Final lab report - Dr. Barbara Cuevas PDF

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Dr. Barbara Cuevas...

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Speed-Accuracy Trade-Off

EXSC 351

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Introduction We experience the concept of speed-accuracy trade-offs while completing many of our daily tasks such as, typing on a keyboard, flipping a light switch, going up and down a flight of stairs, unlocking a door with a key, etc. All these tasks demonstrate how we must trade between speed and accuracy to accomplish certain movements. With mostly any given task we see that the more time we have to respond, the more accurate our results are. When we are presented with a limited amount of time we automatically act quickly, emphasizing speed over accuracy, and our results tend to be less accurate. Fitts’ Law, a model of human psychomotor behavior, enables us to carefully predict movement based on rapid, aimed movement, not simple movements such as walking or writing (Zhao, 2002). Fitts’ Law states that movement time is a logarithmic function of distance when target size remains constant and a logarithmic function of target size when distance remains constant (Zhao, 2002). The equation representing Fitts’ Law, MT= a + b * log2 (2A/W + c), is used to calculate movement time. The element, log2(2A/W + c), is referred to as the Index of Difficulty which measures the difficulty of completing the motion based on the width of the target and the distance of the target, also known as the amplitude (Clegg, 2003). Fitts’ Law can predict a linear relationship between index of difficulty and movement time. Mathematically, Fitts’ Law is a linear regression model through which we can measure the subject’s index of performance using the equation 1/slope or 1/b (Zhao, 2002). This study addresses the question of whether a reciprocal tapping task demonstrates a speed-accuracy trade-off illustrated by Fitts’ Law. Given a limited

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timeframe, how accurate would the participant’s results be as target size and target distance were manipulated?

It was hypothesized that as target size decreased and target distance decreased, accuracy would decrease and index of difficulty would increase, but as target size

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increased and target distance decreased, accuracy would increase and index of difficulty would decrease. Methods Two participants were each given a target template for obtaining the results for this experiment. The participant’s goal was to tap back and forth between the two targets in a pair as many times as possible for 20 seconds while maintaining a percent error of 3% to 7%. All the data was collected for one participant before the students switched roles. The template was positioned so that the movement between the two targets was side to side and not forward and backward. The trial began with the participant holding a pen/pencil normally with the point in the target circle on the left side of a pair. The experimenter simultaneously started the clock and signaled the participant to begin a trial. During each trial, the experimenter will count the number of times the participant taps the right circle. After 20 seconds elapsed, the number of taps in the right circle were recorded in the “Count” column of the data sheet. Next, the experimenter multiplied the number of taps by 2 to get the total number of taps and recorded this value in the “Taps” column. Next, the experimenter counted the number of pen/pencil marks that were completely outside either target and recorded this value in the “Misses” column. The experimenter then calculated the percent error and recorded the result in the “% Error” column of the data sheet using the formula: (Misses / Taps)*100. If on any given trial, the percent error was less than 3% or greater than 7%, the trial was repeated. Finally, the experimenter calculated the MT, per tap, and recorded the result in the “MT” column of the data sheet using the formula: MT = 20 sec / Taps. After the first participant completed 3 trials in each of the 6 conditions for a total of 18 trials, the second participant began the same trial process and his/her data was

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recorded on a separate data sheet. 3 trials in each of the 6 conditions for a total of 18 trials were also completed for the second participant Results: After performing the study, data was collected from the 20 participants. Table 1: Subject

Condition 1

Condition 2

Condition 3

Condition 4

Condition 5

1

0.588

0.455

0.435

0.333

0.323

Conditio n6 0.222

2

0.714

0.588

0.556

0.476

0.455

0.385

3

0.588

0.455

0.476

0.333

0.37

0.25

4

0.5

0.416

0.434

0.294

0.333

0.232

5

0.588

0.455

0.417

0.37

0.256

0.217

6

0.556

0.455

0.435

0.357

0.286

0.238

7

0.67

0.43

0.5

0.36

0.42

0.25

8

0.66

0.4

0.5

0.36

0.43

0.27

9

0.625

0.5

0.455

0.37

0.37

0.25

10

0.526

0.435

0.417

0.333

0.294

0.185

11

0.42

0.5

0.37

0.32

0.31

0.243

12

0.625

0.5

0.476

0.37

0.345

0.213

13

0.55

0.434

0.45

0.4

0.322

0.286

14

0.5

0.417

0.435

0.345

0.333

0.256

15

0.56

0.43

0.48

0.34

0.37

0.26

16

0.476

0.313

0.333

0.25

0.238

0.25

17

0.625

0.4

0.417

0.357

0.345

0.263

18

0.526

0.435

0.417

0.313

0.385

0.263

19

0.714

0.625

0.5

0.435

0.435

0.345

20

0.526

0.417

0.556

0.303

0.385

0.263

Mean Standard Deviation Standard Error

0.57685 0.07824406 8 0.01749590 6

0.453 0.06715966 8 0.01501735 8

0.45295 0.05498849 2 0.01229580 1

0.35095 0.04903647 9

0.35025 0.05873748 5 0.01313410 1

0.25705 0.04387 7191 0.00981 1238

0.01096489

The above table represents the median movement time from the three trials of each condition for each participant. Mean movement time, standard deviation and standard

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error were also calculated. The standard deviation shows that 95% of the participants fell (see above amount) seconds from the mean. Standard error was calculated from the standard deviation from the mean divided by the square root of the number of participants (20). Figure 1:

The above bar graph was created to show the mean movement time for each condition. An error bar is displayed for each condition to show the standard error. Labels above each of the conditions display the index of difficulty and exact mean movement time. The mean movement times ranged from 0.26 seconds being the fastest for condition 6, and 0.58 seconds being the slowest for condition number 1. These movement times

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correlate with the index of difficulty. Condition 1 had the slowest movement time with the maximum index of difficulty, while condition 6 had the fastest movement time and the minimum index of difficulty. Conditions 2 and 3 have similar indexes of difficulty; therefore, their movement times are almost identical, as show in the figure. Figure 2:

The above scatter plot was created to compare the mean movement time versus the index of difficulty for each condition. A linear trend line of y = 0.1058x – 0.0694, was calculated for this data. This regression line gives a distinct numerical value for how the movement time increases as the index of difficulty increases. The y-intercept of 0.0684 means that the subject tapped in the same spot, then their movement time would be about 0.0684 seconds per tap. The slope of the regression line means that as the index of difficulty increases by 1 unit, the subject’s movement time would increase by 0.1058 seconds.

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Discussion: This lab was successfully demonstrated by all 20 participants to serve its purpose in demonstrating the speed-accuracy trade-off in reciprocal tapping. Fitts’ law, which predicts the time it takes participants to reach, with a pointer, some target at width (W) located at a distance (D) (Guiard, 2011). As portrayed in Figure 2, as the index of difficulty increased, the movement time increased; therefore, the participants’ speed decreased. Either increasing the movement distance or decreasing the target size increased the index of difficulty. For the conditions that had the same index of difficulty, their movement times were almost identical (condition 2 and condition 3). As the index of difficulty for hitting the target increased, the movement time of the participant decreased in order for the participant to obtain less error; therefore, supporting our hypothesis. The speed-accuracy trade-off may be useful for practitioners to use in real life situations to help patients learn, or relearn certain motor skills. A real life skill that uses speed-accuracy is typing on a keyboard. The keys on a keyboard are relatively small compared to the size of the average person’s had. Therefore, practitioners should take the speed-accuracy trade-off into consideration when teaching a patient the skill of typing on a keyboard. They should instruct the patient to learn to type slowly, so that they can be more accurate and avoid spelling errors. Visual feedback plays a very important role in speed-accuracy skills. This relates to the open-loop control that is involved in a speed-accuracy skill. It could be hypothesized that as the distance of the two targets gets further, more feedback adjustments need to be made; therefore, the movement time increases. Future research studies on the visual feedback systems could be important in supporting Fitts’ law and why as the index of difficulty increases, the movement time increases as well.

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References: Clegg, Ben. Cognitive Psychology Laboratory. 2003. Available from: http://lamar.colostate.edu/~bclegg/PY453/imagined_movements.pdf. Accessed March 3, 2013. Guiard Y, Olafsdottir H. On the Measurement of Movement Difficulty in the Standard Approach to Fitts' Law. Plos ONE [serial online]. October 2011;6(10):1-15. Available from: Academic Search Complete, Ipswich, MA. Accessed March 6, 2013. Zhao, Haixia. Fitts’ Law: Modeling Movement Time in HCI. October 2002. Available from: http://www.cs.umd.edu/class/fall2002/cmsc838s/tichi/fitts.html. Accessed March 3, 2013.

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