Analysis of measurement scales

: pp. 21-35
Lviv Polytechnic National University

The basic principles of systematization of measurement scales types are describes and analyses in this article. Properties types of the empirical objects and corresponding measurement scales are considered. According to VIM3 (“International vocabulary of metrology: Basic and general concepts and associated terms”), measurement scale (quantity-value scale) is an ordered set of quantity values of quantities of a given kind of quantity used in ranking, according to magnitude, quantities of that kind, for example, Celsius temperature scale, time scale, Rockwell C hardness scale etc. According to the metric determination, depending on the type of the investigated empirical object, in particular, of its properties, and therefore the type of measured value, measurement scales are divided into the following types: nonmetric scales: nominal scales and ordinal scales; metric scales: intervals scales, ratios scales and absolute scales. Metric scales – these are scales, which have the units of measurement (for eg., meter, ampere, m/s). Non-metric scales – these are scales, which do not have units of measurement. According to the form of empirical data obtaining, measurement scales are divided into verbal, numerical and graphic. According to the number of the displayed properties of empirical objects, measurement scales are divided into onedimensional and multidimensional. Nominal scales are formed in the case when a certain property of empirical objects is evident only in respect of equivalence. The main informative parameter of such objects is their quantity (number), which is determined by counting. This feature can be displayed by any number or other mark that does not contain any information about the value size, which is inherent in this property. Nominal scales or scales of names are used in the measurement of objective evidences such as odor, color, blood groups, nationality, marital status, age, gender, work experience, qualifications, telephone numbers, passports, bar codes of products, etc. Ordinal scales are formed in the case when a certain property of empirical objects is shown in relation of equivalence and order (of level). Located according to ascending or descending order, namely, according to the rank, the size of the measured values constitute ordinal scale or rank scale. The ordinal scale or rank scale is expressed in the form of an ordered sequence of points, marked with letters, numbers or symbols that meet certain values size Qі, і=1,2,3,…,п: Q1<Q2<Q3<…<Qп. It is known about the extent of the value Qі that one of them is always less than the next and larger than the previous one, but exactly the sizes are unknown. The hardness of minerals, sensitivity of films, the intensity of earthquakes, volume level and more are measured by the ordinal. Wind power is measured on 12-point Beaufort scale. The intensity of earthquakes is measured on a 10-point Richter scale. Scales which are formed from strictly defined intervals are much more sophisticated, the so-called intervals scales, which are described by the equation Qi - Qj = DQi, j , and the interval DQi, j between the size of value Qі and Qj is exactly known. Value scale can be set on the intervals scale and there is adopted by agreement “conditional zero”. For example, in the Celsius temperature scale one degree (1 °С) is equal to 1/100 interval between the temperature of melting ice, adopted as a starting point (0 °С) and water boiling (100 °С). So, the unit value and its dimension can be set on the intervals scale. According to interval scale it is possible to determine not only that one size is larger (smaller) from the other, but also how much more it is larger (smaller), it means that on intervals scale it is possible to perform mathematical operations such as addition and subtraction. The most advanced, the most informative and the most common of all the measuring scales there are ratios scales, in which the starting point of reference is adopted by the point with really zero size value (“absolute zero”). An example of the ratio scale is Kelvin temperature scale. As the origin the absolute zero of temperature is taken, at which the thermal motion of molecules stops. The second point of reference is the melting temperature of ice. According to Celsius scale interval between the points of reference is 273.15 °С. Therefore, on Kelvin scale it is divided into equal parts, each of which is 1/273.15 of the interval between the points of reference and is called Kelvin. Ratio scale serves for the submission of the measurement result, obtained by experimental comparison of і- size Qі with j-th size Qj according to rule q =Q [Q] . On the ratio scales it is possible to perform all arithmetic operations: addition, subtraction, multiplication and division. In this regard, ratio scales are the most widely used in metrology, particularly for measuring electrical quantities – amperage, voltage, electric resistance and others. The absolute scale – this is a ratio scale (proportional or additive) of dimensionless quantity. The results of measurements in absolute scales can be expressed not only in terms of arithmetic values, but as a percentage, fractions of millionths (p.p.m.), parts per thousand, bits, bytes and decibels. The choice and use of this or that scale and, therefore, measurement methodology depends on empirical objects properties, the type of measured value and obtaining method of measuring information, namely the way of comparison of the of the quantities sizes.

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