4.4. Accuracy and Precision

Accuracy may be defined as how close a measured value is to the "true" value. It is often difficult to establish a "true" value and thus the accuracy of an analysis based upon it. Accuracy is affected if the compositions of the standards are not well known whereas precision is not. Standard compositions are often determined by wet chemistry, but this process also analyzes tiny inclusions in the standard materials making it impossible to establish "true" composition.

Sometimes for the minor elements, microprobe analysis of inclusion free areas in a mineral is the best method for determining the true composition! One way to avoid potential problems with the standard compositions is to use mono-elemental (synthetic) standards. With these materials, one only has to look for impurities and make sure that they are insignificant, not determine their abundances. However, the matrix effects may be so significant that a multi-element standard (similar to the unknown) is required.

Precision refers to how well a given measurement or results can be reproduced. Values can be very precisely determined and still be very inaccurate. Conversely, a number of imprecise analyses may average to a very accurate value. Precision is effectively limited by counting statistics when dealing with X-ray analysis.

Many factors, many out of the control of the analyst, can affect both precision and accuracy. Among them are:

• Incorrect standard values, which affect accuracy and produce systematic errors (high values if standard compositions are higher than they should be, lower if low).
• Focus problems, which can produce significant unsystematic errors and a loss of precision and accuracy. Defocusing the beam on the sample results in imperfect spectrometer optics and reduced count rates. This produces unsystematic errors unless one always misfocuses identically.
• Specimen tilt, which produces systematic errors by changing the take-off angle.
• Irregularities in the sample surface, which are produced during polishing, or despite polishing, also may produce unsystematic errors.
• Errors in matrix-correction factors, which can significantly reduce accuracy especially where correction coefficients are poorly known. The element F is a good example of this--F in apatite should be determined using a fluorapatite standard, while determining F in micas requires a F-rich mica. Errors in the matrix-correction coefficients will produce systematic errors during data reduction. Everyone worries about getting better (correct) data-reduction factors, but not many do anything about it.
• Variations in the thickness of the C-coat, which primarily affect accuracy and cause variable amounts of absorption for soft X-rays. The largest concern for routine analysis is the effect of coat thickness on Na-Ka X-rays. This problem can be significant if standards and unknowns have very different thicknesses of carbon, and will cause systematic variations.
• Incorrect location of backgrounds, which can strongly affect accuracy as can large deadtimes and peak shifts from standard to unknowns (e.g., S).
• Errors in nominal accelerating voltage, which cause systematic errors. The gun accelerating voltage can be checked using the excitation of certain X-ray lines (e.g. Ti-Ka at 4.964 keV and Rb-Ka at 15.200 keV).
• Electronic instability, which primarily reduces precision.