Demand response (DR) is a voluntary program that encourages related stakeholders, in this case electricity consumers, to cut down on usage during periods of high electricity load. One key to fully exploiting DR is to encourage residential customers to join the DR program. Unlike in the DR programs for commercial and industrial customers, for the successful operation of the residential DR program, several issues have to be addressed, one of which is to provide a group-level incentive to participating customers. In particular, the issue comes up when the incentive calculated for a group is not equal to the aggregated incentives for each customer (i.e., non-equal incentive problem). The non-equal incentive problem deteriorates the successful operation of residential DR by decreasing the motivation of DR operators and customers. We first prove the non-equal incentive problem through mathematical and experimental methods. We then propose the novel single group-based indirect incentive calculation method. The basic idea of our approach is to indirectly calculate the incentive for each customer not using the customer's data but using the data of other customers of the same DR group. Through experiments involving the electricity usage data of 42,193 households and the real DR events in Korea, we show that our method solves the non-equal incentive problem in most cases. Furthermore, our method improves the accuracy of the baseline estimation (used for calculating the contribution).