This paper proposes a generalized estimating equations approach for the analysis of spatially correlated binary data when there are large numbers of spatially correlated observations on a moderate number of subjects. This approach is useful when the scientific focus is on modeling the marginal mean structure. Proper modeling of the spatial correlation structure is shown to provide large efficiency gains along with precise standard error estimates for inference on mean structure parameters. Generalized estimating equations for estimating the parameters of both the mean and spatial correlation structure are proposed. The use of semivariogram models for parameterizing the correlation structure is discussed, and estimation of the sample semivariogram is proposed as a technique for choosing parametric models and starting values for generalized estimating equations estimation. The methodology is illustrated with neuroimaging data collected as part of the National Institute of Neurological Disorders and Stroke (NINDS) Stroke Data Bank. A simulation study demonstrates the importance of accurate modeling of the spatial correlation structure in data with large numbers of spatially correlated observations such as those found in neuroimaging studies.