Descriptive Statistics
th
,Thomson
Brooks/Cole, Canada, 2007, 967  988, unless otherwise attributed.
Precision and Accuracy
Two terms are widely used in discussions of the reliability of data: precision and accuracy.
Precision
Precision
describes the reproducibility of results, that is, the agreement between numerical values for two
or more replicate measurements, or measurements that have been made in
exactly the same way.
Generally,
the precision of an analytical method is readily obtained by simply repeating the measurement.
Three terms are widely used to describe the precision of a set of replicate data: standard deviation, variance,
and coefficient of variation. These terms have statistical significance.
Accuracy
Accuracy
describes the correctness of an experimental result expressed as the closeness of the measurement
to the true or accepted value. Accuracy is expressed in terms of either absolute error or relative error. The
absolute error E
of the mean (or average)
of a small set of replicate analyses is given by the relationship
Equation 1
E
=

x
i
where
x
i
is the true or accepted value of the quantity being measured. Often, it is useful to express the
accuracy in terms of the
relative error
E
r
, where
Equation 2
We will be concerned with two types of errors,
random errors,
often called
indeterminate errors,
and
systematic errors,
often called
determinant errors.
We will give random error the symbol
E
d
and systematic
error the symbol
E
s
.
The error in the mean of a set of replicate measurements is then the sum of these two
types of errors:
Equation 3
E
=
E
d
+
E
s
Systematic or Determinant Errors
Systematic errors
have a definite value and an assignable cause and are of the same magnitude for replicate
measurements made in the same way. Systematic errors lead to
bias
in measurement results. Bias is
illustrated by the two curves in Figure 2, which show the frequency distribution of replicate results in the
analysis of identical samples by two methods that have random errors of identical size. Method
A
has no
bias so that the mean
µ
A
is the true value. Method
B
has a bias that is given by
Equation 5
Bias =
µ
B
–
µ
A
Note that bias affects all of the data in a set and that it bears a sign. Systematic errors are of three types:
instrumental, personal, and method.
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View Full DocumentInstrumental Errors
Instrumental errors
are caused by non ideal instrument behavior, by faulty
calibrations, or by use under inappropriate conditions. Typical sources of instrumental errors include drift
in electronic circuits; leakage in vacuum systems; temperature effects on detectors; currents induced in
circuits from 110V power lines; decreases in voltages of batteries with use; and calibration errors in
meters, weights, and volumetric equipment.
Systematic instrument errors are commonly detected and corrected by calibration with suitable standards.
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 Summer '11
 Bonk
 Normal Distribution, Standard Deviation, Th, Rayleigh, th e samp, th e mean

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