Manual and automatic estimates of growth and gain across year levels

Users of statistical software are frequently unaware of the calculations underlying the routines that they use. Indeed, users, particularly in the social sciences, are often somewhat adverse towards the underlying mathematics. Yet, in order to appreciate the thrust of certain routines, it is beneficial to understand the way in which a program arrives at a particular solution. Based on data from the Economic Literacy Study conducted at year 11 and 12 level across Queensland in 1998, this article renders explicit the steps involved in calculating growth and gain estimates in student performance. To this end, the first part of the article describes the Omanual calculation of such estimates using the Rasch estimates of item thresholds of common items at the different year levels produced by Quest as a starting point for the subsequent calibrating, scoring and equating. The second part of the chapter explores the extent to which estimates of change in performance across year levels that are calculated with ConQuest. The article shows that the manual and automatic way of calculating growth and gain estimates produce nearly identical results. This is not only reassuring from a technical point of view but also from an educational point of view as this means that the reader of the non-mathematical discussion of the manual calculation procedure will develop a better understanding of the processes involved in calculating growth and gain estimates.