The oxidation of hydrocarbon fuels proceeds through the attack of small radicals such as H and CH3 on large molecules. These radicals abstract H atoms from the large molecules, which then usually proceed by beta-scission to form C2H4 and C3H6. Quantifying these rates is critical to the development of chemical models for the oxidation of hydrocarbons. Study of this reaction system is confounded by the rapid dissociation of the intermediate radicals, which produces both additional H and additional CH3, making it difficult to separate the behavior of the two radical species under many conditions. In this work, we propose an experimental design algorithm, experimental design through differential information (EDDI), that we apply to measuring H and CH3 attack rates on n-butane using a single-pulse shock tube. This design algorithm is based on the method of uncertainty minimization using polynomial chaos expansions (Sheen, D. A.; Wang, H. Combust. Flame 2011, 158, 2358-2374). We generate a set of proposed measurements covering a wide range of initial reactant concentrations, temperatures, and species concentration measurements, for a total of 160 proposed measurements. To simulate the proposed measurements, we use the jet surrogate fuel model as a candidate model. We then use the EDDI algorithm to identify the best subset of measurements to perform. Seven are elected as the best set. We compare EDDI's performance against an expert-recommended set of measurements. The machine-generated measurement set performs better than the expert-generated experimental set. Therefore, the EDDI algorithm can be used to augment an expert's evaluation of a set of measurements and can be applied to many other database analysis and constraint problems.