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Background: Reducing health inequalities requires interventions that work as well, if not better, among disadvantaged populations. The aim of this study was to determine if the effects of price discounts and tailored nutrition education on supermarket food purchases (percentage energy from saturated fat and healthy foods purchased) vary by ethnicity, household income and education. Method: A 2×2 factorial trial of 1104 New Zealand shoppers randomised to receive a 12.5% discount on healthier foods and/or tailored nutrition education (or no intervention) for 6 months. Results: There was no overall association of price discounts or nutrition education with percentage energy from saturated fat, or nutrition education with healthy food purchasing. There was an association of price discounts with healthy food purchasing (0.79 kg/week increase; 95% CI 0.43 to 1.16) that varied by ethnicity (p=0.04): European/other 1.02 kg/week (n=755; 95% CI 0.60 to 1.43); Pacific 1.20 kg/week (n=101; 95% CI 0.06 to 2.34); Maori --0.15 kg/week (n=248; 95% CI --1.10 to 0.80). This association of price discounts with healthy food purchasing did not vary by household income or education. Conclusions: While a statistically significant variation by ethnicity in the effect of price discounts on food purchasing was found, the authors caution against a causal interpretation due to likely biases (eg, attrition) that differentially affected Maori and Pacific people. The study highlights the challenges in generating valid evidence by social groups for public health interventions. The null findings for tailored nutritional education across all social groups suggest that structural interventions (such as price) may be more effective. [ABSTRACT FROM AUTHOR]