Hick's Law Experiment
Introduction
Hick's Law, also known as the Hick–Hyman law, is named after psychologists William Edmund Hick and Ray Hyman. It describes how the time it takes to make a decision increases logarithmically with the number and complexity of choices.
Frequently Asked Questions
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What does Hick's law say?
Reaction time increases linearly with the logarithm of the number of response alternatives — doubling the choices adds a roughly constant amount of time.
What does the slope mean?
It estimates how quickly you can absorb information for action (bits per second), one of the classic information-theory measures from the 1950s.
Why do more choices cost so little time each?
Because the cost is logarithmic — the decision process appears to divide the options efficiently rather than checking each one in turn.
Where does it show up in design?
Menu depth, control layouts, and warning design all trade on Hick's law: more options always cost time, though familiarity shrinks the cost.
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Hick's Law Definition & Principle
Hick's Law derived from cognitive experiments, measures the 'rate of gain of information' — the time required to process bits of information. Despite common intuition, doubling the number of choices does not double decision time due to its logarithmic nature, where the increase in decision time diminishes as choices grow.
Hick's Law Formulas
The average reaction time 𝑇 is calculated using the formula:
The constant 𝑏 in this formula is derived from experimental data, and the logarithm reflects the depth of decision-making hierarchy, similar to a binary search mechanism. This method efficiently reduces the decision set by categorizing choices.
When choices have unequal probabilities, the formula can be generalized as:
Where 𝐻 is strongly related to the information-theoretic entropy of the decision, The information-theoretic entropy 𝐻 is calculated as:
Where pi refers to the probability of the ith alternative yielding the information-theoretic entropy.
Hick's Law, much like Fitts's Law, emerges because decision-making naturally involves categorizing choices, which logarithmically reduces the set of possibilities rather than requiring a linear evaluation of each option.
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References
- Hick, W. E. (1952). On the rate of gain of information. Quarterly Journal of Experimental Psychology, 4(1), 11-26. 10.1080/17470215208416600
- Hyman, R. (1953). Stimulus information as a determinant of reaction time. Journal of Experimental Psychology, 45(3), 188-196. 10.1037/h0056940
- Jensen, A. R. (2006). Clocking the mind: Mental chronometry and individual differences. Elsevier.
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About This Experiment
This experiment is an educational adaptation for demonstration purposes. It is not a clinical diagnostic tool. Results reflect your performance in this specific session and should not be interpreted as an assessment of your cognitive abilities.
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