Formulas are derived for unbiased sample estimators of any raw or central moment of the frequency distribution of true scores. Explicit and relatively convenient computational formulas are written down for both raw and central moments up to and including the fourth order. Methods for fitting frequency curves to a set of estimated true-score moments are briefly discussed. A general method is developed for obtaining from each examinee's observed score a least-squares estimated of his true score. Detailed computational formulas for making such estimates are given for the case where the regression of true score on observed score is assumed to be linear and for the case where this regression is assumed to be a third-degree parabola. The method can be extended to the case where this regression may be approximated by a parabola of any specified degree.