xxxi
List of Figures
Fig. 1.1 An item from Kelly’s reading test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Fig. 1.2 The relationship between Θ and x (the transduction function)
for thermometers as given in Eqs. (1.1) and (1.2) (scaled values) . . . . 11
Fig. 1.3 A sketch of a transduction relationship between an RCA
measurand (in log metric) and the probability of observing
a correct response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Fig. 2.1 The semiotic triangle, in the generic case (left) and the
specific case (middle), with an example (right).
(Adapted from Ogden & Richards, 1923: p. 11) . . . . . . . . . . . . . . . . . 20
Fig. 2.2 The abstract structure of measurement (first version) . . . . . . . . . . . . . 25
Fig. 2.3 The abstract structure of measurement (second version) . . . . . . . . . . . 27
Fig. 2.4 Measurement systems, including the process of measuring
and the procedure that specifies it . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Fig. 2.5 The abstract structure of measurement (third version) . . . . . . . . . . . . 28
Fig. 2.6 A pictorial representation of the simple ontology we assume
regarding objects and their properties: the object a bears
the properties P 1 [a], P 2 [a], P 3 [a], … . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Fig. 2.7 The objects a 1 and a 2 can be compared with respect to
their common property length, i.e., in principle L[a 1 ] ≈ L[a 2 ]
is either true or false, whereas L[a 1 ] cannot be compared
with the reading comprehension ability of a 2 , RCA[a 2 ],
so that whether L[a 1 ] ≈ RCA[a 2 ] is meaningless . . . . . . . . . . . . . . . . . 30
Fig. 2.8 The abstract structure of measurement (fourth version,
in the case of quantities) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Fig. 2.9 Measurement as a process between the empirical world
and the information world (first version) . . . . . . . . . . . . . . . . . . . . . . . 35
Fig. 2.10 Measurement as a process between the empirical world
and the information world (second version) . . . . . . . . . . . . . . . . . . . . 37
Fig. 2.11 Indirect measurement as a process including one or more
direct measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
List of Figures
Fig. 1.1 An item from Kelly’s reading test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Fig. 1.2 The relationship between Θ and x (the transduction function)
for thermometers as given in Eqs. (1.1) and (1.2) (scaled values) . . . . 11
Fig. 1.3 A sketch of a transduction relationship between an RCA
measurand (in log metric) and the probability of observing
a correct response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Fig. 2.1 The semiotic triangle, in the generic case (left) and the
specific case (middle), with an example (right).
(Adapted from Ogden & Richards, 1923: p. 11) . . . . . . . . . . . . . . . . . 20
Fig. 2.2 The abstract structure of measurement (first version) . . . . . . . . . . . . . 25
Fig. 2.3 The abstract structure of measurement (second version) . . . . . . . . . . . 27
Fig. 2.4 Measurement systems, including the process of measuring
and the procedure that specifies it . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Fig. 2.5 The abstract structure of measurement (third version) . . . . . . . . . . . . 28
Fig. 2.6 A pictorial representation of the simple ontology we assume
regarding objects and their properties: the object a bears
the properties P 1 [a], P 2 [a], P 3 [a], … . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Fig. 2.7 The objects a 1 and a 2 can be compared with respect to
their common property length, i.e., in principle L[a 1 ] ≈ L[a 2 ]
is either true or false, whereas L[a 1 ] cannot be compared
with the reading comprehension ability of a 2 , RCA[a 2 ],
so that whether L[a 1 ] ≈ RCA[a 2 ] is meaningless . . . . . . . . . . . . . . . . . 30
Fig. 2.8 The abstract structure of measurement (fourth version,
in the case of quantities) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Fig. 2.9 Measurement as a process between the empirical world
and the information world (first version) . . . . . . . . . . . . . . . . . . . . . . . 35
Fig. 2.10 Measurement as a process between the empirical world
and the information world (second version) . . . . . . . . . . . . . . . . . . . . 37
Fig. 2.11 Indirect measurement as a process including one or more
direct measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38