10
to specific reference reading comprehension criteria that is known as the criterionreferenced approach, and an example of that will be discussed in Sect. 7.3.5.
1.2.3 An initial view of psychosocial measurement from a
physical science perspective
Some may find it difficult to relate the above account of an RCA test to the traditional idea of a physical instrument such as a thermometer. Seeing the analogies can
be difficult—in particular, it can be hard to conceive how observations of how well
readers respond to RCA items can be compared to how temperature is reflected in a
thermometer—these just do not seem like similar events!
This subsection (itself based on Mari & Wilson, 2014) is intended as a steppingstone between these two worldviews of measurement. It starts with a standard physical measurement context, specifically the measurement of temperature using an
alcohol thermometer, and shows how this can be adapted to a situation analogous to
that for RCA.
With the aim of measuring the temperature Θ[a] of an object a, a thermometer
can be exploited as an indicating measuring instrument, and specifically as a sensor,
which is supposed to behave according to a transduction function (sometimes also
called “observation function”: this is what Fechner called a “measurement formula”, Boumans, 2007: p. 234) assumed to be linear in the relevant range:
x
k
4 / ,
(1.1)
i.e., the measurement principle is that an object a of temperature Θ[a] put in interaction with a thermometer of sensitivity k
−1
generates an expansion of the substance
(e.g., a gas or a liquid) in the thermometer bulb and therefore an elongation
x = Θ[a]/k of the substance in the tube.
9
(We will omit measurement units from now
on, but of course we take the kelvin, K, as the unit of temperature Θ; the metre, m,
as the unit of elongation x; and K m
−1
as the unit of constant k.) Once the instrument
has been calibrated, and therefore a value for k is obtained, the measurement is performed by applying the measurand Θ[a] to the thermometer, getting a value for the
indication x and finally exploiting the inverted version of the law Θ[a] = kx for calculating a value for the measurand.
This relationship (which is linear, due to constant sensitivity) is illustrated in
Fig. 1.2 by the dotted line.
Suppose now that, instead of a thermometer whose behavior is described in Eq.
(1.1), a modified thermometer is available, again characterized by a constant k,
operating according to the following transduction function:
9 The notation Θ[a] is introduced and explained in Footnote 15 of Chap. 2.
1 Introduction
to specific reference reading comprehension criteria that is known as the criterionreferenced approach, and an example of that will be discussed in Sect. 7.3.5.
1.2.3 An initial view of psychosocial measurement from a
physical science perspective
Some may find it difficult to relate the above account of an RCA test to the traditional idea of a physical instrument such as a thermometer. Seeing the analogies can
be difficult—in particular, it can be hard to conceive how observations of how well
readers respond to RCA items can be compared to how temperature is reflected in a
thermometer—these just do not seem like similar events!
This subsection (itself based on Mari & Wilson, 2014) is intended as a steppingstone between these two worldviews of measurement. It starts with a standard physical measurement context, specifically the measurement of temperature using an
alcohol thermometer, and shows how this can be adapted to a situation analogous to
that for RCA.
With the aim of measuring the temperature Θ[a] of an object a, a thermometer
can be exploited as an indicating measuring instrument, and specifically as a sensor,
which is supposed to behave according to a transduction function (sometimes also
called “observation function”: this is what Fechner called a “measurement formula”, Boumans, 2007: p. 234) assumed to be linear in the relevant range:
x
k
4 / ,
(1.1)
i.e., the measurement principle is that an object a of temperature Θ[a] put in interaction with a thermometer of sensitivity k
−1
generates an expansion of the substance
(e.g., a gas or a liquid) in the thermometer bulb and therefore an elongation
x = Θ[a]/k of the substance in the tube.
9
(We will omit measurement units from now
on, but of course we take the kelvin, K, as the unit of temperature Θ; the metre, m,
as the unit of elongation x; and K m
−1
as the unit of constant k.) Once the instrument
has been calibrated, and therefore a value for k is obtained, the measurement is performed by applying the measurand Θ[a] to the thermometer, getting a value for the
indication x and finally exploiting the inverted version of the law Θ[a] = kx for calculating a value for the measurand.
This relationship (which is linear, due to constant sensitivity) is illustrated in
Fig. 1.2 by the dotted line.
Suppose now that, instead of a thermometer whose behavior is described in Eq.
(1.1), a modified thermometer is available, again characterized by a constant k,
operating according to the following transduction function:
9 The notation Θ[a] is introduced and explained in Footnote 15 of Chap. 2.
1 Introduction