Fundamental measurement of the difficulty of test items

Two different procedures were used to measure the difficulties of Scholastic Aptitude Test items: a new distribution-free procedure that uses periodic functions and LOGIST, a well-developed optimization procedure that fits a logistic model. Despite the fact that the two procedures used different data in very different ways, they obtained virtually the same numbers. The new method exemplifies “fundamental” psychological measurement in as much as it is based on counting and ordinal properties of data only.