Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The power calculations are conducted for the two co-primary outcomes, the binary indicator for organic choice and the binary indicator for luxury choice, both elicited through a fully incentivised field experiment involving real physical products and real monetary payment. The use of real consequential choices is expected to yield cleaner and more conservative effect sizes than hypothetical or laboratory analogues, since social desirability inflation and demand effects are substantially reduced when respondents bear real costs. All calculations assume a two-sided test, a significance level of five percent, and a target statistical power of eighty percent.
For the main treatment effect on the organic choice indicator, the comparison of interest is between the organic salience arm and the control arm, each comprising 100 respondents. Baseline choice probabilities for organic chocolate in a Vietnamese urban field setting are not directly available, so the calculations adopt a conservative baseline probability of twenty percent in the control arm, consistent with green product choice shares observed in comparable middle-income country field settings. Under this assumption, a sample of 100 respondents per arm achieves eighty percent power to detect a minimum absolute increase in organic choice probability of approximately 17 percentage points, corresponding to a standardised effect size of Cohen's h equal to approximately 0.40. If the baseline probability is thirty percent, the minimum detectable absolute shift is approximately 19 percentage points. For the luxury choice indicator, the same logic applies in the luxury salience arm versus the control arm comparison, with an assumed baseline luxury choice probability of twenty-five percent and a minimum detectable absolute increase of approximately 18 percentage points.
For the interaction between the continuous attitudinal score and the treatment arm indicator, the power calculation follows the framework for detecting moderated treatment effects in linear probability models. Assuming attitudinal scores are approximately normally distributed with a standard deviation of one Likert scale point, and that the residual standard deviation of the binary outcome after controlling for main effects and covariates is approximately 0.45, the full sample of 300 respondents achieves eighty percent power to detect an interaction coefficient of approximately 0.10 per standard deviation of the attitudinal score. In substantive terms, this means the study can detect a situation in which a one standard deviation increase in green signalling motivation raises the probability of organic choice by an additional ten percentage points in the organic salience condition relative to the control. This threshold is calibrated against the interaction effect sizes reported by Griskevicius, Tybur, and Van den Bergh in their 2010 study, where public visibility moderated green product choice with standardised effects in the range of 0.30 to 0.50. Because the present study uses real consequential choices rather than hypothetical laboratory tasks, effect sizes are expected to be more conservative, and the lower bound of this range is therefore used as the planning assumption.
For the instrumental variables specification, power is necessarily lower due to the efficiency loss relative to ordinary least squares. Assuming a first-stage partial R-squared of approximately 0.15 across the three community observability instruments, the two-stage least squares estimator retains sufficient precision to identify the direction and significance of the status-signalling effect, though confidence intervals will be wider than in the ordinary least squares specifications. The instrumental variables approach is therefore pre-specified as a robustness check on the sign and significance of the attitudinal regressors rather than as the primary source of causal identification. The principal source of causal identification remains the interaction between the randomised informational treatment and the continuous attitudinal scores, which is fully experimental and unaffected by the endogeneity concerns that motivate the instrumental variables approach.
No correction for multiple comparisons is applied in the primary pre-specified specifications, given that the two co-primary outcomes are theoretically symmetric and jointly constitute a single research question about the direction of status-motivated product choice. A Benjamini-Hochberg family-wise error rate correction will be reported alongside uncorrected results for transparency. Attrition is expected to be minimal given the interviewer-administered format, short session duration, and the tangible appeal of real product and monetary payment, but a ten percent buffer is incorporated into the target sample of 300 to absorb unusable observations from failed attention checks or incomplete questionnaires.