Sample size for a discrete choice experiment

Sample size is one of the most common questions in DCE research - and one of the most poorly answered. Rules of thumb give you a starting point; simulation gives you confidence.

This article explains how to estimate sample size for a DCE, from simple rules of thumb to simulation-based power analysis, and the key factors that affect how many respondents you need.

Ben White, 07.07.2026

The sample size question

How many respondents do I need for my DCE? This question has no simple universal answer because the required sample size depends on: the number and complexity of the parameters being estimated, the D-efficiency of the design, the number of choice sets per respondent, the expected heterogeneity in the population, and the precision required for the primary decision being informed.

The most commonly cited rule of thumb - N ≥ 500/t where t is the number of choice sets per respondent - is a rough heuristic that ignores most of these factors. It is a starting point, not a definitive answer.

What drives sample size requirements

The fundamental sample size constraint in DCE research is the number of observations needed to estimate each parameter with adequate precision. A simple MNL model with k parameters needs at least 10–20 times k choice observations to produce stable estimates. With 10 parameters and 8 choice sets per respondent, this implies 10–20 respondents minimum - far too small for reliable estimation in practice.

In practice, the minimum effective sample for a DCE is driven by: the minimum number of respondents per design block (typically 50–100 per block for stable within-block estimation), the precision requirements of the WTP estimates, and regulatory or publication requirements for minimum sample sizes in specific application areas.

For most academic DCE studies, samples of 150–300 respondents with 8–12 choice sets each are adequate. For regulatory submissions (FDA patient preference studies), minimum samples of 200–300 per study arm are common. For transport infrastructure appraisal, samples of 300–500 are typical.

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Calculating sample size in practice

Step 1: Start with the rule of thumb. As a lower bound, use N ≥ 500/t where t is the number of choice sets per respondent. For 8 choice sets, this gives N ≥ 63. This is the absolute minimum - not a target.

Step 2: Apply the Johnson-Orme formula for MNL. A more reliable heuristic: N ≥ 500 × c / (t × a) where c is the number of parameters to estimate, t is the number of choice sets, and a is the number of alternatives. For 10 parameters, 8 tasks, 2 alternatives: N ≥ 500 × 10 / (8 × 2) = 313.

Step 3: Account for blocking. If your design uses b blocks, multiply the per-block minimum by b. Each block needs adequate respondents for stable estimation.

Step 4: Account for attrition and exclusions. Add 15–20% to your target to account for dropout, failed consistency checks, and other exclusions. For a target of 300, recruit 350–360.

Step 5: Conduct simulation-based power analysis for critical studies. For regulatory submissions or large-scale infrastructure studies, use Monte Carlo simulation to estimate the distribution of parameter estimates at different sample sizes and select the N that achieves your target precision.

Worked example - sample size for an environmental DCE

An environmental DCE with 5 attributes (2 levels each for 4, 3 levels for 1) uses an MNL model with 5 parameters. With 8 choice sets per respondent and 2 alternatives, the Johnson-Orme formula gives N ≥ 500 × 5 / (8 × 2) = 156. Adding 20% for attrition gives a recruitment target of 188, rounded to 200.

However, the study uses a 4-block design, with minimum 50 respondents per block required for stable block-level estimation. This gives a minimum of 200 respondents - coincidentally the same. The study recruits 220 respondents to provide a 10% safety margin above the 200 minimum.