GODFREY HODGSON HOLMES TARCA

1. GODFREYHODGSONHOLMESTARCA CHAPTER 5 MEASUREMENT THEORY

2. 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)

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. Permissible operations of scales • Nominal and ordinal scales • no arithmetic operations • Interval scale • addition and subtraction • Ratio scale • all arithmetic operations

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. Reliable measurement • What is reliable measurement? • proven consistency • repeatable or reproducible • precision • Reliability incorporates two aspects • accuracy and certainty of measurement • representative faithfulness

18. 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

19. Accurate measurement • Many accounting measurements are on a ratio scale • This is the most informative scale • Weakest theoretical foundation as they are fiat measurements

20. 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

21. 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

22. 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

23. Measurement issues for auditors • Auditors must determine whether management has made appropriate and reasonable valuations • e.g. at least 12 methods of valuing intangibles

24. 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

25. 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

26. 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