Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Sample size adequacy for the DCE (Stage 1)
Using Orme’s rule-of-thumb,
N≥(500×c)/t×a
with c=5 attribute parameters, t=8 job choices, and a=2 alternatives, the minimum required sample is about 156 respondents. The planned sample of 2,000 individuals (each with 8 tasks) far exceeds this, indicating ample precision to estimate preferences over the main job attributes.
Stage 1 – Preference differences (acceptance probabilities)
For each spouse, I define an acceptance share as the fraction of the 8 offers accepted. At the couple level, I consider the gap: wife’s acceptance share minus husbands. Under conservative assumptions (baseline acceptance probability of 50% and no cross-spouse covariance), the standard deviation of the couple-level gap is 0.25. With 1,000 couples, a two-sided 5% test with 80% power can detect a difference in the mean gap of roughly 0.022 (≈ 2.2 percentage points).
Stage 3 – Joint alignment (whose preference the joint decision follows)
In disagreement cases (where spouses’ private choices differ), I define an indicator equal to 1 if the joint decision follows the wife and 0 if it follows the husband. Under equal bargaining power, the alignment rate is 50%. If couples disagree on about 25% of 8,000 potential couple–job observations, I observe roughly 2,000 disagreement cases. Treating this as a one-sample proportion with baseline 0.5, power calculations indicate that, at 5% significance and 80% power, the MDE is about 0.031 (≈ 3.1 percentage points), i.e. detecting a shift from 0.50 to about 0.531.
Stage 4 – Information treatments and workshop outcomes
Couples are randomized into three arms (control, legal information, household welfare framing), with ~333 couples per arm. The main binary outcomes is husband’s approval of inviting his wife to the workshop.
1. Husband approval of invitation
o Baseline approval rate assumed at 50% (SD ≈ 0.50) under conservative assignment.
o With 333 couples in control and 333 in a treatment arm, a two-sample proportion test (5% significance, 80% power) can detect a treatment–control difference of about 0.10–0.11 (≈ 10–11 percentage points).
Overall, the planned sample provides strong power for detecting modest differences in wives’ and husbands’ job acceptance patterns, in joint bargaining outcomes, and in the effects of information treatments on husbands’ approval and wives’ workshop attendance.