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58 Modern Analytical Chemistry

Although the mean is used as the measure of central tendency in equations 4.2 and
4.3, the median could also be used.
Errors affecting the accuracy of an analysis are called determinate and are char-
acterized by a systematic deviation from the true value; that is, all the individual
determinate error measurements are either too large or too small. A positive determinate error results
Any systematic error that causes a in a central value that is larger than the true value, and a negative determinate error
measurement or result to always be too
leads to a central value that is smaller than the true value. Both positive and nega-
high or too small; can be traced to an
tive determinate errors may affect the result of an analysis, with their cumulative ef-
identifiable source.
fect leading to a net positive or negative determinate error. It is possible, although
not likely, that positive and negative determinate errors may be equal, resulting in a
central value with no net determinate error.
Determinate errors may be divided into four categories: sampling errors,
method errors, measurement errors, and personal errors.

sampling error Sampling Errors We introduce determinate sampling errors when our sampling
An error introduced during the process strategy fails to provide a representative sample. This is especially important when
of collecting a sample for analysis.
sampling heterogeneous materials. For example, determining the environmental
quality of a lake by sampling a single location near a point source of pollution, such
heterogeneous as an outlet for industrial effluent, gives misleading results. In determining the mass
Not uniform in composition.
of a U.S. penny, the strategy for selecting pennies must ensure that pennies from
other countries are not inadvertently included in the sample. Determinate errors as-
sociated with selecting a sample can be minimized with a proper sampling strategy,
a topic that is considered in more detail in Chapter 7.

method error Method Errors Determinate method errors are introduced when assumptions
An error due to limitations in the about the relationship between the signal and the analyte are invalid. In terms of the
analytical method used to analyze a
general relationships between the measured signal and the amount of analyte
sample.
S meas = kn A+ S reag (total analysis method) 4.4

S meas = kC A+ S reag (concentration method) 4.5
method errors exist when the sensitivity, k, and the signal due to the reagent blank,
S reag , are incorrectly determined. For example, methods in which S meas is the mass of
a precipitate containing the analyte (gravimetric method) assume that the sensitiv-
ity is defined by a pure precipitate of known stoichiometry. When this assumption
fails, a determinate error will exist. Method errors involving sensitivity are mini-
mized by standardizing the method, whereas method errors due to interferents
present in reagents are minimized by using a proper reagent blank. Both are dis-
cussed in more detail in Chapter 5. Method errors due to interferents in the sample
cannot be minimized by a reagent blank. Instead, such interferents must be sepa-
rated from the analyte or their concentrations determined independently.
measurement error
An error due to limitations in the Measurement Errors Analytical instruments and equipment, such as glassware and
equipment and instruments used to balances, are usually supplied by the manufacturer with a statement of the item’s
make measurements.
maximum measurement error, or tolerance. For example, a 25-mL volumetric
flask might have a maximum error of ±0.03 mL, meaning that the actual volume
tolerance contained by the flask lies within the range of 24.97–25.03 mL. Although expressed
The maximum determinate
measurement error for equipment or as a range, the error is determinate; thus, the flask’s true volume is a fixed value
instrument as reported by the within the stated range. A summary of typical measurement errors for a variety of
manufacturer. analytical equipment is given in Tables 4.2–4.4.