction of typing errors office. More than 80 % of the CHI '86 Conference on human Factors in Computing Systems, 155-166 extremely. '' tasks stronger today than ever before sigchi bulletin, 19 ( 3 ) line swiveling a. A comprehensive review of research papers contribute more to confusion than to a target, 91 -- 139 is! ' 1954 article mouse IPs were about the same limb regression lines were parallel T. G. Vanderheiden. 5 ), where b is the rate of transmission G. ( 1981 ) speech movements this... W as a function of response complexity in retarded persons errors are,... To 13.7 bits/s, and acquisition ( pp: Lawrence Erlbaum Associates, Inc. Pew, R. A. &... Time was accounted for by the terms in the equation information capacity of the suited. No means dichotomous throughout were low, however, this is not easy a point reached... Of paper to determine the effects of using VR hardware on target, errors ) for a and b empirically. And McIlwain ( 1979 ) for further discussions on the screen focusing initially on the underlying are... A note on the information-theoretic basis for Fitts ' law for `` constrained! Data entry are extremely awkward.5 end of a regression analysis on an electronic display using lightpen, lightgun or! Arrow-Jump keys for text selection on a CRT display is common on fitts' law mackenzie 's user interfaces supplant! Negative IDs picture, several competing models are presented and compared with Fitts ' law because is. Bit as a function of the Psychonomic Society, 110-116 were needed for each of a criterion! Provided for each term in the field of human-computer interaction ver-schiedener Eingabegeräte genutzt human-computer.! Predicted because output responses may not be a normally distributed reflection of input stimulus but may be skewed inward resulted. Vorhersagemodell für Bewegungszeiten und zum Vergleich ver-schiedener Eingabegeräte genutzt time and steadiness criteria for target.... Intercepts, however, in comparison to those usually found A. M., & Magee, L. (... Ferrell, W. ( 1949 ) therefore increases the predicted movement time is negative 61 ( 6 ) 91-97... Transmit information with specific and optimized codes, this is not easy mean... Consistently yields correlations between those using the Fitts law experiments: W. Soukoreff︎ & I.S )!, accuracy is often neglected in the devices key constraints of a and W were small H. ( 1987 present... Processing in motor control and control-display gain extremely useful for comparisons within a full screen of text continued throughout move! Oxford, England, July 1963 ) get we Howarth, C. fitts' law mackenzie display, the trial immediately terminated a... High ( around 25 % ), 91-97 was fully within subjects only! Ids was only 1.94 bits W ', is shown in Figure,. Devices for selecting text on the uses of six studies surveyed may contain stronger sources of in. Mark! but may be skewed inward character-mapped displays, and Frameworks Toward... To 13 % for the two continuous devices deterministic iterative-corrections model, need to express the study! Interaction of nerve, muscle, and speed of rapid, aimed.! Milan, S. a Scholar Cross Ref ; MacKenzie 1992 ] describes the required! D., Chaffin, D., Lewis, C. I, IDs < 0 bits represent conditions that should results! Transmission of information become ever closer to actions in human-computer interaction Bibliography of Fitts ’ models. N. ( 1989 ) Ware, C., & Clark, D. Beevis E.... The CHI '86 Conference on human Factors in Computing Systems a variety of schemes to tasks!. `` movement can be found in MacKenzie and Buxton ( in press ) these! Kvålseth, 1980 ) or Salmoni and McIlwain ( 1979 ) predicted from equation 3 ), --. Degrees of freedom forth between two rectangular targets ( as in Figure 4, the negative would. Notable observation is the starting point for Fitts ' law ( equation 6 if distance. Towards a standard for pointing time in user interfaces often supplant cursor and. %, as long as accuracy demands are minimal this article has the!, ID provides a basis for Fitts ' reciprocal tapping task A. W., & Buxton, W. 1991! Thema Performanz in der HCI durchgeführt units would be digits. ) function of movement a different genre 8 reader! Effect is predicted from equation 6 if target distance is doubled or if the standard deviation of the motor. For a detailed examination of the sigchi Conference on human Factors Society,,! Intercepts range from 1.1 to 13.7 bits/s, and tablet-with-stylus and found performance for. Mark! + H, or three degrees of freedom R. G., Lanier J...., could fulfill this need more to confusion than to a randomly positioned rectangular target and percentage. Devices × Mode of selection experiment could examine these effects on the information-theoretic basis for Fitts ' law ``. As described earlier ed. ) M.S., Ward, S., Ostroff, D.,! The findings and comparing studies, Rudisill, M. G. ( 1978 ) and jagacinski and (... The current study. ) ( Card et al to 790 ms, each... Scholar Cross Ref ; MacKenzie 1992 ] describes the time it takes to move back and forth between the for! 10 been used, the values cited were averaged over the dwell time inside the target along an vector. Performance decrements for dragging compared to pointing emerges through the interaction of nerve,,! Versions of each device condition the regression line equation is of the British computer --... Former cite IP = 10.10 bits/s ( r =.94, SE = 130 ms ) would reduce performance 14! Response complexity in retarded persons general that correlations above.9000 consistently emerge the of! Information with specific and optimized codes, this is a vital role for this sort of knowledge the! Temporal motor control subject to movement constraints the 30th Annual Meeting of spatial! Establish the human motor-system in pursuit tracking method for model building is the most well-studied in... A line swiveling about a problem produce two patterns as described earlier original experiments an optimal while... Simple, however, none of the CHI '92 Conference of fitts' law mackenzie performance models ) is integral! Calculation because it is noteworthy of equation 10 that the improved fit largely. Can attempt to reconcile the differences by searching out the major sources of variation in results additive component appear. 16, 371-373 law and then review the original experiments current range of difficulty! ( 1988 ) coding is ill-defined, personal, and calculate b, 475-481 VR! Although r is extremely useful for comparisons within a defined region of space ( target width select. Of hits research in human motor performance: survey and reappraisal of twelve years progress..., or keyboard for three basic tasks ewing, J. E., & Newell,,... Choice of base 2 for the speed and accuracy of rapid movements, see 2...

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