Apa3120 Unit 3 Lab Report Essay
Lab #3- APA3120 Information Processing Speed-Accuracy Trade-off
Introduction
Paul Fitts’ was the first to discover the relationship between the speed of movement and accuracy requirements. This has become one of the most fundamental principles of motor control. Fitts claims a relationship between task difficulty and movement time. He quantified task difficulty as “index of difficulty” which consists of the ratio of twice the amplitude over width of the target (2Amplitude/Width). This relationship states that when movement amplitude decreases or when target width increases movement time is shorter (Fitts, 1954). Fitts found that the relationship between amplitude and width was given by the equation: MT= a + b[log2(2A/W)]. The empirical constants a and b represent the y-intercept and the slope (Schmidt & Lee, 2011). The purpose of this laboratory was to investigate the linear relationship between the index of difficulty and movement time. Furthermore, the target width-amplitude relationship was observed. The goal was to determine the effect of task difficulty on movement time. Based on Fitts’ law, it was hypothesized that the relationship between movement time and index of difficulty would increase linearly. …show more content…
The laboratory consisted of six trials, each consisted of a different movement amplitude to target width relationship.
Refer to lab protocol for exact measurements. For each trial, the participant had to move a stylus between two targets, moving as fast as possible while maintaining accuracy. Each trial consisted of a fifteen second period, the number of total taps was recorded. Results from five participants were taken. Results represented movement times for index’s of difficulties of 1-4. The index of difficulty was an independent variable, movement time the dependent variable. It was expected that movement time was to increase with an increase in index of
difficulty.
Results
Table 1
Mean movement time in milliseconds for six different conditions (n=5). Index of difficulty and standard deviation included.
Condition
ID
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Mean
SD
1
2
211,3
180,7
157,9
156,3
133,9
168,0
29,3
2
3
194,8
189,9
166,7
154,6
135,1
168,2
24,8
3
4
333,3
375
170,5
241,9
137,6
251,0
101,9
4
1
182,9
147,1
129,3
141,5
127,1
145,6
22,4
5
2
181,7
161,3
135,1
140,2
128,2
149,3
21,9
6
3
189,9
157,9
164,8
153,1
131,6
159,4
21,1
Note. Index of difficulty = log2(2A/W)
Table 2
Mean movement time in milliseconds of each subject for six different conditions (n=5). Standard deviation presented.
Subject:
1
2
3
4
5
Mean MT:
216
212
154.1
164.6
132.3
SD:
58.6
86.2
17.51
38.5
4.07
Figure 1. Group mean of movement time (ms) as a function of six conditions (n=5). The six conditions each had different movement amplitude to target width relationship. Standard errors are represented in the figure by the error bars attached to each column.
Figure 2. Individual movement time (ms) as a function of the index of difficulty [log2(2A/W)]. Line of best fit had an equation of y= 3.2818 + 124.05, y= movement time and x= index of difficulty.
Figure 3 Group mean movement time (ms) as a function of the index of difficulty [log2(2A/W)]. Line of best fit had an equation of y= 29.873 + 99.025, y= movement time and x= index of difficulty.
Expected mean movement time for an index of difficulty of 6 was calculated using the equation from the line of best fit: y= 3.2818x + 124.05. The expected movement time was 143.7 milliseconds. A paired t-test was used to compare group mean movement times between the condition three and condition four results. The t-test revealed no significant difference, t(4)= 2.73,p= 0.0524, such that movement time’s of condition three (mean= 252 ms , SD= 101.9) was slower than movement time’s of condition four (mean= 145.6 ms, SD= 22.5). A pair t-test was also used to compare group mean movement times between conditions two and six. The t-test revealed no significant difference, t(4)= 1.500, p= 0.208, such that movement time’s of condition two (mean= 168.2, SD= 24.8) was slower than movement time’s of condition six (mean= 159.5, SD= 21.1).
Discussion
The index of difficulty is represented by the value of Log2(2A/W), it represents how “difficult” the combination of Amplitude and Width of target was for the subject (Schmidt & Lee, 2011). Movement time is given by the following equation: MT= a + b[log2(2A/W)]. It is the average movement time for a series of taps, computed during a fifteen second time duration (Schmidt & Lee, 2011). A fifteen second time duration is divided by the number of taps observed and is presented as milliseconds/tap. Doubling amplitude and width at the same time would result in the same index of difficulty, and therefore movement time would be the same (Schmidt & Lee, 2011). Fitts’ law implies that an inverse relationship is seen between the difficulty of a movement and the speed at which the movement is performed (Schmidt & Lee, 2011). This is called the speed-accuracy trade-off. Group mean movement times show slight increases in movement time for index of difficulties’ one to three. The mean movement for the index of difficulty of four shows a large increase (please refer to figure 1). Individual results of subject five however did not show such a large difference in movement times between difficulties of index. With each increase in index of difficulty a linear increase in movement time was observed (please refer to figure 2). The group’s movement time results were not linear, results appear scattered (please refer to figure 3). Subject five showed linear increase in movement time. The mean group equation was: y= 29.873x + 99.025 and subject five’s equation was: y= 3.2818x + 124.05. Comparing the two, the group mean equation had a much steeper slope and the y-intercept was smaller. A larger slope in group mean movement time refers to the added movement time caused by increase in index of difficulty by one bit. The slope refers to the sensitivity of the effector to changes in index of difficulty (Schmidt & Lee, 2011). Differences in slopes of the Fitts’ equation have shown to be sensitive to factors such as age, limb used and skill level (Schmidt & Lee, 2011). Data from Kelso (1984) shows a slope of zero after doing 40 000 trials in 20 days. This shows that the slope in the Fitts’ equation can be reduced considerably with practice (Schmidt & Lee, 2011). The speed-accuracy trade-off can be thought of as the balance between accuracy and speed so that information processing is held constant (Schmidt, 2000). Fits’ law shows that the performer has the capability to change the control processes, choosing to either move faster at the expense of accuracy or slow down and have better control of movement. This shows that information processing cannot accommodate an increase in both speed and accuracy. There will be an overload and one of the two factors will adapt in expense to the other. Movement times observed in the experiment could have been influenced by the learning curve effect. The downside to doing six conditions directly following one another is that there is possibility of faster movement times with each condition. Comparing movement time’s from condition one and five there was a visible decrease in all participants data although index of difficulty was identical. The same effect was seen in the results from conditions two and six. Results from Kelso (1984) show evidence that movement time can improve with practice. In a recent study, Michmizos and Krebs investigated the accuracy-speed trade-off in pointing movements involving the ankle. Nine participants completed a series of tasks involving dorsal-plantar movement and inversion-eversion at varying difficulties. Six different targets were set and ranged with difficulties from 2.2 to 3.8 bits of information. The results showed a linear function of performance, and supported Fitts’ law (Michmizos & Krebs, 2013).
Conclusion
The purpose of the experiment was to investigate the relationship between the speed of movement and the difficulty of a task. The results showed evidence of increase in movement time with the increase in task difficulty. Group mean results however did not show a linear relationship between index of difficulty and movement time as stated by Fitts’ law.
References
Fitts, P.M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47, 381-391.
Michmizos, K., & Krebs, H. (2013, November 23). Pointing with the ankle: the speed-accuracy trade-off.. Pub Med. Retrieved February 1, 2014, from http://www.ncbi.nlm.nih.gov/pubmed/2427140
Schmidt, R., & Lee, T. (2011). Principles of Speed and Accuracy . Motor control and learning: a behavioral emphasis (pp. 223-261). Champaign, Ill.: Human Kinetics Publishers.
Introduction
Paul Fitts’ was the first to discover the relationship between the speed of movement and accuracy requirements. This has become one of the most fundamental principles of motor control. Fitts claims a relationship between task difficulty and movement time. He quantified task difficulty as “index of difficulty” which consists of the ratio of twice the amplitude over width of the target (2Amplitude/Width). This relationship states that when movement amplitude decreases or when target width increases movement time is shorter (Fitts, 1954). Fitts found that the relationship between amplitude and width was given by the equation: MT= a + b[log2(2A/W)]. The empirical constants a and b represent the y-intercept and the slope (Schmidt & Lee, 2011). The purpose of this laboratory was to investigate the linear relationship between the index of difficulty and movement time. Furthermore, the target width-amplitude relationship was observed. The goal was to determine the effect of task difficulty on movement time. Based on Fitts’ law, it was hypothesized that the relationship between movement time and index of difficulty would increase linearly. …show more content…
The laboratory consisted of six trials, each consisted of a different movement amplitude to target width relationship.
Refer to lab protocol for exact measurements. For each trial, the participant had to move a stylus between two targets, moving as fast as possible while maintaining accuracy. Each trial consisted of a fifteen second period, the number of total taps was recorded. Results from five participants were taken. Results represented movement times for index’s of difficulties of 1-4. The index of difficulty was an independent variable, movement time the dependent variable. It was expected that movement time was to increase with an increase in index of
difficulty.
Results
Table 1
Mean movement time in milliseconds for six different conditions (n=5). Index of difficulty and standard deviation included.
Condition
ID
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Mean
SD
1
2
211,3
180,7
157,9
156,3
133,9
168,0
29,3
2
3
194,8
189,9
166,7
154,6
135,1
168,2
24,8
3
4
333,3
375
170,5
241,9
137,6
251,0
101,9
4
1
182,9
147,1
129,3
141,5
127,1
145,6
22,4
5
2
181,7
161,3
135,1
140,2
128,2
149,3
21,9
6
3
189,9
157,9
164,8
153,1
131,6
159,4
21,1
Note. Index of difficulty = log2(2A/W)
Table 2
Mean movement time in milliseconds of each subject for six different conditions (n=5). Standard deviation presented.
Subject:
1
2
3
4
5
Mean MT:
216
212
154.1
164.6
132.3
SD:
58.6
86.2
17.51
38.5
4.07
Figure 1. Group mean of movement time (ms) as a function of six conditions (n=5). The six conditions each had different movement amplitude to target width relationship. Standard errors are represented in the figure by the error bars attached to each column.
Figure 2. Individual movement time (ms) as a function of the index of difficulty [log2(2A/W)]. Line of best fit had an equation of y= 3.2818 + 124.05, y= movement time and x= index of difficulty.
Figure 3 Group mean movement time (ms) as a function of the index of difficulty [log2(2A/W)]. Line of best fit had an equation of y= 29.873 + 99.025, y= movement time and x= index of difficulty.
Expected mean movement time for an index of difficulty of 6 was calculated using the equation from the line of best fit: y= 3.2818x + 124.05. The expected movement time was 143.7 milliseconds. A paired t-test was used to compare group mean movement times between the condition three and condition four results. The t-test revealed no significant difference, t(4)= 2.73,p= 0.0524, such that movement time’s of condition three (mean= 252 ms , SD= 101.9) was slower than movement time’s of condition four (mean= 145.6 ms, SD= 22.5). A pair t-test was also used to compare group mean movement times between conditions two and six. The t-test revealed no significant difference, t(4)= 1.500, p= 0.208, such that movement time’s of condition two (mean= 168.2, SD= 24.8) was slower than movement time’s of condition six (mean= 159.5, SD= 21.1).
Discussion
The index of difficulty is represented by the value of Log2(2A/W), it represents how “difficult” the combination of Amplitude and Width of target was for the subject (Schmidt & Lee, 2011). Movement time is given by the following equation: MT= a + b[log2(2A/W)]. It is the average movement time for a series of taps, computed during a fifteen second time duration (Schmidt & Lee, 2011). A fifteen second time duration is divided by the number of taps observed and is presented as milliseconds/tap. Doubling amplitude and width at the same time would result in the same index of difficulty, and therefore movement time would be the same (Schmidt & Lee, 2011). Fitts’ law implies that an inverse relationship is seen between the difficulty of a movement and the speed at which the movement is performed (Schmidt & Lee, 2011). This is called the speed-accuracy trade-off. Group mean movement times show slight increases in movement time for index of difficulties’ one to three. The mean movement for the index of difficulty of four shows a large increase (please refer to figure 1). Individual results of subject five however did not show such a large difference in movement times between difficulties of index. With each increase in index of difficulty a linear increase in movement time was observed (please refer to figure 2). The group’s movement time results were not linear, results appear scattered (please refer to figure 3). Subject five showed linear increase in movement time. The mean group equation was: y= 29.873x + 99.025 and subject five’s equation was: y= 3.2818x + 124.05. Comparing the two, the group mean equation had a much steeper slope and the y-intercept was smaller. A larger slope in group mean movement time refers to the added movement time caused by increase in index of difficulty by one bit. The slope refers to the sensitivity of the effector to changes in index of difficulty (Schmidt & Lee, 2011). Differences in slopes of the Fitts’ equation have shown to be sensitive to factors such as age, limb used and skill level (Schmidt & Lee, 2011). Data from Kelso (1984) shows a slope of zero after doing 40 000 trials in 20 days. This shows that the slope in the Fitts’ equation can be reduced considerably with practice (Schmidt & Lee, 2011). The speed-accuracy trade-off can be thought of as the balance between accuracy and speed so that information processing is held constant (Schmidt, 2000). Fits’ law shows that the performer has the capability to change the control processes, choosing to either move faster at the expense of accuracy or slow down and have better control of movement. This shows that information processing cannot accommodate an increase in both speed and accuracy. There will be an overload and one of the two factors will adapt in expense to the other. Movement times observed in the experiment could have been influenced by the learning curve effect. The downside to doing six conditions directly following one another is that there is possibility of faster movement times with each condition. Comparing movement time’s from condition one and five there was a visible decrease in all participants data although index of difficulty was identical. The same effect was seen in the results from conditions two and six. Results from Kelso (1984) show evidence that movement time can improve with practice. In a recent study, Michmizos and Krebs investigated the accuracy-speed trade-off in pointing movements involving the ankle. Nine participants completed a series of tasks involving dorsal-plantar movement and inversion-eversion at varying difficulties. Six different targets were set and ranged with difficulties from 2.2 to 3.8 bits of information. The results showed a linear function of performance, and supported Fitts’ law (Michmizos & Krebs, 2013).
Conclusion
The purpose of the experiment was to investigate the relationship between the speed of movement and the difficulty of a task. The results showed evidence of increase in movement time with the increase in task difficulty. Group mean results however did not show a linear relationship between index of difficulty and movement time as stated by Fitts’ law.
References
Fitts, P.M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47, 381-391.
Michmizos, K., & Krebs, H. (2013, November 23). Pointing with the ankle: the speed-accuracy trade-off.. Pub Med. Retrieved February 1, 2014, from http://www.ncbi.nlm.nih.gov/pubmed/2427140
Schmidt, R., & Lee, T. (2011). Principles of Speed and Accuracy . Motor control and learning: a behavioral emphasis (pp. 223-261). Champaign, Ill.: Human Kinetics Publishers.