Background Two decomposition methods have been widely used to attribute death differences between two populations to population size, age structure of the population, and age-specific mortality rate (ASMR), but their properties remain uninvestigated. Methods We assess how the two established decomposition methods yield varying results with three-factor factorial experimental designs, illustrating that they are sensitive to the choice of the reference group. We then propose a novel decomposition method to obtain robust decomposition results and use three cases to demonstrate its advantage. Results The three decomposition methods differ fundamentally in their allocation of interactions to the contributions of the three factors. In comparison with the existing methods, the new method is robust to the choice of the reference group. Three case studies showed inconsistent attribution results for the two existing methods but robust results for the new method when the choice of the reference population changes. Conclusions The proposed method offers robust and more justifiable attribution results compared to the two existing methods. This method could be generalized to attribution of group differences of other health indicators.