After you have defined attributes and levels and decided which questionnaire format is best for your study, you need to decide how many conjoint questions (tasks) to ask. This decision depends on how many separate part-worth parameters need to be estimated. The more attributes and levels in your study, the more part-worths to be estimated; and the more parameters to estimate, the longer the questionnaire.
CVA examines the list of attributes and levels in your study and provides an initial recommendation regarding the number of tasks (conjoint questions) to ask. The recommended number of tasks provides three times the number of observations as the number of parameters to be estimated. The number of parameters to be estimated is determined by the formula:
Total number of levels - number of attributes + 1
Although it is mathematically possible to estimate utilities by asking only as many questions as the number of parameters to be estimated, we strongly recommend against this practice when using standard estimation routines (OLS and Monotone Regression). Asking the recommended number of tasks helps ensure enough information to calculate stable estimates for each respondent.
If your design includes many attributes and levels, you may notice that the recommended number of questions exceeds what you could reasonably expect respondents to complete. This leads to a difficult decision. Too few questions limit the degrees of freedom of the design (and the precision of the part-worth estimates); but if you ask too many conjoint questions respondents may become fatigued or bored and provide data of poor quality. In our experience, asking more than about 30 conjoint questions may result in poor quality data. Testing your questionnaire with actual respondents can help you determine an appropriate number of questions to ask for your project.
CVA will not let you specify fewer questions than the number of parameters to be estimated and will warn you if you don't ask at least 1.5x the number of parameters to be estimated. A number of studies in the literature suggest that some experienced conjoint analysts are willing to ask as few as 1.5x the number of questions as parameters to estimate. Indeed, the use of HB estimation may slightly reduce the number of questions you decide to ask respondents, as it estimates part-worths based on information from the current respondent plus information from the other respondents in the same data set.
Note: if using HB estimation, it is possible to ask respondents fewer questions than parameters to be estimated, while still obtaining good aggregate results. (See Sparse Designs and Large Samples for more info.) In that case, the questionnaire design still contains more tasks than parameters to estimate, but each respondent is asked to complete just a random subset of the tasks. Please note that there is loss in information at the individual level by taking this approach (relative to asking respondents to complete all tasks). If having respondents skip tasks, you should use larger sample sizes than usual to compensate for the loss in information.