4 The significance of the concept of a representational scale in accounting
The concept of a representational scale discussed in section 3 may be of fundamental significance to accounting. Mattessich (1964:63) identifies the nominal scale, ordinal scale, interval and ratio scales as the medium through which accounting information is communicated. According to Stevens (1951), the classification of scales into scale types is based on the amount of information about a property that is contained in a scale. This suggests that every measurement scheme should specify the type of scale used in order to indicate the amount of information contained by the measures it produces. It can thus be argued that a scale of measurement is an embodiment of the properties of the phenomenon being measured. It follows that, without the specification of a scale of measurement, it would be not possible to know what a particular numerical assignment represents. Therefore, if accounting were a measurement discipline, it should have been capable of specifying the rules of measurement employed in its measurement processes to give meaning to its numerical assignments. Failure to do so calls into question the status of accounting as a measurement discipline.
Measurement is about stating the relationship between the numerals and the objects. A rule of measurement states the relationship between the numerals and objects (Boyce, Meadow & Kraft, 1994). This means that, if accounting has no specified rules of assigning numerals to objects, it implies that the relations between the numerals and objects are not known. If these relations are not known it would be difficult to determine the meaning of a measurement. It follows that the concept of a scale influences the meaningfulness of a measure. This is reflected by Chambers (1997:38):
In the third place, every measurement scheme requires the specification of the unit in the scale, and the conditions under which unit measurements shall be deemed to be of equal significance. In brief, this requires specification of the meaning of the "standard" unit. This is necessary since measurements may be taken in a variety of non-standard situations, such that the raw or crude measurements are not comparable or addable.
This indicates that a scale used in a process of measurement must be specified. The extract also points out that a scale gives empirical significance to measurements. Thus, a scale specifies the conditions under which a measurement has been made. It is clear from the above extract that the essence of meaningfulness is embodied in the description of the scale type and permissible statistics. This evidently highlights the fact that the statistics that can be performed on a measure lead to the formation of meaningful, or meaningless, statements based on measurements made on those scales. The meaning of a measure is therefore embodied in the description of the meaning of the standard unit. It can thus be concluded that, in the absence of specified scales, accounting measurements lack meaning and are incomparable.
Nevertheless, accounting information is considered comparable in the absence of specified scales of measurement. For example, IASB (2009) points out that users must be able to compare the financial statements of an entity through time in order to identify trends in its financial position and performance. This suggests that it is possible for users of accounting information to compare information from different entities in the absence of specified scales of measurement. The IASB (2009) points out that the measurement and display of the financial effect of like transactions and other events must be carried out in a consistent way throughout an entity and over time for that entity, and in a consistent way for different entities. This highlights the existence of a belief in accounting that measurement is possible in the absence of a specified scale of measurement. It can thus be concluded that the concept of a scale of measurement is not recognized in the accounting discipline.
The nature of accounting measurements demands that the scales of measurement should be specified before they are compared. This is because accounting measurements are dependent on the intuition of the accountant. As Mattessich (1964:79) states:
There neither exists at present the possibility to infer accounting values through "natural laws" (i.e., by fundamental measurement) nor through a combination of two or more fundamental measures that result in derived measurement. Most of the economic and accounting measures belong in the category of measurement by fiat, which is reflected in a certain definitional arbitrariness of our discipline.
This emphasizes that accounting measure-ments are dependent on the intuition of the accountant, as accounting is not a natural, but a social science. The use of the phrase "definitional arbitrariness of our discipline" implies that accounting definitions are not based on consistent rules or plans, but are instead dependent on the context in which they are used. It is clear that accounting measurements are socially constructed. Consequently, this suggests a need to specify clearly the nature of the social context of accounting measurements before they are evaluated. There could be a difference between the kinds of assigning of numbers arising from different procedures of measurement. Therefore, if a scale of measurement was not specified in a measurement discipline, it would not possible to tell whether there were any other numbers that could be assigned as measures of the same property. Such knowledge of other numbers that might be assigned is important in determining the uniqueness of a measure. The number assigned to measure a property of an object is unique once a unit has been assigned to it (Luce et al., 1971). The concept of a scale is thus also important for the quality of uniqueness of measures. A lack of specified scales of measurement implies that the uniqueness of numbers assigned to represent the properties of accounting objects cannot be determined.
The lack of specified scales of measurement has negative implications for the mathematical operations that could be carried out on accounting measurements. Chambers (1997) contends that the scales of measurements (or rather measurements taken in them) have different mathematical characteristics. He also suggests that the addition of measures and other forms of relations (inter alia, subtraction, multiplication or division) is common in accounting processes. As a result, it is necessary to consider the conditions under which addition (and other forms of relation) is mathematically permissible (e.g., the addition of different classes of assets). That is, the values of assets and liabilities are added in the balance sheet and in the income statement without first verifying whether these measurements have been made under the same scale of measurement.
The lack of specified scales causes inconsistencies in the classification of measures in accounting. Chambers (1997:39) notes the following on the classification of measures by the AAA's report (1971) on the foundations of accounting measures:
Among examples of primary measures are counts of physical quantities, and prices of non-monetary goods. In respect of prices, it is said that they may be past, present or future prices. No such stipulation is made in respect of physical counts. Either, therefore, counts and prices are not members of the same class of measures (i.e. primary measures), or both should be treated in the same way (i.e., it should be allowed that physical counts may be past, present or future counts).
The above passage points out that accounting measures that differ are grouped in the same class, and that physical counts and prices are regarded as measures of the same property. It is also clear that there is no specified property represented by physical counts or by prices.
Furthermore, there is no specification of the scale of measurement that could be used to distinguish the extent to which physical counts and prices possess a particular property. Consequently, it is not clear whether physical counts and prices are measures of the same property. This leads to incorrect classification of measures. In this way, the lack of specified scales in accounting casts doubt on the current belief in the literature that accounting is a measurement discipline.
4 The significance of the concept of a representational scale in accounting
The concept of a representational scale discussed in section 3 may be of fundamental significance to accounting. Mattessich (1964:63) identifies the nominal scale, ordinal scale, interval and ratio scales as the medium through which accounting information is communicated. According to Stevens (1951), the classification of scales into scale types is based on the amount of information about a property that is contained in a scale. This suggests that every measurement scheme should specify the type of scale used in order to indicate the amount of information contained by the measures it produces. It can thus be argued that a scale of measurement is an embodiment of the properties of the phenomenon being measured. It follows that, without the specification of a scale of measurement, it would be not possible to know what a particular numerical assignment represents. Therefore, if accounting were a measurement discipline, it should have been capable of specifying the rules of measurement employed in its measurement processes to give meaning to its numerical assignments. Failure to do so calls into question the status of accounting as a measurement discipline.
Measurement is about stating the relationship between the numerals and the objects. A rule of measurement states the relationship between the numerals and objects (Boyce, Meadow & Kraft, 1994). This means that, if accounting has no specified rules of assigning numerals to objects, it implies that the relations between the numerals and objects are not known. If these relations are not known it would be difficult to determine the meaning of a measurement. It follows that the concept of a scale influences the meaningfulness of a measure. This is reflected by Chambers (1997:38):
In the third place, every measurement scheme requires the specification of the unit in the scale, and the conditions under which unit measurements shall be deemed to be of equal significance. In brief, this requires specification of the meaning of the "standard" unit. This is necessary since measurements may be taken in a variety of non-standard situations, such that the raw or crude measurements are not comparable or addable.
This indicates that a scale used in a process of measurement must be specified. The extract also points out that a scale gives empirical significance to measurements. Thus, a scale specifies the conditions under which a measurement has been made. It is clear from the above extract that the essence of meaningfulness is embodied in the description of the scale type and permissible statistics. This evidently highlights the fact that the statistics that can be performed on a measure lead to the formation of meaningful, or meaningless, statements based on measurements made on those scales. The meaning of a measure is therefore embodied in the description of the meaning of the standard unit. It can thus be concluded that, in the absence of specified scales, accounting measurements lack meaning and are incomparable.
Nevertheless, accounting information is considered comparable in the absence of specified scales of measurement. For example, IASB (2009) points out that users must be able to compare the financial statements of an entity through time in order to identify trends in its financial position and performance. This suggests that it is possible for users of accounting information to compare information from different entities in the absence of specified scales of measurement. The IASB (2009) points out that the measurement and display of the financial effect of like transactions and other events must be carried out in a consistent way throughout an entity and over time for that entity, and in a consistent way for different entities. This highlights the existence of a belief in accounting that measurement is possible in the absence of a specified scale of measurement. It can thus be concluded that the concept of a scale of measurement is not recognized in the accounting discipline.
The nature of accounting measurements demands that the scales of measurement should be specified before they are compared. This is because accounting measurements are dependent on the intuition of the accountant. As Mattessich (1964:79) states:
There neither exists at present the possibility to infer accounting values through "natural laws" (i.e., by fundamental measurement) nor through a combination of two or more fundamental measures that result in derived measurement. Most of the economic and accounting measures belong in the category of measurement by fiat, which is reflected in a certain definitional arbitrariness of our discipline.
This emphasizes that accounting measure-ments are dependent on the intuition of the accountant, as accounting is not a natural, but a social science. The use of the phrase "definitional arbitrariness of our discipline" implies that accounting definitions are not based on consistent rules or plans, but are instead dependent on the context in which they are used. It is clear that accounting measurements are socially constructed. Consequently, this suggests a need to specify clearly the nature of the social context of accounting measurements before they are evaluated. There could be a difference between the kinds of assigning of numbers arising from different procedures of measurement. Therefore, if a scale of measurement was not specified in a measurement discipline, it would not possible to tell whether there were any other numbers that could be assigned as measures of the same property. Such knowledge of other numbers that might be assigned is important in determining the uniqueness of a measure. The number assigned to measure a property of an object is unique once a unit has been assigned to it (Luce et al., 1971). The concept of a scale is thus also important for the quality of uniqueness of measures. A lack of specified scales of measurement implies that the uniqueness of numbers assigned to represent the properties of accounting objects cannot be determined.
The lack of specified scales of measurement has negative implications for the mathematical operations that could be carried out on accounting measurements. Chambers (1997) contends that the scales of measurements (or rather measurements taken in them) have different mathematical characteristics. He also suggests that the addition of measures and other forms of relations (inter alia, subtraction, multiplication or division) is common in accounting processes. As a result, it is necessary to consider the conditions under which addition (and other forms of relation) is mathematically permissible (e.g., the addition of different classes of assets). That is, the values of assets and liabilities are added in the balance sheet and in the income statement without first verifying whether these measurements have been made under the same scale of measurement.
The lack of specified scales causes inconsistencies in the classification of measures in accounting. Chambers (1997:39) notes the following on the classification of measures by the AAA's report (1971) on the foundations of accounting measures:
Among examples of primary measures are counts of physical quantities, and prices of non-monetary goods. In respect of prices, it is said that they may be past, present or future prices. No such stipulation is made in respect of physical counts. Either, therefore, counts and prices are not members of the same class of measures (i.e. primary measures), or both should be treated in the same way (i.e., it should be allowed that physical counts may be past, present or future counts).
The above passage points out that accounting measures that differ are grouped in the same class, and that physical counts and prices are regarded as measures of the same property. It is also clear that there is no specified property represented by physical counts or by prices.
Furthermore, there is no specification of the scale of measurement that could be used to distinguish the extent to which physical counts and prices possess a particular property. Consequently, it is not clear whether physical counts and prices are measures of the same property. This leads to incorrect classification of measures. In this way, the lack of specified scales in accounting casts doubt on the current belief in the literature that accounting is a measurement discipline.
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