Ch 4 Measurement

WHAT IS MEASUREMENT o o o o o o

Measurement is a significant part of scientific inquiry Quantative data can impart greater information that qualitative date in many instances In accounting, measurement attributes are reported in accounting reports Measurement = establish of a scale Need to see what scale accounting fits into What can we do with each scale?

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Campbell – one of the first people to deal with the issue of measurement defined it as “the assignment of numerals to represent properties of material systems other than numbers in virtue of the laws governing those properties” The “systems” in Campbell’s definition is what noted measurement theorist Stevens called “objects or events” – examples: assets, people, distance etc Stevens’ definition of measurement only requires that the assignment of number only to be done according to the rules – this approach has been criticised because one needs restrictions on the type of rules that can be used” Properties = the specific aspects of the character of the systems such as weight, length We always measure properties and not systems themselves Campbell’s definition requires numerals to be assigned to properties according to the laws governing the properties, whereas Steven’s definition requires only that that the assignment is done according to the rules

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Involves linking the formal number system to some property of objects or events by means of semantic rules (representing reality) • In accounting measure profit by: – Assigning value to capital – Calculating profit as the change in capital over the period Know that in accounting – 2 fin stats – BL and PL – profit is basically the balance closing balance of owners equity minus the opening balance of owners equity SCALES    

Every measurement is made on a scale. A scale is created when a semantic rule is used to relate the mathematical statement to objects or events. The scale shows what information the numbers represent, thus giving meaning to the numbers. The type of scale created depends on the semantic rules used. According to Stevens, scales can be described in general terms as nominal, ordinal, interval or ratio.

Nominal Scale: o When numbers are used to label the events/persons/ objectives being studied i.e. the numbers are used to denote different objects, categories or classes – just a form of classification o Numbers are most often applied in a disorganised manner, with the numbers representing nothing other than an id for the objects they denote. o Weakest type of measurements o Example: the labelling of different computers in a network ie pc1, pc2 and so on, or the numbers given to the players in a sports team ie jersey 10, jersey 20 and so on. o This scale is typically not used in accounting, only possible suggestion is the labelling of assets/liabilities eg asset 1 asset 2 etc . 1

Ordinal Scale o A scale where numbers are used to rank the objects being studied in respect to a given property/characteristic. o A weakness of an ordinal scale is that it provides no other information about the objects being studied that than the order of best to worst performing – it provides no information on how different the studied objects really are. o No arithmetic calculations possible o Example: sprinters ranked on the basis of what position they finish the race – looking at the rank you only know who finishes first or last etc – you don’t know if their times were only a second apart or if they were much further. o In accounting could be used to rank profit centres on the level of profit made. Also net present value o Also use d to evaluate investments which are then ranked PERMISSABLE OPERATION – No arithmetic applications are available Interval Scale: o The interval scale imparts more information than the ordinal scale. o Not only is the ranking of the objects known with respect to the given property, but the distant between the intervals on the scale is equal and known. o A measuring system that has numbers on a continuous scale, with equal intervals between points on the scale o The zero point on the scale is arbitrary (not fixed ) - i.e. artificial selection o Allows for objects to be ranked in respect of a given property (like the ordinal scale) , but also provides users information about the distance between the objects. o Not all arithmetical transactions are available – can only add or subtract - can not not do anything else will produce no meaning o o

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An example is Celsius temperature system – on this scale equal volumes of temperature are noted by equal volumes of expansion with an arbitrary zero point on the scale (chosen as freezing point – denoted as 0 degrees ) For instance if the temp in Sydney is 25 degrees and the temp in Penrith is 30 degrees, the difference in the numbers can be translated to represent the differences in the characteristics of the objects studied – ie. That it is 5 degrees hotter in Penrith. Standard cost accounting is one example where the interval scale is used in accounting.

Ratio Scale: The most informative scale, the characteristics of which are as follows 1. The rank order of objects is known 2. The intervals between the objects is known – equal intervals that remain unchanged 3. A unique origin of a natural zero point The invariance of the scale allows users to know the extent to which a theory remains unchanged/basically the same Example: the measurement of length in centimetres/metres or the currency in dollars/cents Measuring assets in dollar values If A= 10m and B=20M you can say that B is 10m longer than A, but also that B is twice the size of A 2

Most mathematical applications are available +, -, /, x, algebra, geometry, calculus and stats – this is why this type of scale is called a ratio Can be used to extract meaning

Ratio scales are applied to accounting. All measures used in the financial statements have a natural origin ($0). Intervals between measurement units are identical amounts of currency, and are known. And the rank order of the objects or events measured with respect to their value is known. However, to the extent that different measurement methods are applied – historical cost, net realisable value and present value, for instance – the scale is the same. But while the scale is ratio, the relative measures are not always meaningful because the attributes being measured are not the same.

Types of measurement     

The question of testing a theory relates to the question of the different kinds of measurement. Campbell mentioned two kinds: fundamental and derived measurement. Recall that in Campbell’s definition of measurement he stated that the numbers are assigned according to the ‘laws’ governing the property. For Campbell, measurements can take place only when there are confirmed empirical theories (laws) to support the measurements. A further type of measurement, fiat measurement, was mentioned by Torgerson as being additional to the fundamental and derived measurements discussed by Campbell.

Fundamental measurements • numbers assigned by reference to natural laws • e.g. length, volume

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Fundamental measurements are when numbers are assigned to objects through their natural order - natural law of length or volume

A fundamental measurement is one where the numbers can be assigned to the property by reference to natural laws and which does not depend on the measurement of any other variable. Properties such as length, electrical resistance, number and volume are fundamentally measurable. A ratio scale can be formulated for each of these properties on the basis of laws relating the different measures (quantities) of the given property. The interpretation of the numbers depends on the confirmed empirical theory that governs the measurement operation.

Derived measurement

Derived similar to fundamental – but depends on the measurement of 2 or more quantities • • 3

depends on the measurement of two or more other quantities e.g. density (mass & volume)

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Types of measurement According to Campbell, a derived measurement is one that depends on the measurement of two or more other quantities. The measurement of density is an example. It depends on the measurement of both mass and volume. Derived measurement operations depend on known relationships to fundamental properties. They are based on a confirmed empirical theory (laws) relating the given property to other properties. In accounting, an example of derived measurement is profit. It is derived from the addition and subtraction of income and expenses.

Fiat measurements • based on arbitrary definitions • numerous ways in which scales can be constructed • may lead to poor confidence • e.g. measurement of income

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Typical of the social sciences and accounting Measurements that are made in relation to certainty of measurements Based on Arbitrary definitions Accounting is not governed by natural law Measurement of income Profit – revenue – expenses Just invented

It is typical in the social sciences, and in accounting, to use an arbitrarily established definition to relate certain observable properties (variables) to a given concept, without having a confirmed theory to support this relationship. For example, in accounting we do not know how to measure the concept of profit directly. Rather, we assume that the variables of revenues, gains, expenses and losses are related to the concept of profit and can therefore be used to give us an indirect measure of profit. We use an arbitrary definition to relate the variables to the concept. However, under Campbell’s stringent classification, measurements can be made only if confirmed empirical theories exist to support them. Under Campbell’s requirement, then, many of the measurements in the social sciences, including our measurement of profit, cannot be considered measurements. In order to justify most of the measurements in the social sciences, Torgerson argued that one other category of measurement should be added to Campbell’s list: measurement by fiat (Fiat means decree, edict). Such measurements would encompass those based on arbitrary definitions (e.g. the measurement of profit in accounting). However, Torgerson points out that the major problem with measurement by fiat, because it is not based on confirmed theory, is the numerous ways in which the scales can be constructed. In accounting, for example, the various accounting standards board determine accounting scales by fiat, not by reference to confirmed measurement theories. Therefore, there are many measurement alternatives so confidence in any particular scale may be low.

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Coming back to our earlier example, do we know, for example, that the specific way we measure profit is valid? It may be one of a hundred ways to measure profit and as long as the particular way we measure it is not based on confirmed theory, there is no good reason for confidence in its results. One can be justifiably more confident in fundamental measurements than in fiat measurements as a measurement tool. Fiat measurements are weak, as they are not based on confirmed theory; instead they are based on/derived from natural law (drawing from the social sciences). Inventory costing is a fiat (constructed) measurement.

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Sources of error It is important to state that NO MEASUREMENT IS FREE FROM ERROR EXCEPT COUNTING SOURCES OF ERRORS IN MEASUREMENTS 1- Measurement Numbers are stated imprecisely: The rule to assign numbers to a property nor If you ask someone to measure something but the steps and procedures are inappropriate or correct, but are interpreted incorrectly, the wrong information will be generated 2- Measurer 3- Instrument 4- Environment – extreme changes in the temp can effect instruments. But the environ can affect the accountant. Pressure from management can effect the accountant’s decisions 5- Attributes unclear The lender is not stupid The operations of the firm Salary is normally in contract If you increase your assets as the same time you increase your asserts Ration considers to be true If you are not sure about the outcome Some assets are hard to put a valoue on Measurement may not be clear if the attribute can not be measured directly For example if you want to measure the mechanical ability of people, this is not a directly measureable characteristic

Have do decide what attribute to measure to look at to measure - where the difficulty lies not persee the measurement method

The attribute can be difficult to choose The problem of vagueness of the attribute in accounting can be a common issue in accounting

The main purpose of accounting is to reflect “values”

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No measurement is free of error except counting. We can count the number of chairs in a certain room and be exactly correct. But except for counting, all measurements involve errors. SOURCES of Error The sources of error in measurement include the following, which are not mutually exclusive: - Measurement operations stated imprecisely. The rule to assign numbers for a given property usually consists of a set of operations. A set of operations may not be stated precisely and therefore may be interpreted incorrectly by the measurer. For example, the calculation of profit involves numerous operations, such as cost classifications and allocations between assets and expenses which are often interpreted differently by different accountants. - Measurer. The measurer may misinterpret the rule, be biased, or apply or read the instrument incorrectly. For example, if ten people measured the length of a certain room, there would probably be ten different results, which may all be close, but still at variance with one another. - Instrument. Many operations call for the use of a physical instrument, such as a ruler or a thermometer, which may be flawed. - Environment. The setting in which the measurement operation is performed can affect the result. For example, weather conditions may affect the instrument or the measurer. More generally, noise may distract the measurer or, in accounting, pressure from management may affect the accountant’s decisions. If the pressure causes bias by the accountant, the ‘error’ is deliberate and non-random. If the pressure (e.g. from heavy workload) causes concentration lapses and distraction, the source of error can be labelled ‘environmental’. Random errors are often caused by environmental factors. - Attribute unclear. What is to be measured may not be clear, especially if the measurement involves a concept which cannot be measured directly. The problem of vagueness of the attribute is not uncommon in accounting. What is the value of a non-current asset? Is it the present value, acquisition cost, current cost or selling price? Given that a major purpose of accounting is to reflect ‘values’, it is important to clearly define the attribute ‘value’. Is it value in use, value in exchange, or some other attribute that the accountant should measure? The problem lies in defining the attribute to be measured, not the measurement method per se. If all measurements except accounting inherently involve errors, then how can any statement that includes a measurement be regarded as true? The problem is that many expect perfection when there cannot be any. What we need is to establish limits of acceptable error. If any measurement falls within these limits then it can be considered true, i.e. a fact.

Reliability and accuracy Reliable measurement

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proven consistency

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repeatable or reproducible

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accuracy and certainty of measurement

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representative faithfulness

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Reliability and accuracy

Accurate measurement •

how close the measurement is to the ‘true value’ of the attribute measure

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‘true value’ may not be known

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consistency of results, precision and reliability may not lead to accuracy

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Consistency of results, precision and reliability do not necessarily lead to accuracy

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Accuracy has to do with how lose the measurement is to the true value of the attribute measure – the bullseye so to speak

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The problem os measurements is that true value may not be known

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Accurate is different to reliable – accurate means a refection of the true value of the asset One of the major arguments underlying accounting True value – only when you sell the object in a market Need to balance reliability and accuracy There is not true value of an item Consumer and what they ARE WILLING TO PAY DIFFER Two examples ON Why there is not True value This is why marketing is so smart – you have decide the right price

RELIABLE Measurement It is often required that before elements such as assets, liabilities, income and expenses are recognised in financial statements, the elements should be capable of reliable measurement. What is meant by reliable measurement? Reliability refers to the proven consistency of either an operation to produce satisfactory results or the results (the numbers) themselves for a particular use. In statistics, reliability demands that measurements be repeatable or reproducible, thereby demonstrating their consistency. The notion of reliability incorporates two aspects: the accuracy and certainty of measurement, and the representative faithfulness of disclosures in relation to the underlying economic transactions and events. The measurement aspect concerns the precision of measurement. Reliability of measurement pertains to the precision with which a specific property is measured by use of a given set of operations. 8

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ACCURATE Measurement Although a measurement procedure may be highly reliable, given very precise results, it may not produce accurate results. A certain rifle in the hands of an expert sports shooter may be highly reliable in enabling successive shots to be placed close together, but if the sight is not properly aligned, those shots will not be around the bullseye. Consistency of results, precision and reliability do not necessarily lead to accuracy, The reason is that accuracy has to do with how close the measurement is to the ‘true value’ of the attribute measure, the ‘bullseye’, so to speak. Fundamental properties, such as the length of an object, can be determined to be accurate by comparing the object with a standard that represents true value. We can, for example, use a ruler as a representation of the standard. The problem is that for many measurements the true value is not known. In order to measure accurateness in accounting, we need to know what attribute we should measure to achieve the purpose of the measurement. The objective of accounting mentions the ‘usefulness’ of the information. Accuracy of measurements therefore relates to the pragmatic notion of usefulness, but accountants are not in agreement as to what the specific, quantitative standards are that are implied. Instead of using the term ‘accuracy’, which is so often understood to mean arithmetical precision, it may be prudent to use the term of the social scientists, ‘validity’.

ANSWER Reliability refers to the proven consistency of a measurement or the operations from which the measurement is derived. We can speak of a measurement (the number) being reliable, or of the set of operations (instrument) being reliable. In statistics, reliability refers to the agreement of results – consistency among repeated application of the operation to a large number of cases. In statistics, the variable must be random; therefore, the reliability relates to the random error in measurement, the unsystematic error component. If the random error is minimal, then the measurement is reliable. Reliability does not necessarily lead to accuracy. The reason is that accuracy has to do with how close the measurement is to the ‘true value’ of the attribute measured. In statistics, the true value is presented by the mean. In accounting, ‘true value’ pertains to the pragmatic notion of usefulness, which is expressed in the objective of accounting. Because the term ‘accuracy’ is so often misunderstood, the term ‘validity’ has been suggested to denote the same idea. We can speak of a valid measurement in the sense that it is appropriate for the stated purpose – that is, the measurement hits the ‘bullseye’ or is sufficiently close to it. Another way of putting it is to say, the measurement is relevant. Accuracy or validity relates to the relevance of accounting information.

Measurement in Accounting •

Two fundamental measures –

Capital & profit

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Capital can be defined & derived in various ways

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Concepts of capital & profit have changed over time

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Number of concepts of fundamental measurement

All measurements – accept counting have errors BUT WE STILL CHOOSE TO BOTHER MEARUING WHY IS THIS Not the accuracy of the final measurements

Concepts can be defined in several ways – arbitrary Cost Accountign – 100k the oginal capital 500 is the accounting profit This isunder cost accounting

In sixmonths time – the costs are changed – you cann no longer afford to buy B.c of capital base Tom ianitn operation capital So you can maintain selling 100 jumoers

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