GODFREYHODGSON

HOLMESTARCA

CHAPTER 5 MEASUREMENT THEORY

Importance of measurement

Campbell: The assignment of numerals to represent

properties of material systems other than numbers

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Assignment of numerals to objects or events according to rules. (Stevens)Assignment of numerals to objects or events according to rules. (Stevens)

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

• 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 uncertaintyWe 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

• 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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