Decision-making I: Hick’s Law

KINESIOL 2MC3

Mike Carter, Ph.D.
cartem11@email.com

Department of Kinesiology | McMaster University

September 09 2025

Last class

Review: Studying motor skills

  • Define motor skills and distinguish it from related concepts.

  • Describe four characteristics of motor skills.

  • Explain different taxonomies used to classify motor skills.

  • Identify and describe some common variables used to measure motor skill performance.

TAKE-HOME MESSAGE:
There are some foundational terms and concepts in the study of motor control and learning that often get used incorrectly in both everyday life and professional sports.

Today’s class

Lecture objectives

  • Discuss how reaction time can be used an index of motor preparation.

  • Identify and describe the 3 stages of information-processing.

  • Describe how the property of a stimulus can influence reaction time.

  • Explain how Hick’s Law describes the relationship between the number of response choices and reaction time using examples.

TAKE-HOME MESSAGE:
Although reaction time is one of the simplest performance measures, its use has had a profound influence on the development of motor behaviour research.

Conceptual model of information-processing

Conceptual model of information-processing

We can fractionate the reaction interval using EMG

Image from Ballanger and Boulinguez (2009)

Activity

Common reaction time tasks

  • we can use each type to learn about different information-processing activities

Stimulus modality and intensity affect reaction time

Hypothetical data for illustrative purposes

Stimulus modality and intensity affect reaction time

Hypothetical data for illustrative purposes

Real-world example: 2004 Olympics


  • Mean reaction time data from the 100 m sprint and 110/100 m hurdles events grouped based on starting lane position
  • Lane 1 significantly faster than lanes 2-8

Approximate data from Brown et al. (2008) through plot digitization

Activity

The number of stimulus-response alternatives affects reaction time

Approximate data based on Merkel (1885) through plot digitization of Schmidt and Lee (2011)

The number of stimulus-response alternatives affects reaction time

  • choice reaction time increases a near constant amount each time the number of stimulus-alternatives is doubled

  • Hick (1952) and Hyman (1953) both showed that when reaction time was plotted against the logarithm to the base 2 of the number of choices, the relationship was linear

  • this relationship is known as Hick’s Law

Approximate data based on Merkel (1885) through plot digitization of Schmidt and Lee (2011)

Hick’s Law

\[RT = a + b\log_{2}(N)\]

where:

  • a = y-intercept
  • b = slope
  • N = number of S-R alternatives
  • log2(N) = bits of information
    • One bit = the amount of information needed to reduce the original uncertainty in half

Hick’s Law

  • converting the number of stimulus-response alternatives to bits
  • i.e., amount of information
  • recall that one bit is the amount of information needed to reduce the original uncertainty in half

Hick’s Law

\[RT = a + b\log_{2}(N)\]

  • the y-intercept (\(a\)) is the expected reaction time when no choice is required
  • reflects the baseline speed when minimal information needs to be processed

Hick’s Law

\[RT = a + b\log_{2}(N)\]

  • the slope (\(b\)) is the expected increase in reaction time (i.e., the cost) when the number of stimulus-response alternatives is doubled
  • the slope reveals differences in processing speed

Exceptions to Hick’s Law

  • if the stimulus is tactile
    • direct stimulus-response relationship
  • if response is a saccade
    • eye movements to targets are natural and biologically important
  • if extended practice is undertaken
    • after 42,000 practice trials, the typical reaction time difference between a 2-choice task and a 4-choice task was eliminated (Mowbray and Rhoades 1959)

An everyday example

An everyday example

Lecture objectives

  • Discuss how reaction time can be used an index of motor preparation.

  • Identify and describe the 3 stages of information-processing.

  • Describe how the property of a stimulus can influence reaction time.

  • Explain how Hick’s Law describes the relationship between the number of response choices and reaction time using examples.

TAKE-HOME MESSAGE:
Although reaction time is one of the simplest performance measures, its use has had a profound influence on the development of motor behaviour research.

What questions do you have?

Next class: Decision-making II

References

Ballanger B, Boulinguez P. EMG as a key tool to assess motor lateralization and hand reaction time asymmetries. Journal of Neuroscience Methods 179: 85–89, 2009.
Brown AM, Kenwell ZR, Maraj BK, Collins DF. "Go" signal intensity influences the sprint start. Medicine & Science in Sports & Exercise 40: 1142–1148, 2008.
Hick WE. On the rate of gain of information. Quarterly Journal of Experimental Psychology 4: 11–26, 1952.
Hyman R. Stimulus information as a determinant of reaction time. Journal of Experimental Psychology 45: 188, 1953.
Merkel J. Die zeitliche verhältnisse der willenstätigkeit. Philosophische Studien 2: 73–127, 1885.
Mowbray G, Rhoades M. On the reduction of choice reaction times with practice. Quarterly Journal of Experimental Psychology 11: 16–23, 1959.
Schmidt RA, Lee TD. Motor control and learning: A behavioral emphasis. Human Kinetics, 2011.