Previous research has indicated that correlations between Piagetian and psychometric tests and chronological age are influenced by the size of the age range of the sample groups. To examine whether the size of the age range and mean age are related to the size of the correlations between Piagetian and arithmetic tests, Spearman rank-order correlations were obtained between these age-related variables and the Piagetian and arithmetic test correlations. Age range size was not related to the size of the Piagetian and arithmetic test correlations, however, an inverse and the size of the correlation between Piagetian and arithmetic tests, and the size of the correlation between PIagetian and arithmetic tests, indicating that groups with younger mean ages tended to have larger correlations than groups with older mean ages. The data suggest that a moderate relationship exists between Piagetian and arithmetic tests. Furthermore, no systematic differences occurred in the size of the Piagetian-arithmetic correlations between standardized and nonstandardized arithmetic tests. Many conserving children perform higher on arithmetic tests than do their nonconserving peers, although some nonconserving children nevertheless attain comparable levels of arithmetic performance. These results suggest that Piagetian tests might be used as a diagnostic aid for children who are experiencing difficulties in arithmetic. (Author/CKJ)