GODFREY
HODGSON
HOLMES
TARCA
CHAPTER 5
MEASUREMENT THEORY
Importance of measurement
Campbell:
The assignment of numerals to represent
properties of material systems other than
numbers
Assignment of numerals to objects or events
according to rules.
(Stevens)
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Importance of measurement
• Involves linking the formal number system to
some property of objects or events by means
of semantic rules
– e.g. semantic rules in accounting are represented
by transactions
• In accounting we measure profit by:
– first assigning a value to capital
– then calculating profit as the change in capital
over the period
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Scales
• Every measurement is made on a scale
• Created when a semantic rule is used to relate
the mathematical statement to objects or
events
• The scale shows what information the
numbers represent
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Nominal scale
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In this scale, numbers used only as labels
Numbers represent classification
e.g. numbering footballers
e.g. the classification of assets and liabilities
into different classes
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Ordinal scale
• In this scale, rank orders objects with respect
to a given property
– e.g. tallest to shortest person
– e.g. investment alternatives that are ranked 1, 2, 3
according to the size of their net present values
• Intervals between the numbers are not
necessarily equal
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Interval scale
• In this scale, rank orders objects with respect
to a given property
• The distance between each interval is equal
and known
• An arbitrarily selected zero point exists on the
scale
– e.g. celsius temperature scale
– e.g. standard cost accounting
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Ratio scale
• In this scale, rank orders objects with respect
to a given property
• Intervals between objects are known and
equal
• A unique origin exists
– e.g. measurement of length
– e.g. use of dollars to measure assets and liabilities
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Permissible operations of
scales
• Invariance of a scale means that the
measurement system will provide the same
general form of the variables, and the decision
maker will make the same decisions
• This is not the case in accounting – there is
more than one accounting system
• The information they provide will differ and
different decisions will be made
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Permissible operations of
scales
• Nominal and ordinal scales
– no arithmetic operations
• Interval scale
– addition and subtraction
• Ratio scale
– all arithmetic operations
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Types of measurement
• There must be a rule to assign numbers before
there can be measurement
• The formulation of the rules gives rise to a
scale
• Measurement can be made only on a scale
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Fundamental measurements
• Numbers are assigned by reference to natural
laws
• Fundamental properties are additive
– e.g. length, number and volume
• In accounting there is considerable debate
over the nature of fundamental value
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Derived measurements
• Is one that depends on the measurement of
two or more other quantities
• Depends on known relationships to
fundamental properties
– e.g. the measurement of density depends on the
measurement of both mass and volume
– e.g. the measurement of profit depends on the
measurement of both income and expenses
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Fiat measurements
• Typical in social sciences including accounting
• Based on arbitrary definitions - e.g. of profit
• Numerous ways in which scales can be
constructed
• May lead to poor levels of confidence in the
scale – e.g. there are hundreds of ways to
measure profit
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Reliability and accuracy
• No measurement is free of error except
counting
– e.g. we can count the chairs in a room and be
exactly correct
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Sources of error
The sources of error include the following:
• Measurement operations stated imprecisely
• Measurer
• Instrument
• Environment
• Attribute unclear
• Risk and uncertainty
We need to establish limits of acceptable error
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Reliable measurement
• What is reliable measurement?
– proven consistency
– repeatable or reproducible
– precision
• Reliability incorporates two aspects
– accuracy and certainty of measurement
– representative faithfulness
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Accurate measurement
• Consistency of results, precision and reliability
do not necessarily lead to accuracy
• Accuracy has to do with how close the
measurement is to the ‘true value’ of the
attribute measure - representation
• ‘True value’ may not be known
– e.g. in accounting accuracy relates to the
pragmatic notion of usefulness
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Accurate measurement
• Many accounting measurements are on a ratio
scale
• This is the most informative scale
• Weakest theoretical foundation as they are
fiat measurements
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Measurement in accounting
• Two fundamental measures
– capital & profit
• Capital and profit can be defined & derived in
various ways
• Concepts of capital & profit have changed
over time
– number of concepts of fundamental measurement
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Measurement in accounting
• Two notable developments in international
standards (2005, IASB)
– profit measurement and revenue recognition
should be linked to timely recognition
– the fair value approach should be adopted as the
working measurement principle
At no stage has the principle of capital maintenance
been explicitly discussed
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Measurement issues for
auditors
• The focus of profit measurement has shifted
from matching revenues and expenses to
assessing the changes in the fair value of net
assets
– e.g. immediate recognition of impairment losses
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Measurement issues for
auditors
• Auditors must determine whether
management has made appropriate and
reasonable valuations
– e.g. at least 12 methods of valuing intangibles
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Measurement issues for
auditors
• It is possible for several different but
reasonable measurements and impairment
losses to be recognised by management
• These would all be acceptable to an auditor if
management have
– applied the valuation models correctly
– used appropriate data
– made appropriate assumptions
– acted in a consistent manner
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Summary
• Measurement involves the formal linking of numbers to some property or
event via semantic rules
• Rules used to assign numbers are determined according to four scales
• Invariance of a scale means the measurement system will provide the
same general form of the variables and the decision maker will make the
same decisions
• There are three different types of measurement
• Reliability refers to consistency, and accuracy refers to the representation
of a fundamental value
• The two fundamental measures in accounting are capital and profit and
they are both derived measures
• The existence of alternative valuation methods creates auditing issues
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Key terms and concepts
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Measurement
Nominal scale
Ordinal scale
Interval scale
Ratio scale
Invariance of a scale
Fundamental measurements
Derived measurements
Fiat measurements
Reliability in measurement
Accuracy in measurement
Capital and profit as derived measurements
Appropriate measurement in an auditing context
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