We consider parameters determined by the inversion of slug-test head recovery data with the homogeneous-parameter model of Cooper et al. <1967> to be weighted spatial averages of transmissivity and storage defined at a smaller scale. We quantify the spatial averaging using a power-average spatial filter expression. We determine the form of the filter function and the power exponent using numerically simulated slug-test data. The filter function that describes how smaller-scale transmissivity is weighted by slug tests displays an approximate 1/r2 behavior, with r the radial distance from the well. The radius of the cylinderical volume that is averaged by the slug test is inversely proportional to the square root of the storage coefficient (larger averaging volume with smaller storage). The power exponent grows from -0.19 to 0.345 as the ratio of the characteristic scale of the heterogeneity to the characteristic scale of the averaging volume grows, although a power exponent of zero, corresponding to geometric averaging, provides good results for most simulations. Our results show that while slug tests are useful to estimate transmissivity, they have dubious value for estimating storage coefficients. We find that the transmissivity estimate is unbiased and does not appear to be strongly influenced by storage properties. The storage coefficient estimate is, however, strongly influenced by the transmissivity and is biased. We investigate the interaction between storage coefficient and transmissivity by examining an analytical slug-test model that contains two annular zones, each with distinct transmissivity and storage coefficient.