1. GODFREY HODGSON HOLMES TARCA
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