Often researchers were stunned when asked about the meaning of their data analysis findings; whether they are measuring what is supposedly to be measured.

These issues of meaningfulness and measurement are explored at length by Fisher. The basic point is that the content of tests and surveys ought to be used to illustrate mathematical relationships between abilities and difficulties visually and conceptually without confusing them with the mathematical relationships themselves. We need to look right through the sample of items used to illustrate the construct and keep the pure thought of the construct in mind, in the manner of the numerical and geometrical figures that are understood to paradigmatically define meaningful representation by, again, a wide range of diverse philosophers. Meaningful measurement requires what Rasch called parameter separation, what Ronald Fisher called statistical sufficiency, and what Luce and Tukey called conjoint additivity.

There is a basic principle of meaningfulness accepted by a wide cross-section of different philosophical viewpoints that justifies the use of fundamental measurement models like Rasch's Measurement Model. Mundy's general theory of meaningful representation states that: "The hallmark of a meaningful propositions have truth-value independent of the choice of representation, within certain limits. The formal analysis of this distinction leads, in all three areas viz; measurement theory, geometry, and relativity, to a rather involved technical apparatus focusing upon invariance under changes of scale or changes of coordinate system." The same focus on the independence of figure and meaning, or scale and proportion, emerges in a wide variety of other works on the creation of qualitative mathematical meaning.

Hence, reseachers must understand the needs what is to be measured and knows whether they are measuring what is supposedly to be measured. Rasch offers a new paradigm in making a measurement more meaningful.

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