The aim of this paper is to address two research questions related to the policy goal of having all children ready to learn at kindergarten entry. First, to what extent are children's cognitive and achievement skills higher when they experience higher quality preschools? Second, are the effects of preschool center quality on these school readiness skills different by demographic (i.e. race/ethnicity, gender, maternal education) or child characteristics (i.e. child's initial cognitive/achievement skills, attention, problem behaviors)? All data included in these secondary data analyses were collected in preschool center-based care. This paper applies meta-analytic techniques to summarize results from original analyses of four longitudinal databases to estimate variation in preschool program quality impacts by demographic and child characteristics. The consistency of the generally null results and the precision with which they are estimated across the four databases, multiple outcomes, and multiple child care quality measures suggests the following: (1) there are at best very modest preschool center quality main effects on both cognitive and achievement child outcomes and (2) there is generally an absence of "differential" preschool center quality effects on school readiness for subgroups of children defined by demographic or child characteristics. However, readers should bear in mind that preschool center quality may not be adequately measured in currently available databases. (Contains 4 tables and 3 figures.)