Purpose: Counting and exact arithmetic rely on language-based representations, whereas number comparison and approximate arithmetic involve approximate quantity-based representations that are available early in life, before the first stages of language acquisition. The objective of this study was to examine the impact of language abilities on the…

The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to…

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…