Speed Accuracy Trade-Off

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Brooke Williams
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1 Speed Accuracy Trade-Off Purpose To demonstrate the speed accuracy trade-off illustrated by Fitts law. Background The speed accuracy trade-off is one of the fundamental limitations of human movement control. Although there are some exceptions introduced in chapter 5 of your textbook, the general rule is that we are less accurate when we move faster. Fitts Law describes the relationship between movement time, movement amplitude, and target width in aiming movements that use a combination of open- and closed-loop control. In such tasks, the first part of the movement is very rapid and controlled in an open-loop fashion. As the performer gets closer to the target, though, the movement is characterized by closed-loop adjustments to ensure accuracy. A good example of such a combination of open- and closed-loop control is when you put your key into the lock on your door. When you first pull your key from your pocket, you move your hand very rapidly toward the lock, but you slow down as the key gets closer to the lock. Fitts law shows that movement time (MT) is influenced by the combination of movement amplitude and target width as represented in the variable index of difficulty (ID): MT = a + b*id This is an equation describing a line, in which the constants, a and b, represent the intercept and slope, respectively. ID represents the relationship between movement amplitude (A) and target width (W). Mathematically, ID is this: ID = log 2 (2A/W) For a general understanding of Fitts law, it is important to remember that ID increases as movement amplitude (A) increases or as target width (W) decreases. Because ID involves the ratio of amplitude and width, we always need to consider both to get an accurate idea of the ID for a movement. Sometimes the ID remains the same because changes in amplitude are offset by changes in target width. Here are examples: A (cm) W (cm) ID When the amplitude of the movement is exactly half the width of the target, the ID is 0. This represents a case in which the targets overlap and you can simply tap the same spot. Because there is no accuracy demand in this case, no information needs to be processed to complete the tapping action.

2 The following graph is based on data from a student who completed this lab. Her results (circles) fall very close to the line described by the following equation: Average MT (seconds/tap) MT = *ID Index of Difficulty (ID) We can see that MT increases as the ID gets larger, so she moved slower as the accuracy demand increased. The intercept (a =.0) tells us that if she had simply tapped the same spot (i.e., when ID = 0), her movement time would have been about.0 second per tap. The slope (b =.08) tells us that her movement time would increase by about.08 second per tap each time the ID increases by one unit. ID can be increased by one unit by cutting the target in half or by doubling the movement amplitude (while holding the other value constant). Both the intercept and the slope in the equation for MT are thought to represent the information processing capability of the performer. They will be different for slightly different task demands or for different individuals, but performance across a number of trials by a single individual is predicted quite accurately for a range of ID values in the same task (e.g., reciprocal tapping). Equipment stopwatch calculator wooden pencils Instructions Students will take turns in the roles of experimenter and participant. The participant will complete 8 trials of a reciprocal tapping task, in each of 6 conditions. A template is provided. On the template, each condition is labeled and includes three sets of circular targets. Each set of two targets will be used for a single trial. The experimenter will time each trial, count the number

3 of taps and misses, and calculate the percent error (%) and average movement time (MT) per tap for the trial. All data should be collected for one participant before students switch roles. Position the template so that movement between the two targets will be side to side (not forward and backward). The participant s goal is to tap back and forth between the two targets in a pair as many times as possible in 20 seconds while maintaining a percent error level of to 7%. A trial begins with the participant holding a pencil normally with the point in the target circle on the left side of a pair. The participant can use his or her free hand to hold the tapping template. The experimenter will simultaneously start the clock and signal the participant to begin a trial. During the trial, the experimenter will count the number of times that the participant taps the right side of the pair (count all taps even if they are misses). As soon as the trial is over, the experimenter will record the number of counted taps in the count column of the data sheet and then multiply that value by 2 to get the total number of taps for both sides. Then the experimenter will count the number of pencil marks that are completely outside either target (on the line counts as a hit) and calculate percent error and record the result on the data sheet (see the following calculation formulas). If percent error is less than % or greater than 7%, the trial must be repeated. If you need to repeat several trials (which is not uncommon), you can print multiple copies of the template, erase the pencil marks (you need to erase only those outside the target), or flip the paper over and use the back (just trace the outlines of the targets first so they are clearly visible). For each condition, the participant must complete three acceptable trials. After all of the trials have been completed, the experimenter will calculate the average movement time (MT) in seconds per tap for each trial and record the result on the data sheet (see calculation formulas). For each condition, the experimenter will circle the median value on the data sheet. Each student will use the median values to create a scatter plot (see previous figure) and a bar graph (see following figure). For the scatter plot, graph the median MT values as a function of ID (your graph should look like the first graph in the background section of this lab). Label the y-axis with the appropriate values. Use a straightedge to draw a line that you think best fits the data points and extend it to the y-axis to approximate the intercept. For the bar graph, draw a bar for each condition indicating the median MT value. Label the y- axis with the appropriate values for your data. Also label each bar with the index of difficulty (ID) and the median MT value for that condition. Here is an example from the data presented previously:

4 MT (s) ID = 6 AMT =0.5 ID = 5 AMT = 0.44 ID = 5 MT = 0.4 ID = 4 ID = 4 MT = 0.6 AMT = 0.4 ID = AMT = Condition Calculation Formulas Taps = Count x 2 % = (Misses Taps) x 00 MT = 20 s Taps

5 Data Sheet: Participant: Experimenter: Circle the median (middle) value out of the three in each condition: Condition (example) Condition Condition 2 Condition Condition 4 Condition 5 Condition 6 Trial A W ID Count Taps Misses % MT (cm) (cm) (-7%)

6 Scatter Plot Graph the median MT values for each condition (y-axis) as a function of ID (x-axis). Label the y-axis with the appropriate values. Use a straightedge to draw a line of best fit and extend it to the y-axis to approximate the intercept. MT (s) Index of Difficulty (ID) Bar Graph Draw a bar for each condition (x-axis) indicating the median MT value (y-axis). Label the values on the y-axis. Label each bar with the corresponding ID and MT (see data table above). MT (s) Condition

7 Discussion Describe how your results illustrate the speed accuracy trade-off in reciprocal tapping described in chapter 5 of your textbook, especially with respect to the roles played by movement distance (amplitude) and target size (width). Discuss a few factors other than the ID that might have influenced your results.

8 Condition Trial Trial Condition 2 Trial Trial 8

9 Condition Condition 5 Trial Trial Trial Trial Condition 4 Condition 6 Trial Trial Trial Trial 9

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