Movement and Fitts' Law Flashcards
Fitts’ Law
- Paul Fitts (1912-1965)
- Psychologist
- Pioneer in Human Factors
- Modelling the performance of human movement
- How long does it take to make a movement
to a known target? - How does this depend on the distance and
size of the target? - How difficult are different movement tasks?
- How long does it take to make a movement
Fitts’ Experiment
Fitts’ Experiment
Fitts’ Experiment
Fitts’ Experiment
Speed-Accuracy Trade-off
- We can move faster when we are allowed to be less accurate
- We can be more accurate, when we move more slowly
- The speed-accuracy trade-off is fundamental to input in HCI
- When we increase speed of input, we reduce accuracy of input
- When we move faster, we make more errors
Example: Mouse Tracking Speed
- Control-display gain is a scale factor in mapping input to movement on the display:
CDgain = Vdisplay/Vcontrol
- Example
- Mouse moves 3cm and cursor moves 3cm: CD gain = 1.
- Mouse moves 3cm and cursor moves 6cm: CD gain = 2
- Low CD gain
- Move cursor slowly
- Great for precise input
- Inefficient for larger movement
- High CD gain
- Great for quick movement across display
- Efficient for gross positioning
Index of Difficulty (ID)
- Combine distance and width in a single measure of difficulty:
ID = log2 (D/W + 1)- Measured in bits
- Example:
- Target 1 and Target 2 have same ID
- T2: larger distance, but also larger width
Building a Fitts’ Law Model
Fitts’ Law:
- The relationship between task difficulty and movement time is linear
- MT = a + b * ID
- MT = a + b * log2(D/W + 1)
Fitts’ Law Formulation
MT = a + b * ID = a + b * log2 (D/W + 1)
- MT is a Movement Time
- ID is a property of the movement task, measured in bits
- ID is independent of the device used to perform the movement
- b is the rate at which movement time increases with difficulty of the task, measured in seconds/bit
- a is a time constant, e.g., for preparing the movement, measured in seconds
- a and b are device-dependent, on the body part and/or device used to perform the movement
Predicting movement time
+ 1
- MT = a + b * log2(D/W + 1)
- a = 0.028 s
- b = 0.112 s/bit
How long does it take to select a target that is 21 inches away and 3 inches wide?
MT = 0.028 + 0.112 * log2 (?)
Movement analogy to communication
- Fitts’ Law look similar to the Shannon-Hartley Theorem
- Capacity C of communication channel depends on bandwidth B and signal-to-noise ratio S/N
- C = B * log2(S/N + 1)
- Fitts’ Law analogy:
- Movement is a signal that carries information (by selecting input)
- Accuracy of the movement is like noise: when accuracy drops there are more errors in the information conveyed
- Throughput: rate of information transfer in bit/s
Throughput of input (simplified)
- How difficult is it to click on (tap on) the highlighted field?
- For example: MT = 250ms for A and MT = 1s for D
- How do A and D compare in throughput
-Suppose you make the same selection 10 times at a high speed
- Fast movement means it will not be so accurate (more noise)
- For example: speed is 250ms
- In which of the four cases do we have the highest throughput?
Throughput
- Throughput is a composite measure that takes both speed and accuracy into account
TP = ID/MT [in bit/s]
- If we ignore the time constant in Fitts’ Law then
TP = 1/b
Throughput in a Fitts’ Law Model
- b is the slope in s/bit (time needed per bit)
- 1/b is the reciprocal, in bit/s
-> in the example 8.93 bit/s - Steeper slope -> ? throughput
- Flatter slope -> ? throughput
Throughput of devices / muscle groups
- Mouse tasks, perceived difficulty:
- select a word: “hardest easy task”
- select a char: “easiest hard task”
- Mouse throughput 10.4 bit/s
- 1991 data! Further optimization since
-Fingers have higher throughput, 40 bit/s - For adjacent buttons, not in general
- 1991 data! Further optimization since
- Head pointing is less efficient, 4.2 bit/s
- Select a word in the time mouse pointing can select a character
