Michell (1997): Quantitative Science

Question 1

It is argued that establishing quantitative science involves two research tasks, what are these?

Answer 1

the scientific one of showing that the relevant attribute is quantitative; and the instrumental one of constructing procedures for numerically estimating magnitudes.

Question 2

Why is it proposed that psychologists resist the introduction of of philosophical considerations into their science?

Answer 2

Psychologists resist the intrusion of philosophical considerations into their science, as if such considerations could somehow threaten its genuine achievements. Resistance is especially stiff in the methodological area where the tone was set by the founder of quantitative methods in psychology, G T Fletcher.

Question 3

Why is this resistance to philosophical objections problematic?

Answer 3

The attitude that any science should insulate itself against criticism is anti-scientific. If principled criticism is not answered in a principled way then the doubts raised remain. Philosophical criticism in the methodological area has a special function. If the methods of science are not sanctioned philosophically then the claim that science is intellectually superior to opinion, superstition and mythology is not sustained.

Question 4

What philosophical view of the world in is the one presumed in natural science ?

Answer 4

The natural scientific attitude and the one that promises the most coherent defence of science is that of empirical realism (i.e. that of an independently existing natural world which humans are able to successfully cognize via observational methods, at least sometimes).

Question 5

How is psychology in danger of losing the great intellectual tradition of quantitative, experimental science?

Answer 5

Many psychological researchers are ignorant with respect to the methods they use. This ignorance is not so evident at the instrumental level, i.e. that of using techniques of data collection and analysis, although there is a surprising degree of ignorance even here. The ignorance I refer to is about the logic of methodological practices, i.e.
about understanding the rationale behind the techniques. Ignorance of this logic may mean not knowing the right empirical questions to ask or, even, that there are any in this context.

Question 6

What is meant by an attribute? What is theorised about them in quantitative science?

Answer 6

An attribute is a range of properties or relations that can vary from instance to another (e.g. length is an attribute of objects and objects have different lengths). In quantitative science, certain attributes, such as temperature and length, are assumed to be measurable. Thus it is theorised that an attribute has a quantitative structure.

Question 7

.What is meant by a quantitative attribute?

Answer 7

A quantitative attribute (or quantity) is an attribute whose instances are related to one another both ordinally and additively. Keep in mind that no all attributes are quantitative (e.g. sex is an attribute but it is not quantitative).

Question 8

Explain the terms quantitative structure, quantities and magnitudes

Answer 8

Following a well-established usage, specific instances of a quantity are called magnitudes of that quantity (e.g. the length of this page is a magnitude of the quantity, length). Magnitudes of a quantity are measurable because, in virtue of quantitative structure, they stand in relations (ratios) to one another that can be expressed as real numbers.

Question 9

What makes magnitudes measurable?

Answer 9

Magnitudes are measurable because they are in relation to one another and this can be expressed as real numbers. In other words they are ratios or a special kind of relation that occurs between magnitudes of the same quantity. Hence, the ratio of one magnitude of a quantity to another is the size of the first relative to the second (i.e. ratios are relative magnitudes).

Question 10

what do Holder’s set of seven axioms entail?

Answer 10

Holder’s set of seven axioms define a continuous quantity

Question 11

How did Michell utilise these 7 axioms?

Answer 11

Michell (1994) uses these axioms to form a succinct definition of the same concept. According to Mitchell, a range of instances of an attribute, Q, is a continuous quantity if and only if five conditions hold

Question 12

What is the first condition set by Holder?

Answer 12

1. Any two magnitudes of the same quantity are either the same or different, and, if they are different, then there must also be a third magnitude. This third magnitude would be the difference between them. Of the following, one and only one of the following is true
   (i) a = b,
   (ii) there exists c in Q such that a = b+c,
   (iii) there exists c in Q such that b = a + c ;

In the above and following conditions the addition is not of numbers but of magnitudes of a quantity (e.g. specific lengths, say).

Question 13

What is the second condition set by Holder?

Answer 13

2. A magnitude entirely composed of two discrete parts is the same regardless of the order of composition, i.e. for any a and b in Q , a + b = b + a ;

Question 14

What is the third, fourth and fifth conditions set by Holder?

Answer 14

3 . A magnitude which is a part of a part of another magnitude is also a part of that same magnitude, the latter relation being unaffected in any way by the former, i.e.
for any a , b and c in Q , a + ( b + c ) = ( a + b ) + c ;

4. For each pair of different magnitudes of the same quantity there exists another between them, i.e. for any a and b in Q such that a > b, there exists c in Q, such
   that a > c > b; and

5 . Given any two sets of magnitudes, an ‘upper’ set and a ‘lower’ set, such that each magnitude belongs to either set but none to both and each magnitude in the upper set is greater than any in the lower, there must exist a magnitude no greater than any in the upper set and no less than any in the lower, i.e. every non-empty subset of Q that has an upper bound has a least upper bound.

Question 15

What do conditions 4 and 5 ensure?

Answer 15

Condition 4 ensures density while condition 5 ensures continuity of a quantity., thus, be thought of as containing no gaps in the sequence of its magnitudes.

Question 16

When is a magnitude considered greater than another?

Answer 16

One magnitude is only greater than another if an only if the latter is a part of the former.

Question 17

What does the + sign mean in these conditions?

Answer 17

+ is not the same as the mathematical operation. It indicates the relation between magnitudes.

For example, a + b = c means that magnitude c is entire composed of discrete parts a and b. If magnitudes stand in relation to one another, it does not mean that its addition will contain the magnitudes themselves. Additionally, it is the relation between magnitudes not numbers.

Question 18

How is scientific measurement defined?

Answer 18

If an attribute is quantitative then it is measurable. Hence, scientific measurement is the numerical estimation of the ratio of a magnitude of a quantitative attribute to a unit of the same attribute.

Question 19

What is meant by a unit?

Answer 19

Unit is a more or less arbitrarily selected magnitude of a quantity, singled out to be the instance against which any other is to be compared. If the unit is known, then expressing the magnitude of any other instance of the quantity relative to the unit means that the magnitude of that instance is defined and known via the unit (e.g. meter is a unit of length).

Question 20

Why is showing that an attribute is quantitative difficult?

Answer 20

Showing evidence that an attribute is quantitative is complicated and some of the conditions stated are not directly testable. In fact, many physical quantities (e.g. temperature and density) have only indirect evidence that they are quantifiable.

Question 21

What effect have these issues with measurement had on psychology?

Answer 21

This has been a source of confusion over the last century in Psychology and measurement theory and had led to false conclusion that measurement is atheoretical, purely observational based upon theoretical structures.

Question 22

What should presuppose theory according the Michell?

Answer 22

According to Michell, measurement should always presuppose theory. Thus, a scientist should always seek to see if something is quantitative and measurable ,not hypothesising that it is measurable based on previous theories.

Question 23

What two tasks comprise establishing a quantitative science?

Answer 23

1. Scientific Task
   Experimentally investigating the hypothesis that the relevant attribute is quantitative.
2. Instrumental Task
   Devising procedures to measure magnitudes of the attribute shown to be quantitative.

Question 24

How are psychology attributes distinct to psychology? Why is this problematic?

Answer 24

Psychology attributes are distinct to psychology in that they do not belong to the network of quantitative attributes measurable using the methods of the physical sciences. However, psychologists continue to hypothesise that the attributes they are measuring are quantitative in an attempt to construct a science analogous to physics.

Question 25

Do psychologists use the same definition of measurement as in physics?

Answer 25

The definition of measurement in psychology is widely different from that in other sciences. This definition is Stevens’ (1946), which states that “measurement is the assingment of numerals to objects or events according to rule.” This definition is seen in most publications.

Question 26

What did Fechner (1860) contribute to the field of psychological measurement?

Answer 26

Fechner (1860) attempted to establish a quantitative psychology by linking his quantitative psychology to quantitative physical via his psychophysical law, supplemented his law with a range of measurement methods, and persuades others that these methods were indeed measurement as used in physics. He believed that reality was fundamentally quantitative and hence psychophysics must be quantitative.

Question 27

What view opposed Fechner’s ideas?

Answer 27

This idea was opposed by the quantity objection, the thesis that psychological attributes are not quantitative (e.g. Kantian view).

Question 28

Who was Fechner’s main critic and what did he claim?

Answer 28

Fechner’s main critic was von Kries (1882) who argued that sensations do not have additive relations to one another hence it can’t be said that a sensation is ten times another intensity.

Question 29

How did Fechner respond to this criticism of sensations and additivity?

Answer 29

Many shared this view but Fechner did not find it necessary to present evidence that intensities of sensations are additive. This is because he believed that because he could determine that one stimuli was noticeably different from its immediate predecessor then it differed by one unit of sensory intensity.

Question 30

What effect had Fechner’s views on psychology?

Answer 30

Fechner is the founding father of quantitative psychology and his work establish the quantitative paradigm in psychology and was emulated by others in his field. Thus, a focus on the instrumental task was set while the scientific task was completely ignored and thought “unnecessary.”

Question 31

____ was influenced by Fechner’s view and went on to teach ______.

Answer 31

Wundt was influenced by Fechner’s view and went on to teach Spearman.

Question 32

What did Spearman do with this information?

Answer 32

Spearman later on proposed a quantitative theory to explain intellectual performance. He carries out tests to test this theory but were not sensitive to exploring whether or not the postulated abilities were quantitative in structure. Much like Fechner, he believed that psychological attributes had to be quantitative and the primary problem was to devise ways to measure these attributes.

Question 33

What two motivations did Spearman do for not partaking in this scientific task?

Answer 33

1. Quantitative Imperative
   Spearman supported the idea that measurement is a necessary feature of all science.
2. Practicalism
   He also believed that psychology should provide a quantitative basis for practical applications in these areas and he had expressed the hope that his research would produce “practical fruit of almost illimitable promise.”

Question 34

Why can practicalism be problematic?

Answer 34

Practicalism, the view that science should serve practical ends, can corrupt the process of investigation. Scientific knowledge should be neither useful nor useless in itself. It is only so when taken in relation to other interests such as political.

“When scientific questions seem intractable, an impatient
practicalism may presume upon nature. Unable to admit that such questions cannot yet be answered, the practicalist may blindly collude in the pretence that they do not exist by ignoring them, especially when the psychological expectations and social rewards are high.”

Question 35

Why were/ are quantitative psychology and “applied psychological measurement” anomalies within a discipline trying to be a science ?

Answer 35

There can be no applied science if there is no science. However, at this time methodology was based open constructions of procedures that would yield numerical data (not scientific). These procedures were then marketed as forms of “scientific measurement”. Hence, both quantitative psychology and “applied psychological measurement” were anomalies within a discipline trying to be a science because psychologists either declined to or did not know how to consider this fundamental scientific issue

Question 36

What decision did the British Association for the Advancement of Science make in 1940? What was their main reason for this?

Answer 36

In 1 940, a committee established by the British Association for the Advancement of Science determined that psychophysical methods did not constitute scientific measurement. The main criticism was that the additivity of psychological attributes had not been displayed and hence it could not be supported that psychophysical methods measured anything.

Question 37

What did this decision inspire?

Answer 37

After this decision, a series of rash papers were written to defend these psychological practices or to try and redefine measurement in way that would legitimise psychology’s scientific grounding. This set the ground for Stevens’ early paper on measurement theory and his later definition of measurement.

Question 38

What was the purpose/ outcome of defining a new measurement for psychology? Besides the definition, what else did Steven’s assert in his paper?

Answer 38

By setting his own definition of measurement, the committee’s main criticism that psychological attributes lacked additivity was no longer relevant to psychology. Besides setting the definition of measurement, Stevens’ also developed his theory of four types of measurement scales (nominal, ordinal, interval, and ratio) and a doctrine of permissible statistics.

Question 39

What philosophical implications did Stephen’s new theory hold?

Answer 39

After setting this definition, he replaced the natural scientific attitude of realism to a form of relativistic subjectivism. Steven adopted both operationist (a form of positivism which defines scientific concepts in terms of the operations used to determine or prove them) and logical positivism (scientific knowledge is the only kind of factual knowledge and that all traditional metaphysical doctrines are to be rejected as meaningless). His representation theory of measurement, with an emphasis on numerical representation and formalist conception of numerical systems was positivistic. He took Bridgman’s (1927) operationism, according to which the meaning of a concept is synonymous with the operations used to identify it and applied it to psychology

Question 40

What four arguments did Steven’s use when adopting operationalism?

Answer 40

1. “Propaedeutic science”
   Because operationism implies a relativity to the observer in all science, psychology then is the “propaedeutic science” or the study of the observer.
2. Sensory discrimination
   All scientific operations can be reduces to the operation of sensory discrimination.
3. Psychophysics
   The operational methods of psychophysics are central to the study of sensory discrimination.
4. Scaling methods
   The scale methods put forth by Stevens allow the central question of psychophysics to be certainly answered.

Question 41

According to Stevens, if the meaning of a scientific concept is given by the operations (i.e. procedures) used to identify it, it follows that….. ?

Answer 41

According to Stevens, if the meaning of a scientific concept if given by the operations (i.e. procedures) used to identify it, then it follows that the empirical relations numerically represented in measurement must likewise be defined by the operations. Thus, measurement is possible because of this relation between empirical ones and numerical ones.

Question 42

What consequences did Steven’s claims have for psychology?

Answer 42

Prior to his reformulation of measurement, psychologists were already ignoring the scientific issues relating to measurement. His definition legitimised this practice and it was rapidly adopted into psychology and was cited in major texts as the only definition of measurement.

Question 43

How did Suppes & Zinnes (1963) contribute to the field of psychological measurement?

Answer 43

Suppes & Zinnes (1963) developed a theory which had a more stricter definition of measurement than Stevens’. Measurement was a homomorphism (i.e. a special relation between elements of two systems) between independent existing empirical and numerical relational systems. Thus, it was not enough to just make numerical assignments but to show the independence of the two systems involved.

Question 44

How did Luce & Tukey (1964) then contribute to the field?

Answer 44

Shortly after, Luce & Tukey (1964) also published their own theory of conjoint measurement. This theory showed several indirect tests for the hypothesis that attributes are quantitative and made explicit the condition which non-additive empirical structures are really additive at a deeper level.

Question 45

“Ignorance and error only become pathological when there are mechanisms in place within that system that supports it. “

How does Michell apply this to the field of psychology? (2)

Answer 45

According to Michell, there is a systematically sustained methodological thought disorder in Psychology. Methodological thought disorder is the sustained failure to cognise relatively obvious methodological fats.

In addition, behind psychological research there is an ideological support structure or discipline-wide, shared system of beliefs which maintain both the dominant methodological practices and the content of the dominant methodological educational programs.

Question 46

In what three realms does this methodological thought disorder manifest itself according to Michell?

Answer 46

This manifests in (1) the contents of textbooks, (2) the contents of methodology courses, and (3) the research programmes of psychologists.