# What is the minimum sample size for discrete choice experiment?

I was wondering if there is a minimum sample size for conducting discrete choice experiment. From what I know, if choosing the number of sample size is a problem, one can resort to using the magic number of 400+. Although it would be nice to have such sample size, but then this kind of experiment is expensive, so 400+ or more may be impractical. I have read several journal articles about DCE and I was surprised that their sample sizes did not even reached 400.

• This is a difficult question to answer, given the information provided above. Without knowing the number of attributes (and levels) in your experimental design and the number of questions you plan to ask of each respondent, I cannot provide a justifiable answer. Do keep in mind that the quality of your experimental design can greatly affect the variance of your parameter estimates and, therefore, increasing the efficiency of your design is equivalent to increasing your sample size. – user16892 Nov 15 '12 at 20:37
• @Anderson. I see. So it really depends on the design of my experiment, my research questions, etc. I guess I have to carefully design my experiment to get the minimum and "optimum" sample size to avoid unnecessary costs. Thanks very much Anderson. – archie Nov 15 '12 at 23:56

According to Orme (2010), one rule of thumb for an acceptable sample size is:

$$n \geq 500c/ta,$$ where:

• n is the number of respondents,
• t is the number of is the number of tasks,
• a is number of alternatives per task (not including the none alternative),
• c is the number of analysis cells. When considering main effects, c is equal to the largest number of levels for any one attribute. If you are also considering all two-way interactions, c is equal to the largest product of levels of any two attributes.

For example, if you are only considering main effects in a 3×3×4 design with three alternatives (plus one for 'choose none') and twelve choice tasks per respondent (without placing respondents into different blocks), you will need at least:

$$n \geq 500×4/(12×3)\approx56$$ respondents.

Online conjoint analysis tools will, such as Conjoint.ly, will be able to calculate this automatically when you set up an experiment.