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Accuracy:
Accuracy:
The use of the word "accurate" - free of error - in referring to a scientific observation or scientific method sometimes obscures the fact that even the best methods and observations are only relatively free from error. The use of the single word "accurate" also hides the fact that a number of separate elements contribute to over-all freedom from error. "Accurate" is frequently used to refer indiscriminately to the effect of any of these elements, or to the combined effects of all of them on the freedom from error of a system. Effective use of a method or observation requires that we know the ways and degrees to which the data are free of error, not that we know only that the data are "accurate" or "inaccurate".
The elements to be taken into account in a complete evaluation of a method or system can be derived from the properties of the quantitative relationship between the "input" and the "output" for the system. The input-output relationship, for all its generality, has specific application--and specific names--in different scientific fields and for different kinds of experimental or observational systems. In physics and engineering, the "stress-strain diagram" is a special representation of the input-output relationship; in pharmacology, the "dose-effect curve" is an example of the input-output relationship. In quantitative chemical analyses, the "calibration curve" is an example of the input-output relationship. Generally, "input" can be looked on as the measured value of an independent variable or "measurand"; "output" can be viewed as a measurement made under non-standard or test conditions.
"Accuracy", as formally defined, and the elements that contribute to it can be only briefly outlined here.
Accuracy
In engineering, "accuracy" is the ratio of the "error" of a system to the range of values for output that are possible, i.e., the ratio of error to so-called Full-Scale Output. Error is defined as the algebraic difference between an indicated output value and the true measure of the input or measurand. Error, as defined by the engineer, is most like "precision" as defined below.
Validity
The degree to which output reflects what it purports to reflect, i.e., input; the degree to which output is a function of known input and it alone. For example, does an essay examination validly measure a student's knowledge of material, or is it invalid, actually measuring his literary skill or the state of the grader's digestion?
Reliability
The degree to which the input-output relationship is reproducible if the relationship is studied repeatedly under comparable conditions. For example, if a student took the same examination twice, or in two forms, would he get the same grade both times? If the same work were reviewed by two graders, would they both assign the same mark?
Sensitivity
The lowest value of input that can be inferred with a given degree of validity and reliability from measurements of output. Analogous to the usage for the word "threshold" is the phrase "threshold dose". The engineer uses the word "threshold", however, to mean the smallest change in input that will result in change in output.
Amplification
The amount of change in measured output per unit change in input. The slope of the input-output, or dose-effect, curve. (Engineers sometimes refer to "amplification" as "sensitivity".)
Precision
The capacity of the system to discriminate between different values of input; the "fineness" with which different values for input can be inferred from measured values of output. The pooled deviation of observed from expected values of output, all divided by the amplification, yields the "index of precision". The square of the reciprocal of the index of precision is the measure of the amount of information that can be delivered by the system.
Specifically, precision is computed in several steps. First, the deviation of each observed value of output from the corresponding predicted value is squared; predicted values are determined from the curve relating input and output for all the data. The squared deviations are summed and divided by N-2, the number of "degrees of freedom"; the square root of the quotient is determined and is a number analogous to the standard deviation. This "root mean square deviation" is then divided by the slope of the input-output curve, i.e., the amplification, to yield the "index of precision "; it is assumed that the input-output relationship is linear.
Comparability
The ability of a system to deliver data that can be compared in standard units of measurement and by standard statistical techniques with the data delivered by other systems. While not a critical component of accuracy, comparability of data generated by a system is critical to evaluating its accuracy and usefulness.
Economy
The ability of a system to deliver data of high information content at a low overall cost per item of data; economy does not, of course, contribute to " accuracy" but is an important determinant of the practical usefulness of a system or method.
Activity, Intrinsic:
See Intrinsic Activity.
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