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Choice Reaction and Hick's Law — Why More Options Slow You Down
The differences between simple reaction, choice reaction and Go/No-go, Hick's law on how reaction time grows with the number of options, and what commission and omission errors mean.
Reaction time tasks fall into three broad types: simple reaction, with only one signal; choice reaction, where you pick a different response for each signal; and Go/No-go, where you respond only to a specific signal and hold back on the rest.
Simple vs. choice reaction
In simple reaction, the decision "press when the signal comes" is made in advance, so there is almost no decision stage. In choice reaction, time is added to distinguish the signal and choose the right response, so reaction time gets longer.
Hick's law
Hick (W. E. Hick, 1952) and Hyman (R. Hyman, 1953) showed that as the number of options increases, reaction time increases in proportion to the logarithm of the number of options. It is commonly written as follows.
RT = a + b · log₂(n + 1)
Here n is the number of equally likely options, and a and b are constants determined by the person and the task. The increase from 1 to 2 options is much larger than from 8 to 9. It's also often cited to explain why users hesitate when there are many menus or buttons.
The Go/No-go task
Go/No-go is a task with two options: "press" or "hold back". On this site, the ● circle is Go and ✕ is No-go, with 5 Go and 3 No-go stimuli appearing in random order. Two kinds of errors are counted separately.
- Commission error — Pressing on ✕. It reflects a tendency to press impulsively.
- Omission error — Failing to press ● within 1.5 seconds. It indicates a lapse in attention.
The speed–accuracy trade-off
The harder you try to press quickly, the more commission errors you make; the harder you try not to make mistakes, the slower you react. This is called the speed–accuracy trade-off. When looking at Go/No-go results, you need to consider reaction time and commission errors together. If your reaction time got faster but your commission errors also increased, it's more likely you rushed than that you improved.
Age and choice reaction
In Der & Deary (2006), an analysis of 7,130 UK adults, simple reaction time changed little until around age 50, but four-choice reaction time slowed throughout adulthood. This means tasks with a decision stage are more affected by age.
Sources
- Hick, W. E. (1952) On the rate of gain of information. Quarterly Journal of Experimental Psychology 4(1):11–26
- Hyman, R. (1953) Stimulus information as a determinant of reaction time. Journal of Experimental Psychology 45(3):188–196
- Der G., Deary I. J. (2006) Psychology and Aging 21(1):62–73