Pumping tests are routinely interpreted from the analysis of drawdown data and their derivatives. These interpretations result in a small number of apparent parameter values which lump the underlying heterogeneous structure of the aquifer. Key questions in such interpretations are (1) what is the physical meaning of those lumped parameters and (2) whether it is possible to infer some information about the spatial variability of the hydraulic parameters. The system analyzed in this paper consists of an aquifer separated from a second recharging aquifer by means of an aquitard. The natural log transforms of the transmissivity, ln T, and the vertical conductance of the aquitard, ln C, are modeled as two independent second‐order stationary spatial random functions (SRFs). The Monte Carlo approach is used to simulate the time‐dependent drawdown at a suite of observation points for different values of the statistical parameters defining the SRFs. Drawdown data at each observation point are independently used to estimate hydraulic parameters using three existing methods: (1) the inflection‐point method, (2) curve‐fitting, and (3) the double inflection‐point method. The resulting estimated parameters are shown to be space dependent and vary with the interpretation method since each method gives different emphasis to different parts of the time‐drawdown data. Moreover, the heterogeneity in the pumped aquifer or the aquitard influences the estimates in distinct manners. Finally, we show that, by combining the parameter estimates obtained from the different analysis procedures, information about the heterogeneity of the leaky aquifer system may be inferred