Definitions | Measurement is an activity undertaken to determine a value, status or trend in performance or effectiveness to help identify potential improvement needs. Measurement can be applied to any ISMS processes, activities, controls and groups of controls.
Definition 3.1 Physicists traditionally consider the measurement as “a process by which one can convert physical parameters to meaningful numbers” (ISO/IEC GUIDE 99:2007 2007; JCGM 100:2008 2008).
Paraphrasing N. R. Campbell (Final Report, p. 340),. we may say that measurement, in the broadest sense, is defined as the assignment of numerals to objects or events according to rules. The fact that numerals can be assigned under different rules leads to different kinds of scales and different kinds of measurement. The problem then becomes that of making explicit (a) the various rules for the assignment of numerals, (b) the mathematical properties (or group structure) of the resulting scales, and (c) the statistical operations applicable to measurements made with each type of scale.
To the British committee, then, we may venture to suggest by way of conclusion that the most liberal and useful definition of measurement is, as one of its members advised, "the assignment of numerals to things so as to represent facts and conventions about them." The problem as to what is and is not measurement then reduces to the simple question: What are the rules, if any, under which numerals are assigned? If we can point to a consistent set of rules, we are obviously concerned with measurement of some sort, and we can then proceed to the more interesting question as to the kind of measurement it is. In most cases a formulation of the rules of assignment discloses directly the kind of measurement and hence the kind of scale involved. If there remains any ambiguity, we may seek the final and definitive answer in the mathematical group-structure of the scale form: In what ways can we transform its values and still have it serve all the functions previously fulfilled? We know that the values of all scales can be multiplied by a constant, which changes the size of the unit. If, in addition, a constant can be added (or a new zero point chosen), it is proof positive that we are not concerned with a ratio scale. Then, if the purpose of the scale is still served when its values are squared or cubed, it is not even an interval scale. And finally, if any two values may be interchanged at will, the ordinal scale is ruled out and the nominal scale is the sole remaining possibility. This proposed solution to the semantic problem is not meant to imply that all scales belonging to the same mathematical group are equally precise or accurate or useful or "fundamental." Measurement is never better than the empirical operations by which it is carried out, and operations range from bad to good. Any particular scale, sensory or physical, may be objected to on' the grounds of bias, low precision, restricted generality, and other factors, but the objector should remember that these are relative and practical matters and that no scale used by mortals is perfectly free of their taint.
Definition 3.6 “Measurement is the assignment of numbers to properties of objects or events in the real world by means of an objective and empirical operation, in such a way as to describe them. The modern form of measurement theory is representational: numbers assigned to objects/events must represent the perceived relations between the properties of those objects/events” (Finkelstein and Leaning 1984).
Paraphrasing the above considerations, measurement is an operation of objective description of reality: different measurements of the same entity (in the same operating conditions) should result in the same output, independently from subjects. We suppose there is no “error” and uncertainty in an ideal measurement process (i.e., the effect of environment and other influential variables is negligible). It is also an empirical operation: “Measurement has something to do with assigning numbers that correspond to or represent or “preserve” certain observed relations” (Roberts 1979).
Going into the representation theory of measurement, a measurement can be seen as a representation of an observable property/feature of some objects into a set of symbols/numbers (Roberts 1979; Finkelstein 2003).
(…) Focusing on F, this other mapping is a one-to-one function: the relations among symbols should match the relations among empirical manifestations. Since the most commonly used symbols are numbers, typical relations are the mathematical ones. The matching between empirical and symbolic relations (i.e., F : R → P) entails that: (i) we should not introduce new relations among symbols, which do not reflect any existing relation among empirical manifestations (i.e., “promotion” of relations) or (ii) we should not omit to reflect some relations among empirical manifestations, through corresponding relations among symbols (i.e., loss/degrade of relations). According to Roberts (1979), “in measurement we start with an observed or empirical relational system and we seek a mapping to a numerical relational system which preserves all the relations and operations observed in the empirical one”. Similarly, Dawes and Smith (1985) state that “whatever inferences can be made in the symbolic/numerical relational system apply to the empirical one”. (…) The mapping functions (M and F) must be objective, i.e., they should lead to the same result, independently of the individual who performs the mapping.
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