Head Start is the largest publicly funded preschool program in the U.S., and one of its primary goals is to improve the school readiness of low-income children. As has been widely reported, the first randomized trial of Head Start in the program's history found some evidence that it is achieving this goal. Receiving one year of Head Start had small impacts on children's cognitive outcomes, with impacts on cognitive impacts concentrated in the language and literacy domain. However, effects largely faded out by the end of first grade (U.S. Department of Health and Human Services 2010). In explaining these results, some have pointed to the variation in quality across Head Start centers. This study uses data for the first follow-up year of the Head Start Impact Study to examine variation in Head Start's impacts on children. Researchers examine whether there is statistically significant variation in Head Start's impacts on children's cognitive and socio-emotional outcomes across individual children, subgroups of children, and Head Start centers. To do so, researchers use a new and innovative methodology for estimating sources of variation in program impacts. In total, 4,440 children in 202 center groups were randomized to treatment or control in the original Head Start Impact Study. The sample is comprised of the subset of children within these 202 center groups for whom there was outcome data available during the study's first follow-up year (N=3,785 children, or 85% of the children originally randomized). Children randomized to treatment were offered a seat in a classroom in a Head Start program in fall 2002 for the 2002-2003 school year. Children randomized to control conditions were free to take up any available early childhood program except for the program provided by the Head Start to which they had applied and had not won a seat. In fall 2002 and in spring 2003, study children were tested by a trained child assessor on an extensive battery of cognitive and socio-emotional assessments. Parents were also surveyed in fall 2002 and spring 2003 on basic demographic information and on dimensions of their children's behavior. Children were followed through third grade, and other data were gathered from various sources (e.g. additional child testing, teacher and center director interviews, direct observations of classroom quality). The analysis is based on data from the fall 2002 and spring 2003 child testing and parent survey only. One important feature of the analysis was comparison of residual outcome variances for treatment and control group members. The analysis of the statistical significance of across-center variance in impacts on children distinguishes between: (1) variation in program effect "estimates"; and (2) variation in program "effects." Findings suggest that Head Start had impacts on individual residual variance that have not yet been recognized in analyses of these data. Specifically, Head Start reduced the individual residual variance for treatment group members versus control group members on two important early skills--receptive vocabulary and early math. These findings suggest that Head Start was successful in improving the vocabulary and early numeracy skills of children with lower levels of such skills at entry, with such effects concentrated among dual-language learners and Hispanic children. Tables are appended.