Lecture 11a: Principles of Speed & Accuracy (Fitts' Law)

Question 1

Paul Fitts and Fitts’ Law

Answer 1

former colonel in the US airforce & professor in engineering psychology
aviation safety
- field of study: human factors (cognitive ergonomics)

developed equation describing the relation between speed and accuracy (Fitts’ Law)

Question 2

WW2 cockpit vs. Modern cockpit

Answer 2

improving the placement of controls in an airplanes cockpit for minimizing human error and improving speed or response

Question 3

Fitts’ Law: Logarithmic Speed-Accuracy Tradeoff

Answer 3

• fitts’ law states that MT is constant whenever the ratio of the movement amplitude to target width remains constant. So very long movements to wide targets require about the same time as very short movements to narrow targets
• speed-accuracy tradeoff is the tendency for people to sacrifice or trade off speed in order to maintain acceptable levels of accuracy as one of the most fundamental principles of movement behavior
• movement time increased by a constant amount whenever the distance the move doubled or whenever the size of the target was reduced by half (WN)

Question 4

Fitts’ Task

Answer 4

• tap between the two targets as many times as quickly as you can and as accurately as you can
• if you tap outside of the target, more than 5% of the time the entire trial does not count
• example: 87 taps completed within 30 seconds, average MT = 30 seconds, divided by 87
  ◦ average MT for this task is
  345 ms per movement (0.345
  seconds)

Question 5

Fitts’ Task: tap back and forth between 2 targets what happens to accuracy as you speed up?

Answer 5

your accuracy declines as you speed up which is known as the speed-accuracy tradeoff

Question 6

Fitts’ Task: tap back and forth between 2 targets what happens to speed if target size decreases?

Answer 6

speed decreases as you will tap slower increasing movement time

Question 7

Fitts’ Task: tap back and forth between 2 targets what happens to speed as distance increases?

Answer 7

speed decreases and movement time will increase

Question 8

Fitts’ Task: tap back and forth between 2 targets what happens to accuracy as size decreases?

Answer 8

accuracy decreases and movement time will increase

Question 9

How much is accuracy expected to be?

Answer 9

• accuracy expected to be > 95% of the time (so accuracy held constant, MT free to vary)
  ◦ if they were more than 5%
  inaccurate the trial was not
  counted most of the time
  because accuracy was held
  somewhat constant

Question 10

What do you manipulate in Fitts’ Law to influence movement time?

Answer 10

target amplitude (distance between targets from midpoint to midpoint of each target

target width (measured as width of the target)

Question 11

Fitts’ Law: Relationship between Movement Time (MT), Amplitude (A) and Target Width (W)
logarithmic speed-accuracy trade off (formula)

Answer 11

MT = a + b[Log2(2A/W)]
- fitts’ law describes a tradeoff between speed and accuracy
- if we want greater speed then there is decreased accuracy and if we want greater accuracy then there is decreased speed

Question 12

Index of Difficulty

Answer 12

Log2(2A/W)
according to this function, as A increases, and/or W decreases, ID should increase
- increase in ID → longer MT (that is speed would decrease)

Question 13

Fitts’ Law: MT = a + b[Log2(2A/W)] - creates a linear line

Answer 13

equation of a line
y = a + bx
y = MT
x = log2(2a/W)

b = slope (rise/run)
(rate of increase of MT as ID increases by 1)

a = y-intercept
(MT WHEN ID = 0 → basically tapping on the spot)
- the targets are essentially overlapping when index of difficulty is