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Errors In Chemical Analyses
Mean , arithmetic mean , and average (x) are synonyms for the quantity obtained by dividing the sum of replicate measurements by the number of measurements in the set.
where, xi represents the individual values of x making up a set of N replicate measurements.
The median is the middle result when replicate data are arranged in order of size. Equal number of results are larger and smaller than the median. For an odd number of data points, the median can be evaluated directly. For an even number, the mean of the middle pair is used.
x
x
N
i i
N
1
Results from replicate determinations
Accuracy
Accuracy is the closeness of a measurement to the
true or accepted value and is expressed by the
error. Accuracy measures agreement between a
result and its true value but precision describe the
agreement among several measurements. We can
never determine accuracy exactly because the true
value of a measured quantity can never be known
exactly. We need to use an accepted value.
Accuracy is expressed in terms of either absolute
or relative error.
Illustration of accuracy and precision
Relative Error
Relative error of a measurement is the absolute
error divided by the true value.
The percent relative error is given by the
expression,
Relative error also expressed in parts per
thousand (ppt).
E
x x
x
r
i t
t
Absolute error in nitrogen determination
Gross Errors
They usually occur only occasionally, are often large, and may cause a result to be either high or low. Gross error leads to outliers. This error causes the result differs significantly from the rest of the results.
Bias measures the systematic error associated with an analysis. It has a negative sign if it causes the result to be low and a positive sign otherwise. Bias has a definite value, an assignable cause and are about the same magnitude for replicate measurements. Bias affects all the data in a set in the same way.
How do Systematic Errors Arise?
There are three types of systematic errors:-
- Instrumental errors are caused by the
imperfections in measuring devices and
instabilities in their components.
- Method errors arise from nonideal chemical
or physical behavior of analytical systems.
- Personal errors results from the carelessness,
inattention, or personal limitations of the
experimenter.
Detecting Systematic Errors
Systematic instrument errors are usually
corrected by calibration. Periodic calibration
of equipment is always desirable.
Personal errors can be minimized by care and
self-discipline. Errors that result from a known
physical disability can usually be avoided by
carefully choosing the method.
Method errors or bias of an analytical method
is estimated by analyzing standard reference
materials.
Standard reference materials are substances sold by the National Institute of Standard and Technology and Certified to contain specified concentrations of one or more analytes. The concentration of the components in these materials has been determined in one of three ways:
- By analysis with a previously validated reference method.
- By analysis by two or more independent, reliable measurement methods.
- By analysis by a network of cooperating laboratories.
