Objectivity, Units of Measurement and Zeroes

Objectivity is the cornerstone of measurement. Measurement values must be completely independent of the particular instruments used and the particular conditions of measurement surrounding their use. A critical distinction, however, exists between the specific or local objectivity achieved by Rasch, and the general objectivity of measures in physical science.

Local Objectivity requires that differences between object measures and indicant calibrations be sample and test independent. Since the Rasch model can be derived from this property (RMT 1:1 p.5), it is necessarily a property of any set of data that fit the Rasch model. This means that when data fit, apart from specified random error, two indicants must differ by the same amount no matter which sample of objects actually responds to the indicants. Similarly, two objects must differ by the same amount no matter which samples of indicants (from the relevant construct) are used to implement the measurement procedure. Consequently, when data fit the Rasch model, then the relative locations of objects and indicants on the underlying continuum for a construct are sample and test independent.

But local objectivity does not address the problem of an absolute frame of reference with absolute units and an absolute zero. The measurement unit for local independence, a linear translation of the local logit, is defined by the stochastic nature of the data, not by substantive aspects of what is being measured. Consequently accidental changes in the way that data are collected can change the level of stochasticity and so the logit size of relative measures.

Relative measures share a local specificity which manifests itself as perturbations in the substantive length of the logit (definition of the unit of measurement) and a location indeterminacy which depends on where the zero point is set (usually magnitudes of item difficulties are reported relative to the mean calibration of a particular set of items).

General Objectivity, approximated by measures in physics and chemistry, is the property that absolute location of an object on, for example, the Celsius scale, is independent of the instruments and conditions of measurement. This absolute location implies substantively defined zero point and measurement units. Temperature theory is well enough developed that thermometers can be constructed without reference to data. Thermometers are manufactured and distributed without checking their calibrations against data with known values. We know enough about liquid expansion, gas laws, glass conductivity and viscosity to construct usefully precise measurement devices from theory alone.

General objectivity does not require a construct theory, but is facilitated by one. Pan balances, employing simple weight concatenations, have been used to produce generally objective measures of weight. But spring balances and bathroom scales, based on the construct theory of Hooke's law, are smaller, faster and cheaper. The consequence of using a construct theory and associated calibration equations is that general objectivity is achieved. Measurement of the temperature of two objects results in more than sample independence for the difference between their temperatures. There is also sample independence for the point estimate of each objects temperature.

General objectivity could be obtained in social science. We could select "the one ounce" test item. Then, as Thorndike suggested in 1904, following the model of the pan balance, we could construct other "one ounce" items, and then measure ability and calibrate other items in these "standard ounces". But this would leave us dependent on our choice of the initial item and our ability to maintain its status, in the way that physical measurement systems were once dependent on a selection for a "standard ounce" and its protection from change.

When, instead, a construct theory is used to build calibration equations, it is possible to specify and maintain a zero point and a unit of measurement independent of any instrument or indicant. When this separating of measurement framework and instrument is achieved the frame of reference is unaffected by the act of measuring and all location and scaling indeterminacies are resolved by the construct theory. The kind of measurement that results resembles what we are familiar with in physical science.

In social science, calibrating instruments (e.g., items) through theory alone accomplishes two essential outcomes. (1) The unit of measurement can be specified and maintained independent of who is being measured or what instrument is doing the measuring. Thus, the substantive meaning of the size of a logit would not change with targeting, misfit, errors in item difficulties or variation in respondent involvement. (2) The choice of zero point can also be specified and maintained by the theory. This would permit absolute quantities (rather than merely relative measures) to be separated from the particulars of the instrument and context of measurement.

In summary, specific or local objectivity as achieved with the Rasch model ensures that relative measures, the differences between objects or between indicants, are independent of the conditions of measurement. In contrast, general objectivity ensures that absolute measures, the amounts themselves, are similarly independent.

Repeatability and Reproducibility A "quantity" is an amount expressed in a "specified" unit. A unit is specified through the calibration equations that operationalize the construct theory. These equations are used to define and maintain the unit of measurement independent of the method and instant of measurement. A "specified" unit transcends the instrument and thereby achieves the status of a quantity. Without this transcendent quality units remain local and dependent on particular instruments and samples for their absolute expression.

One test for whether the unit of measure has been specified, and maintained independent of the instrument, is to compare repeatability and reproducibility. Repeatability refers to the consistency with which a single instrument or item bank produces the same quantity following replications of the measurement procedure. Reproducibility refers to the consistency with which different item developers can produce the same quantity following replications of the measurement procedure. Evidence that the unit of measure is specified and maintained comes from measuring the same person with different instruments and obtaining statistically comparable quantities with each instrument. This "separation" of measure and instrument is an aspect of measurement that is taken for granted in the physical sciences, but is rarely contemplated, let alone attempted, in the behavioral sciences.

As with all things of value, the separation of the unit of measure from the instrument has a price. This price is denominated in units of uncertainty. An absolute quantity is necessarily less precise, i.e., measured with more error, than is a locally best relative measure. In practice, the utility of substantively meaningful and instrument-independent measures is worth the small loss in precision.

Jack Stenner
Metametrics Inc.
2327 Englert Drive #300
Durham NC 27713

Objectivity, Units of Measurement and Zeroes. Stenner A. J. … Rasch Measurement Transactions, 1997, 11:2 p. 560-561.

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Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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