Slide AKT 405 Teori Akuntansi 5 Godfrey
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
Assignment of
of numerals
numerals to
to objects
objects or
or events
events
according
(Stevens)
according to
to rules.
rules.
(Stevens)
2
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
3
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
4
Nominal scale
•
•
•
•
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
5
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
6
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
7
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
8
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
9
Permissible operations of
scales
• Nominal and ordinal scales
– no arithmetic operations
• Interval scale
– addition and subtraction
• Ratio scale
– all arithmetic operations
10
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
11
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
12
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
13
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
14
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
15
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
16
Reliable measurement
• What is reliable measurement?
– proven consistency
– repeatable or reproducible
– precision
• Reliability incorporates two aspects
– accuracy and certainty of measurement
– representative faithfulness
17
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
18
Accurate measurement
• Many accounting measurements are on a ratio
scale
• This is the most informative scale
• Weakest theoretical foundation as they are
fiat measurements
19
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
20
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
21
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
22
Measurement issues for
auditors
• Auditors must determine whether
management has made appropriate and
reasonable valuations
– e.g. at least 12 methods of valuing intangibles
23
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
24
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
25
Key terms and concepts
•
•
•
•
•
•
•
•
•
•
•
•
•
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
26
27
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
Assignment of
of numerals
numerals to
to objects
objects or
or events
events
according
(Stevens)
according to
to rules.
rules.
(Stevens)
2
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
3
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
4
Nominal scale
•
•
•
•
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
5
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
6
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
7
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
8
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
9
Permissible operations of
scales
• Nominal and ordinal scales
– no arithmetic operations
• Interval scale
– addition and subtraction
• Ratio scale
– all arithmetic operations
10
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
11
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
12
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
13
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
14
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
15
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
16
Reliable measurement
• What is reliable measurement?
– proven consistency
– repeatable or reproducible
– precision
• Reliability incorporates two aspects
– accuracy and certainty of measurement
– representative faithfulness
17
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
18
Accurate measurement
• Many accounting measurements are on a ratio
scale
• This is the most informative scale
• Weakest theoretical foundation as they are
fiat measurements
19
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
20
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
21
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
22
Measurement issues for
auditors
• Auditors must determine whether
management has made appropriate and
reasonable valuations
– e.g. at least 12 methods of valuing intangibles
23
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
24
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
25
Key terms and concepts
•
•
•
•
•
•
•
•
•
•
•
•
•
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
26
27