47
be considered as being parallel to those for instruments aimed at measuring nonphysical properties. Furthermore, extensions to nonquantitative properties are possible, as discussed by Mencattini and Mari (2015).
Let us designate the values of the property being measured as x i , the corresponding values of the indication as y i , and the values of the (vector of the) influence
properties affecting the indication y i as z i ; hence the inverse f of the calibration function is such that y i = f(x i , z i ).
Sensitivity, according to the VIM (JCGM, 2012: 4.12, adapted), is the “quotient
of the change in an indication value of a measuring system and the corresponding
change in a value of a property being measured”, under the supposition that the
influence properties remained constant; hence
sens instrument x z
f x
x z f x z
x
, ,
,
,
ª ¬
º ¼
'
'
/
for a sufficiently small change Δx. The sensitivity of the spring may be a function
of the value x of the property being measured in the appropriate unit (meters per
newton in the SI), describing how much the spring elongates in response to a change
of the applied force, while all influence properties remain constant. An instrument
such that the indication value depends linearly on x has constant sensitivity, and an
instrument whose sensitivity is zero for a given set of forces is useless for measuring
a force in that set. The topic of sensitivity, although well established in the metrological literature, is less common in the literature on psychosocial measurement;
4
this is also true for the next several instrument parameters. Hence, although equivalents can be defined, we will not discuss the equivalents until the account gets to
precision, below.
Selectivity is basically insensitivity to influence properties; while the property
being measured is constant, the selectivity of an instrument with respect to a given
influence property can be evaluated as
sel instrument z x
z f x z
z f x z
, ,
,
,
ª ¬
º ¼
'
'
/
for a sufficiently small change Δz. The selectivity of the spring with respect to temperature is a value in the appropriate unit (kelvin per metre in the SI), describing
how much the spring elongates in response to a change in the environmental temperature, while the applied force and all other influence properties remain constant:
the lower the selectivity, the better the instrument.
5
Stability is basically insensitivity to time, thus under the acknowledgment that f
may depend on time; while both the property being measured and the influence
properties are constant, the stability of an instrument can be evaluated as
4 In addition, this concept of sensitivity should be distinguished from the analogous term used in
biostatistics; the same comment applies to selectivity.
5 The definition in the VIM (JCGM, 2012: 4.13) takes into account all influence properties at the
same time, and therefore remains qualitative. Moreover, the VIM itself notes (4.13, Note 1) that in
some contexts selectivity is considered as insensitivity to influence properties of the same kind as
the measurand.
3.2 The quality of measurement and its results
be considered as being parallel to those for instruments aimed at measuring nonphysical properties. Furthermore, extensions to nonquantitative properties are possible, as discussed by Mencattini and Mari (2015).
Let us designate the values of the property being measured as x i , the corresponding values of the indication as y i , and the values of the (vector of the) influence
properties affecting the indication y i as z i ; hence the inverse f of the calibration function is such that y i = f(x i , z i ).
Sensitivity, according to the VIM (JCGM, 2012: 4.12, adapted), is the “quotient
of the change in an indication value of a measuring system and the corresponding
change in a value of a property being measured”, under the supposition that the
influence properties remained constant; hence
sens instrument x z
f x
x z f x z
x
, ,
,
,
ª ¬
º ¼
'
'
/
for a sufficiently small change Δx. The sensitivity of the spring may be a function
of the value x of the property being measured in the appropriate unit (meters per
newton in the SI), describing how much the spring elongates in response to a change
of the applied force, while all influence properties remain constant. An instrument
such that the indication value depends linearly on x has constant sensitivity, and an
instrument whose sensitivity is zero for a given set of forces is useless for measuring
a force in that set. The topic of sensitivity, although well established in the metrological literature, is less common in the literature on psychosocial measurement;
4
this is also true for the next several instrument parameters. Hence, although equivalents can be defined, we will not discuss the equivalents until the account gets to
precision, below.
Selectivity is basically insensitivity to influence properties; while the property
being measured is constant, the selectivity of an instrument with respect to a given
influence property can be evaluated as
sel instrument z x
z f x z
z f x z
, ,
,
,
ª ¬
º ¼
'
'
/
for a sufficiently small change Δz. The selectivity of the spring with respect to temperature is a value in the appropriate unit (kelvin per metre in the SI), describing
how much the spring elongates in response to a change in the environmental temperature, while the applied force and all other influence properties remain constant:
the lower the selectivity, the better the instrument.
5
Stability is basically insensitivity to time, thus under the acknowledgment that f
may depend on time; while both the property being measured and the influence
properties are constant, the stability of an instrument can be evaluated as
4 In addition, this concept of sensitivity should be distinguished from the analogous term used in
biostatistics; the same comment applies to selectivity.
5 The definition in the VIM (JCGM, 2012: 4.13) takes into account all influence properties at the
same time, and therefore remains qualitative. Moreover, the VIM itself notes (4.13, Note 1) that in
some contexts selectivity is considered as insensitivity to influence properties of the same kind as
the measurand.
3.2 The quality of measurement and its results