231
comprehension across paragraphs or texts, but the transducers (i.e., the reading
comprehension items) are instead always focused on specific words or phrases
within a sentence.
7.4.2.2 Regarding the definition and dissemination of the public scale
and calibration
We assume that at a given time the instrument has been calibrated against some
reference objects, i.e., measurement standards, with reference properties Θ[s j
*
] and
corresponding values θ j . This requires, first of all, that the public scale Θ[s j
*
] → θ j
was effectively disseminated, from the primary realization of the definition of the
reference properties (and therefore of the unit, in the case of quantities), via a metrological traceability chain. Thus, along the chain and across contexts, inaccuracies
and instabilities may affect the reproduction of the reference properties in such a
way that the properties of the primary standards may differ from the properties
Θ[s j
*
] of the working standards. This leads to uncertainties in the public scale
Θ[s j
*
] → θ j used for the instrument calibration. Moreover, calibration requires some
empirical processes to be performed, i.e., transduction and matching, in which
influence properties may affect the instrument indication and therefore the construction of the local scale X i
*
→ x i . These uncertainties in both the public scale and the
local scale combine to form a calibration uncertainty affecting the calibration map
x i ↔ θ j , as depicted in Fig. 7.22. As noted above, the creation of public reference
objects in the human sciences may be based on the means of sum scores of specified
groups (e.g., Grade 6 students in a given school system taking a RCA test). This can
lead to calibration uncertainty if the means change over time, and these changes are
not accounted for in the public scale, as with the Flynn (1987) effect.
7.4.2.3 Regarding transduction and matching
As with any empirical process, the specifications in the measurement procedure will
not be entirely realized when the measuring instrument is operated. This is due, first
of all, to the unavoidably limited stability and selectivity of the transducer. Moreover,
there could be errors in matching the transduced property X m with respect to the
reference properties X i
*
in the local scale (e.g., the so-called reading errors in the
case of instruments with analog scales). In addition, the local scale could also be
affected by instabilities, resulting in a time-dependent mapping X i
*
→ x i , which is
only uncertainly known. These issues lead to a non-null instrumental uncertainty.
One example for RCA would be where the RCA test is simply mis-scored, whether
by human or machine.
Finally, the fact that the object under measurement must somehow interact with
the transducer may induce an unwanted change in the state of the object, which in
turn produces an interaction uncertainty, as depicted in Fig. 7.23. An example of
this in RCA testing would be where the text passage that was used contained ele7.4 Measurement quality according to the model
comprehension across paragraphs or texts, but the transducers (i.e., the reading
comprehension items) are instead always focused on specific words or phrases
within a sentence.
7.4.2.2 Regarding the definition and dissemination of the public scale
and calibration
We assume that at a given time the instrument has been calibrated against some
reference objects, i.e., measurement standards, with reference properties Θ[s j
*
] and
corresponding values θ j . This requires, first of all, that the public scale Θ[s j
*
] → θ j
was effectively disseminated, from the primary realization of the definition of the
reference properties (and therefore of the unit, in the case of quantities), via a metrological traceability chain. Thus, along the chain and across contexts, inaccuracies
and instabilities may affect the reproduction of the reference properties in such a
way that the properties of the primary standards may differ from the properties
Θ[s j
*
] of the working standards. This leads to uncertainties in the public scale
Θ[s j
*
] → θ j used for the instrument calibration. Moreover, calibration requires some
empirical processes to be performed, i.e., transduction and matching, in which
influence properties may affect the instrument indication and therefore the construction of the local scale X i
*
→ x i . These uncertainties in both the public scale and the
local scale combine to form a calibration uncertainty affecting the calibration map
x i ↔ θ j , as depicted in Fig. 7.22. As noted above, the creation of public reference
objects in the human sciences may be based on the means of sum scores of specified
groups (e.g., Grade 6 students in a given school system taking a RCA test). This can
lead to calibration uncertainty if the means change over time, and these changes are
not accounted for in the public scale, as with the Flynn (1987) effect.
7.4.2.3 Regarding transduction and matching
As with any empirical process, the specifications in the measurement procedure will
not be entirely realized when the measuring instrument is operated. This is due, first
of all, to the unavoidably limited stability and selectivity of the transducer. Moreover,
there could be errors in matching the transduced property X m with respect to the
reference properties X i
*
in the local scale (e.g., the so-called reading errors in the
case of instruments with analog scales). In addition, the local scale could also be
affected by instabilities, resulting in a time-dependent mapping X i
*
→ x i , which is
only uncertainly known. These issues lead to a non-null instrumental uncertainty.
One example for RCA would be where the RCA test is simply mis-scored, whether
by human or machine.
Finally, the fact that the object under measurement must somehow interact with
the transducer may induce an unwanted change in the state of the object, which in
turn produces an interaction uncertainty, as depicted in Fig. 7.23. An example of
this in RCA testing would be where the text passage that was used contained ele7.4 Measurement quality according to the model