Magnitude estimation and categorical rating scaling in social sciences: a theoretical and psychometric controversy

This paper revisits a half-century long theoretical controversy associated with the use of magnitude estimation scaling (MES) and category rating scaling (CRS) procedures in measurement. The MES procedure in this study involved instructing participants to write a number that matched their impression of difficulty of a test item. Participants were not restricted in the range of numbers they could choose for their scale. They also had the choice of disclosing their individual scale. After the MES task was completed, participants were given a blank copy of the test to rate the perceived difficulty of each item using a researcher-imposed categorical rating scale from 1 (very easy) to 6 (very difficult). The MES and CRS data were both analyzed using Rasch Rating scale model. Additionally, the MES data were examined with Rasch Partial Credit model. Results indicate that knowing each person's scale is associated with smaller errors of measurement.