Two of the most popular methods for obtaining equal-interval scales for educational measurement are discussed: Thurstone's method and Item Response Theory (IRT). Between-grade growth on these scales is compared; while unstandardized differences show different trends for the two scales, standardized differences that take standard deviations into account show very similar growth patterns for the two scales. IRT is used with simulated data to demonstrate that comparisons of growth at different percentiles is not appropriate when observed scores, which contain error of measurement, are the basis of the percentiles. Another IRT simulation demonstrates that normalized observed scores will not necessarily be linearly related to underlying normally distributed traits when error variance affects the observed score distribution. When achievement is multidimensional and changes with age, it is not possible to obtain an equal-interval scale that extends over test levels. The outcome of the use of unidimensional IRT with multidimensional tests is discussed, and several alternative IRT scales are outlined. Finally, a brief discussion of statistical analyses of achievement scales is presented. (Author)