Measurement scales

The activity of the hydrogen ion is affected by the properties of the solvent in which it is measured. Scales of pH only apply to the medium, ie, the solvent or mixed solvents, eg, water—alcohol, for which the scales are developed. The comparison of the pH values of a buffer in aqueous solution to one in a nonaqueous solvent has neither direct quantitative nor thermodynamic significance. Consequently, operational pH scales must be developed for the individual solvent systems. In certain cases, correlation to the aqueous pH scale can be made, but in others, pH values are used only as relative indicators of the hydrogen-ion activity. 

Streiner D L and Norman G R (2001), Health Measurement Scales, Oxford Medical Publications, Oxford. 

Making a measurement of any kind involves comparing the unknown (i.e. the test sample being measured) with a standard. The standard provides the link to the measurement scale being used (e.g. a ruler to measure length, a standard weight to measure mass, a pure chemical substance to determine the amount of a compound present). This is illustrated in Figure 5.1. 

Hierarchical characteristics of the four types of measurement scale. 

Type of measurement scale Possesses name Possesses order Possesses distance Possesses meaningful origin... 

Four types of measurement scale can be used for assigning values to varying amounts of a property associated with a system input or system output [Summers, Peters, and Armstrong (1977)]. In order of increasing informing power, they are nominal, ordinal, interval, and ratio scales. The characteristics at determine a measurement scale s level of sophistication are name, order, distance, and origin. The characteristics of the four types of measurement scale are shown in Table 1.3. The nominal scale possesses only one of these characteristics the ratio scale possess all four characteristics. 

There are many reasons why it is important to understand which type of measurement scale is being used to describe system inputs and outputs. One reason is that most statistical techniques are not applicable to data arising from all four types of measurement scales the majority of techniques are applicable to data from interval or ratio scales. 

Indicate which type of measurement scale (nominal, ordinal, interval, or ratio) is usually used for the following characteristics time, mass, library holdings, gender, type of heart attack, cholesterol level as measured by a clinical chemical laboratory, cholesterol level as reported by a doctor to a patient, pipet volume, and leaves on a plant. 

Indicate which type of measurement scale (continuous or discrete) is usually used for the characteristics listed in Problem 1.24. 

Every shot should include an item of measurable scale as a size reference. It is common to include a ruler/scale or some other object of known size in any close-up view (3 feet or less, 1 meter or less). Tape measures can also be used to show the size of objects and the distance of objects from each other. The orientation of the tape measure can also be used to show the orientation of the photograph. 

It is important when choosing a particular measurement scale to answer a number of questions. Is the choice that is made of clinical relevance How is the endpoint to be measured Can we measure the clinical endpoint directly, or must we choose an indirect approach Is the choice that is made sensitive enough to measure real treatment effects Having collected the information how are we to analyse it Some of these issues are illustrated in the following sections. 

Measurement uncertainty is the most important criterium in both method validation and IQC. It is defined as a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand [14]. The measurand refers to the particular quantity or the concentration of the analyte being measured. The parameter can be a standard deviation or the width of a confidence interval [14, 37]. This confidence interval represents the interval on the measurement scale within which the true value lies with a specified probability, given that all sources of error are taken into account [37]. Within this interval, the result is regarded as being accurate, that is, precise and true [11]. 

Until now, the most sensible basic interacting quantum device known to us is the photon. Nevertheless, if the photon possesses an inner structure, as assumed in de Broglie s model, it would imply measurements beyond the photon limit. Since it was assumed that the quantum systems are to be described by local finite wavelets in the derivation of the new uncertainty relations, the measurement space resulting from those general relations must depend on the size of the basic wavelet used. As the width of the analyzing wavelet changes, the measurement scale also changes. This can be seen in the plot in Fig. 20. 

In specifying the results of measurements taken with a Rockwell hardness tester, both standard type and Super, the measuring scale is indicated, e.g., //RA, Hrc, Hr45N, and so on. Scale N is applicable for hard materials and the remaining special scales, for soft materials (brass, lead, zinc, organic materials, gypsum and lime-based materials). 

Lee S-B, Luss H (1987) Multifacility-Type Capacity Expansion Planning Algorithms and Complexities. Operations Research 35 249-253 Leskinen P (2000) Measurement Scales and Scale Independence in the Analytic Hierarchy Process. Journal of Multi-Criteria Decision Analysis 9 163-174... 

Abstract The authors propose definitions and terminology for protocols on traceability links, generally to the international system of units, for specific chemical-analytical measurements in accordance with recognized principles of science. These definitions and terms could be useful in science, technology, commerce or law. A chain of such links leads from a measurand in a sample up to a unit in the International System of Units or, if unavailable, to a value on an internationally recognized measurement scale. The quality of such a chain is quantified by combining all recognized uncertainties estimated for all its links. These uncertainties of... 

System of Units (SI) [5] or, where that is not possible, up to a unit on an agreed and conventional measurement scale. 

Abstract In continuing their attempt to bring general issues concerned with trustworthy chemical measurements to review and international discussion, the authors propose basic aims and requirements for protocols of chemical-measurement procedures with traceability to the SI or, where this is not possible, to units of internationally recognized measurement scales. Documents describing such protocols could be useful in science, technology, law, or trade. Concepts and definitions for protocols have been introduced in Part I of this contribution. Part II here deals with the development and application of protocols for intended in-laboratory, commercial, national, or international recognition. Protocols deal with measure-... 

Here we propose the additional concepts under which analysts can formally substantiate and record their traceability link. A chain of such links should lead from the value of a quantity in a sample or reference material (RM) up to the value of a relevant unit in the International System of Units (SI) [5] or - where this is not possible - up to internationally agreed measurement scales. A protocol records specific details of scientifically reliable measurement procedures for the benefit of equity in trade and commerce, as well as for legal interpretations of scientific realities. Some ideas in this article go beyond established international understandings these are presented for debate and possible refinement. 

In the case of turbidity measurement, the traceability chain should begin with the value of turbidity in a sample (the quantity being measured) then progress through higher levels of authority up to the unit of turbidity on an agreed and conventional measurement scale, based on the values assigned to RMs, stated in standard specifications, international recommendations or other reference documents. 

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