Treatment of Experimental Data

The usual objective of performing an experiment in analytical chemistry is to obtain one or more numerical results. Between the recording of measured values and the reporting of results there are processes of numerical calculations, some of which may involve averaging or smoothing the measured values, but most of which involve the application of formulas derived from theory.

Our concern with the treatment of experimental data does not end when we have obtained a numerical result for the quantity of interest. We must also answer the question: "How good is the numerical result?" Without an answer to this question, the numerical result may be next to useless. The expression of how "good" the result may be is usually couched in terms of its accuracy, i.e., a statement of the degree of the uncertainty of the result. A related question, often to be asked before the experiment is begun, is "How good does the result need to be?" The answer to this question may influence important decisions as to the experimental design, equipment. and degree of effort required to achieve the desired accuracy.

Indeed, it may be useful to discuss the matter also in economic terms. The "economic value" of the numerical result of an experiment often depends on its degree of accuracy. To claim too high an accuracy through ignorance, carelessness or self-deception is to cheat the "consumer" who makes decisions on the basis of this result. To claim too low an accuracy through overconservatism or intellectual laziness lessens the value of the result to the "consumer" and wastes resources that have been employed to achieve the accuracy that could rightfully have been claimed.

Calculations and Presentation of Data

Mathematical processing of data is frequently required in order to obtain the desired quantitative results. At an initial stage, numerical methods are intrinsic since data consist of a set of observed "points" - usually pairs x_i, y_i of a dependent quantity y_i. measured for a specified value of the independent variable x_i.

Of course, y could be a function of two variables x and z, in which case one often holds z constant and measures y while varying x, then changes z to a new constant value and repeats the process. An example would be the measurement of the pressure of a gas as a function of volume at a series of constant temperatures.

One can use numerical techniques to fit the data with a functional form: best line y(x) through the points in an x-y plot or best surface y(x, z) in a three-dimensional computer-graphics display.

See also: Graphs & graphical methods.