Re-discovering Measurement
4. Measurement Concepts
4.1 Measurement concepts: some basic definitions
(72) Let us begin by considering what we mean by "measurement". The Oxford Dictionary of English defines
"measure" as follows:
(73) As a verb:
- ascertain the amount or degree of something by using an instrument or device marked in standard units
- take an exact quantity of something
- judge someone or something by comparison with a certain standard
(74) As a noun:
- the size, length or amount of something as established by measuring
(75) Measurement is defined as "the action of measuring something".
(76) A related concept is "Unit of measure", defined as "a quantity chosen as a standard in terms of
which other quantities may be expressed".
(77) It is evident that in order to measure something in a way that provides insight to others, there
needs to be some level of agreement about the unit(s) of measure.
4.2 Measurement fundamentals
(78) The analysis in this paper draws heavily on the summary of measurement theory, information theory,
and accounting theory included in the Issue Paper published by the Fédération des Experts
Comptables Européens (FEE) in
April 2003 entitled: Principles of Assurance: Fundamental Theoretical Issues related to Assurance in Assurance Engagements,
referred to henceforth in this document as the "FEE Paper". An extract of the key sections of the FEE paper relating to
information, measurement, and accounting theory can be found on the NPI website
at http://npi.valuemeasurement.net.
(79) In its review of measurement theory, the FEE paper reminds us of some measurement fundamentals:
- Measurement relates to objects; or more precisely, properties of objects; or even more precisely, properties of
"systems"; or even more precisely still, indicants of properties of systems. (For purposes of this paper, it will in
most cases be sufficiently precise to refer to measuring "properties of objects".)
- To measure something involves quantification of properties, based on some mathematical model. Quantification
does not necessarily mean "numerical": valid measurement scales can be:
- nominal (determining whether something does or does meet some criterion);
- ordinal (a scale in which things are arranged in rank order);
- interval (a scale on which equal intervals between objects represent equal differences) or
- ratio (a scale on which the ratios of the numbers assigned accurately reflect ratios of the magnitudes of the objects
being measured.)
Financial measures represent a ratio scale.
4.3 Measuring Value
(80) According to the Oxford Dictionary of English, "value" or "values" have several connotations:
- the "regard that something is held to deserve; the importance, worth, or usefulness of something";
- the "material or monetary worth of something";
- the "worth of something compared to the price paid or asked for it";
- "principles of standards of behaviour; one's judgement of what is important in life";
- and "the numerical amount denoted by an algebraic term: a magnitude, quantity or number".
(81) A "Valuation" is defined as "an estimation of the worth of something, especially one carried our
by a professional valuer". Related concepts include: value added, value analysis, value engineering, value-free, value
judgement, value-laden, valueless, value received, valuable, and valuable consideration.
(82) These definitions lead to the following observations and questions:
- Is value ever "absolute", or is it always relative? For practical purposes, it is almost always true that value is
"in the eye of the beholder".
- Values expressed in currency (e.g., this car is worth $10,000) seem more absolute than "moral" values, but even
in every-day life, we differentiate between monetary cost and value to a potential buyer.
- Transaction value is in fact an amount that sits somewhere between the perceived value of something to a buyer
and the perceived value to the seller: normally, a buyer will complete a transaction only if the acquisition cost is
less than the value perceived by the buyer.
- This logic suggests that "perspective" or "context" is relevant to any value measurement. In other words, every value
measure inherently reflects a specific perspective, even if that perspective is not explicitly referenced or even
recognized as such.
(83) If we reassemble the term "value measurement" or "quantification of value", the following
observations emerge:
- Like all measures, one would assume that the "value" we want to measure or quantify is a property of an object or system.
- The difficulty that arises is that if all value is relative or contextual, this would suggest that value is not strictly
a property of an object or system, since we also need to take into account the perspective of the "beholder".
(84) This would suggest that value might be a property of a relationship that includes the object or
system and the beholder, not of the object or system per se.
(85) If we don't want to go this far, at a minimum, we need to associate the idea of a "perspective"
or "context" with the value-related property of the object or system.
(86) To comprehend the significant of any quantification of value, it is therefore essential to:
- be aware of the object and properties being measured;
- be aware of the perspective
- understand the underlying mathematical system.
4.4 Measuring Performance
(87) According to the Oxford Dictionary of English, to perform is to "carry out, accomplish,
or fulfil" an action, task or function. "Performance" has several connotations:
- the "act of presenting a play, concert, or other form of entertainment";
- the "action or process of performing a task or function";
- a "task or operation seen in terms of how successfully it is performed";
- the "capabilities of a machine, product, or vehicle".
Related concepts include: performance art, performance bond.
(88) These definitions lead to the following observations and questions:
- Is performance "absolute", or "relative"? To the extent that we wish to differentiate between different
levels of performance, it can be argued that performance is always measured in relation to some point of reference,
such as an objective (e.g. performance targets), a standard (e.g., 9s sigma), or precedent (e.g., last year's performance).
- Do we need to take "perspective" into account, as in the case of value? In other words, is performance in the eye
of the beholder? Logic would suggest that perspective is a factor not so much in the interpretation of the reference
point as in the selection of the reference point. That is, different beholders might choose difference reference points
for evaluating performance, but performance could be objectively determined in relation to each of those reference points
without taking perspective into account.
- Any organization with multiple stakeholders faces the possibility that different stakeholders may adopt different
reference points for differentiating between satisfactory and unsatisfactory performance.
(89) If we reassemble the term "performance measurement", or "quantification of performance", the
following observations emerge:
- Is the "performance" we want to measure or quantify a property of an object or system, or a property of an object or
system in some sort of relationship with the reference point?
- It seems likely that performance can be a property of an object or system, but that it has no real meaning apart from
one or more reference points, whether or not those reference points are defined implicitly or explicitly.
- To comprehend the significant of any quantification of performance, it is therefore essential to:
- be aware of the object and properties being measured;
- be aware of the reference point;
- understand the underlying mathematical system.
4.5 Summary
(90) In sum, as we develop criteria for differentiating among different measurement approaches, we must keep
in mind:
- That measurement pertains to a "property" of an object or system, not to the object or system itself. To understand the
meaning of a measure, it is important to be clear about what it is, and is not, measuring.
- That all value measures are "relative" to a particular perspective, whether or not that perspective is explicit.
To comprehend the significant of any quantification of value, it is essential to:
- be aware of the object and properties being measured;
- be aware of the perspective; and
- understand the underlying mathematical system.
- That all performance measures are "relative" to one or more reference points, whether or not these are explicit.
To comprehend the significant of any quantification of performance, it is therefore essential to:
- be aware of the object and properties being measured;
- be aware of the reference point; and
- understand the underlying mathematical system.
