On an identity between the Gaussian and Rasch measurement error distributions: Making the role of the instrument explicit

The paper shows an identity between the Gaussian error distribution of replicated measurements and the Rasch model error distribution of inferred, replicated assessments in ordered categories when the thresholds defining the categories are equidistant. The paper concludes by articulating three senses in which the discrete Rasch distribution, in which the role of the instrument is made explicit as it is in modern physics, can be seen as a generalisation of the continuous Gaussian distribution.