Our single-item, GSRH questions demonstrated good reproducibility, reliability, and strong concurrent and discriminant scale performance with an established health status measure.

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Rasch's unidimensional models for measurement show how to connect object measures (e.g., reader abilities), measurement mechanisms (e.g., machine-generated cloze reading items), and observational outcomes (e.g., counts correct on reading instruments). Substantive theory shows what interventions or manipulations to the measurement mechanism can be traded off against a change to the object measure to hold the observed outcome constant. A Rasch model integrated with a substantive theory dictates the form and substance of permissible interventions. Rasch analysis, absent construct theory and an associated specification equation, is a black box in which understanding may be more illusory than not. Finally, the quantitative hypothesis can be tested by comparing theory-based trade-off relations with observed trade-off relations. Only quantitative variables (as measured) support such trade-offs. Note that to test the quantitative hypothesis requires more than manipulation of the algebraic equivalencies in the Rasch model or descriptively fitting data to the model. A causal Rasch model involves experimental intervention/manipulation on either reader ability or text complexity or a conjoint intervention on both simultaneously to yield a successful prediction of the resultant observed outcome (count correct). We conjecture that when this type of manipulation is introduced for individual reader text encounters and model predictions are consistent with observations, the quantitative hypothesis is sustained.

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Huge resources are invested in metrology and standards in the natural sciences, engineering, and across a wide range of commercial technologies. Significant positive returns of human, social, environmental, and economic value on these investments have been sustained for decades. Proven methods for calibrating test and survey instruments in linear units are readily available, as are data- and theory-based methods for equating those instruments to a shared unit. Using these methods, metrological traceability is obtained in a variety of commercially available elementary and secondary English and Spanish language reading education programs in the U.S., Canada, Mexico, and Australia. Given established historical patterns, widespread routine reproduction of predicted text-based and instructional effects expressed in a common language and shared frame of reference may lead to significant developments in theory and practice. Opportunities for systematic implementations of teacher-driven lean thinking and continuous quality improvement methods may be of particular interest and value.

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Academia's mathematical metaphysics are briefly explored en route to an elaboration of the qualitatively rigorous requirements underpinning the calibration and unambiguous interpretation of quantitative instrumentation in any science. Of particular interest are Gadamer's emphases on number as the paradigm of the noetic, on the role of play in interpretation, and on Hegel's sense of method as the activity of the thing itself that thought experiences. These point toward and overlap with (1) Latour's study of the metrological social networks through which technological phenomena are brought into language as modes of being that can be understood, and (2) the way that Rasch's models for measurement comprise a potential beginning for metaphysically astute, qualitatively and quantitatively integrated, mathematical methods in the social sciences. The paper closes with observations on the general problem that is philosophy, the need to remain open to multiplicities of meaning even as clear understandings are sought and obtained.