Measuring

Definition (Deobold B. Van Dalen)
Definition (Abraham Kaplan)
Definition (C. West Churchman)
Classification (Deobold B. Van Dalen)
Function (Deobold B. Van Dalen)
Function (Abraham Kaplan)
Features (Abraham Kaplan)
Pitfalls (Deobold B. Van Dalen)
Pitfalls (Abraham Kaplan)
Estimates (Abraham Kaplan)
Variables (Deobold B. Van Dalen)

Definition

[1979] Deobold B. Van Dalen, Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York, First edition 1962.
“The term ‘measure’ may refer to
            - the act of;
            - the result of;
            - the instrument for;
            - the graduated units used in measuring.”
“In general measurement involves
            - assigning a set of numerals
            - to a set of entities
            - in accordance with some logically acceptable rule.”
(Chapter 5, p. 102)

[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“... neither mathematics nor measurement must be identified with the treatment of quantity.”
“Measurement, in most general terms, can be regarded as the assignment of numbers to object (or events or situations) in accord with some rule. The property of the objects which determines the assignment according to that rule is called a magnitude, the measurable attribute; the number assigned to a particular object is called its measure, the amount or degree of its magnitude.”
“The only decisive feature of all measurements ... is ‘symbolic representation’. Measurement ‘permits things to be represented conceptually, by means of symbols.’ The point to this representation is that manipulation of the symbols in terms of those relationships among them which the assignment has made significant will reveal corresponding relationships among the objects to which they have been assigned.” (Chapter V, pp. 175-178)

[1968] C. West Churchman, The Systems Approach, Dell Publishing, New York, Second Edition Revised and Updated 1979.
“Measurement is ... the activity of creating precise, accurate, and general information. Precision and accuracy enable us to make refined choices and hence to reduce the risk of error.”
"General’ information is information that can be used in a wide variety of times and places.” (Chapter 10, p. 161)

Classification

[1979] Deobold B. Van Dalen, Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York, First edition 1962
- (1) Nominal Scale
“The most primitive level of measurement is a nominal scale in which the only function of the numerals is (a) to identify (label) individual entities or (b) to classify a set of entities in accordance with their similarities and differences with respect to some property.” “Numbers on a nominal scale are qualitative; they have no quantitative implications; they do not represent a quantity, size, amount or degree of a property.” (e.g. the number of each footballer in a team)
- (2) Ordinal Scale
“The numbers on an ordinal scale provide information not only about
(a) the individual identity or classificatory category of entities but also about
(b) their rank order on some underlying property continuum.
Ordinal scales yield more information than nominal scales because they distinguish not only differences in kind but also the relative degree of difference.”
- (3) Interval Scale
“The numbers on an interval scale provide information not only about
(a) identity and (b) rank order of the entities, but also about (c) differences in magnitude from an arbitrary point of origin.”
“On an interval scale, one begins to count or add successively not from an absolute zero point that represents total absence of a property, but from an arbitary or artificial zero point.”
- (4) Ratio Scale
“A ratio scale, the highest level of measurement, possesses all the properties of an interval scale: (a) identity, (b) rank order, and (c) additivity. In addition (c) it begins measurement from an absolute (‘true’ or natural) zero
point signifying the total absence of the property.” “Because the zero point is fixed on a ratio scale, at absolute zero, all fundamental arithmetic operations are possible.” (Chapter V, pp. 109-117)

Function

[1979] Deobold B. Van Dalen, Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York, First edition 1962
“Measurement is ... an efficient tool that enables you to obtain knowledge about phenomena." (p. 98)
“The use of numbers and abstract symbols, which conveys blocks of meaning about measurement operations and the relations of data, simplifies, standardizes, and speeds up the communication process.” (p. 100)
“The purpose of measurement is to acquire information about a set of entities with respect to their possession of a property. A set or class of entities is a well-defined collection of similar particulars.” (p. 103)

[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania
“Measurement, in a word, is a device for standardization, by which we are assured of equivalences among objects of diverse origin.” (p. 173)
“A second function of measurement, one which shows its scientific importance, is to make possible more subtle discriminations and correspondingly more precise descriptions.” (p. 174)
“... measurement makes it possible to apply to inquiry available mathematical techniques, whether for purposes of verification, prediction, or explanation.”
(p. 175)
“It is this fact, that measurements embody within themselves whole systems of laws, which is at bottom what makes measurement of such scientific significance.” (pp. 188-189)

Features

[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“No problem is a purely qualitative one in its own nature; we may always approach it in quantitative terms.” (p.176)
“... I would say that whether we can measure something depends, not on that thing, but on how we have conceptualized it, on our knowledge of it, above all on the skill and ingenuity which we can bring to bear on the process of measurement which our inquiry can put to use.” (p. 176)
“The point is that both quality and quantity are misconceived when they are taken to be antithetical or even alternative." "... whether something is identified as a quality or as a quantity depends on how we chose to represent it in our symbolism.” “The transformation of quantity into quality, or conversely, is a semantic or logical process, not a matter of ontology.” (p. 207)

Pitfalls

[1979] Deobold B. Van Dalen, Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York, First edition 1962.
Two types of error in measurement are common:
a) systematic errors which affect the validity of measuring instruments.
(Does the instrument measure what it is supposed to measure?) (Did the questions asked on a test or questionnaire actually elicit responses that are indicants of the property being investigated?).
b) random errors which reflect the reliability of the instruments.
(Will the same results be obtained if an entity is measured again and again with this instrument by the same person or by some other person under the same conditions?).
(from Chapter 5, p. 124)

[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“... no measurement is quite free from error.” (p. 199)
(1) “One source of error is inherent to the measuring instrument. For every
instrument there is a limit to the discriminations it can make.” (p. 199)
“The discriminating power of an instrument or procedure of measurement is known as its sensitivity. One source of error, then, is insufficient sensitivity.”
(p. 200)
(2) “A second type of error consists in the fact that when a measurement is repeated it does not, in general, yield identical results. There is inevitably a certain amount of variation among the outcomes of repeated measurements; they are said to be subject to a ‘random fluctuation’.” “...reliability... is ... a measure of the extent to which a measurement remains constant as it is repeated under conditions taken to be constant.” “... reliability is often interpreted as a kind of intersubjectivity: the agreement of different observers on the measures to be assigned in particular cases.” (p. 200)

Estimates

[1964] Abraham Kaplan, The Conduct of Inquiry. Methodology for Behavioural Science, Chandler Publishing Company, Scranton, Pennsylvania.
“Measures of complex situations which do not easily lend themselves to scalar quantification - like the effectiveness of a psychotherapeutic technique, or the influence of a political boss - are most often arrived at with the help of a ‘human yardstick’. Estimates are made by a panel of presumably competent observers, and some suitable statistical combination of these is then taken as the measure of the magnitude in question.”
“This combination does not, however, make such measurement subjective, in any pejorative sense. All measurement yields, not a property intrinsic to the object being measured taken in isolation, but a relation between that object and the others serving as standards of measurement.” (Chapter V, pp. 211- 212)

Variables

[1979] Deobold B. Van Dalen, Understanding Educational Research. An Introduction, McGraw-Hill Book Company, New York, First edition 1962.
“A property is a concept or logical construct that describes a particular characteristic which is common to all members of a set, such as punctuality or IQ, but on which members of the set vary.”
“In a scientific investigation, the term property is synonymous with the term variable.”
“An indicant is something that points to the property and helps define it. Indicants of the property of punctuality might be ‘is never tardy to class’, ‘hands in term paper on or before the due date’, and ‘is among the first people to arrive for meetings’.”
“What is measured is not a set of entities (e.g. fifty students) but indicants of some property of the entities.” (Chapter V, p. 104)
“There are two types of variables (properties):
- Continuous: “A continuous variable represents a continuous progression from the smallest possible amount to the largest possible amount, with measurement theoretically possible at any point along the continuum.” (example: height, weight)
- Discrete: “A discrete (or discontinuous) variable is one for which measurement and classification are possible only in whole units. A discrete variable, which belongs to the kind of measurement called nominal, can be either of the following:
- a two-category variable (e.g. living-dead)
- a multiple category variable (e.g. the country in which a person is born: Norway, England, or Spain, etc.).”
(from Chapter V, p. 105)

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