Grooves on Ganymede are interpreted as extensional tectonic features whose regular spacing is an indicator of the thickness of a brittle surface layer, or ''lithosphere,'' at the time of deformation. We have performed a statistical analysis of groove spacing on Ganymede, taking Fourier transforms of 157 photometric profiles across sets of grooves and examining the resultant power spectra for peaks representing the dominant topographic periodicities. The distribution of groove spacing on Ganymede is approximately lognormal, with a minimum of ~3.5 km, a maximum of ~17 km, and a mean of 8.4 km. There is no correlation of groove spacing with latitude or longitude. The most striking feature of the geographic distribution is that while groove spacing tends to be quite constant within a given groove set, it can vary substantially from one groove set to another in a geographic region. An exception is the Uruk Sulcus region, with a mean groove spacing of 6.5 km and very little variability. We examine several models that relate the observed groove spacing to lithospheric thicknesses. The most important conclusion is that lithospheric thickness varied significantly from one groove set to the next while the grooves were being formed. We examine four possible causes for the heterogeneous distribution: variation in time of formation during a period in which the global mean heat flow was changing, variation in strain rate from one groove set to the next, local excursions in geothermal gradient caused by variations in the vigor of underlying convective upwellings, and local excursions in geothermal gradient caused by resurfacing events. The first three appear viable, while the fourth requires very rapid groove formation due to the short cooling times involved.