# How long does it take to decide for an multiple choice option with increasing number of choices?

I am trying to estimate the duration of an empirical experiment. In that experiment, the participant has to progress through as many trials as possible, and every trial is a simple multiple choice question like Which color do you like more? Red, Blue or Green. The experiment should last 30 minutes, and one goal is that the participant has given as much feedback as possible. Feedback is every choice that has been displayed, not only those choices the participant decided for in every particular trial.

Obviously, the participant should evaluate every choice available in a trial, and therefore time to answer should increase. However, I assume that this is not linearly correlated.

I.e. is there some heuristic available that enables me to extrapolate from time needed to answer a question with two choices to time needed to answer a question with 20 choices?

• Are all questions opinions with no objectively correct answers? – kindredChords Jan 27 '17 at 3:50
• Yes, every answer is a good answer. However, the participant will have to think which answer to choose. But all questions will be equally hard. – helt Jan 27 '17 at 8:07

## 2 Answers

A starting point is Hick's Law: As noted in the URL, the visual complexity of the choice space may be important independent of the informational complexity of the question options

The answer time as function of the number of choices will theoretically follow a marginal decreasing convex function. There is a constant time dependent on the complexity of the question, and then a variable time dependent on the number of multiple options. I believe that in order to derive the exact functional form of this function you must make some experiments and then adjust it to the specific response times you get from your sample