Statistical Treatment of
Analytical Data
ANALYSIS OF ERRORS
 Analytical chemistry is based on reliability,
reproducibility & accuracy of results.
 However, every measurement has some degree of
uncertainty which is called as error in analytical
chemistry.
 The error is nothing but the difference between the
experimental mean value & a ‘true value’.
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ANALYSIS OF ERRORS
 It is impossible to perform a chemical analysis
that is error free or without uncertainty.
 no analysis is free of error or “uncertainty”!!
 Our goals are to minimize errors &..
•
…….. to calculate the size of the errors.
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ANALYSIS OF ERRORS
 ‘We can only hope to minimize errors &
estimate their size with acceptable
accuracy’ !!!
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ANALYSIS OF ERRORS
 Precision & Accuracy
 are commonly associated with any discussion of error.


Precision = reproducibility of a measurement
Accuracy = measure of the closeness to true
value.
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Accuracy and Precision
Illustration of accuracy and precision using the pattern of darts on a dartboard
ANALYSIS OF ERRORS
 Three general types of errors occur in lab
measurements:

random error,

systematic error, &

gross errors.
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ANALYSIS OF ERRORS
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The Nature of Random Errors
• All measurements contain random errors.!
– Random, or indeterminate, errors occur
whenever a measurement is made.
– Caused by many small but uncontrollable
variables.
– The errors are accumulative.
Random errors
• are produced by any one of a # of unpredictable &
unknown variations in the experiment.
• These changes may occur in the measuring
instruments or in the environmental conditions.
– eg fluctuations in room temperature, fluctuations in line
voltage, mechanical vibrations, etc
Systematic Errors
• Systematic errors or determinant error have a
definite value, an assignable
cause,..
– & are of about the same magnitude for replicate
measurements made in the same way.
Systematic Errors
• are instrumental, methodological, or personal
mistakes.
• These cause"lopsided" data….
– which is consistently deviated in one direction from
the true value.
Examples of systematic errors:
– an instrumental error results when a
spectrometer drifts away from calibrated
settings;
– a methodological error is created by using the
wrong indicator for an acid-base titration;
– a personal error occurs when an experimenter
records only even numbers for the last digit of
burette volumes.
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Instrumental Errors
• are caused by non ideal instrument behavior, by
faulty calibrations, or by use under inappropriate
conditions
• Pipets, burets, and volumetric flasks may hold or
deliver volumes slightly different from those
indicated by their graduations.
• Calibration eliminates most systematic errors of this
type.
Instrumental Errors
• Electronic instruments can be influenced by
– noise,
– temperature,
– pH and are also subject to systematic errors.
• Errors of these types usually are detectable
and correctable.
Method Errors
• The nonideal chemical or physical behavior of the
reagents and reactions on which an analysis is based
often introduce systematic method errors.
• Such sources of nonideality include
–
–
–
–
–
the slowness of some reactions,
the incompleteness of others,
the instability of some species,
the lack of specificity of most reagents,
and the possible occurrence of side reactions that
interfere with the measurement process.
Personal Errors
• Result from the carelessness, inattention, or
personal limitations of the experimenter.
• Many measurements require personal
judgments.
• eg
– estimating the position of a pointer between two
scale divisions,
– The color of a solution at the end point in a titration,
– the level of a liquid with respect to a graduation in a
pipet or buret.
Personal Errors
• Judgments of this type are often subject to
systematic, unidirectional errors.
A universal source of personal error is prejudice,
or bias.
Number bias is another source of personal error
that varies considerably from person to person.
Personal Errors
• The most frequent number bias encountered
in estimating the position of a needle on a
scale involves a preference for the digits 0 and
5.
• Also common is a prejudice favoring small
digits over large and even numbers over
odd.
Systematic errors
• Systematic errors can be identified &
eliminated by
– careful inspection of the experimental methods,
– cross-calibration of instruments,
– & examination of techniques.
Gross errors
 are caused by experimenter carelessness or equipment failure.
 These "outliers" are so far above or below the true value that they
are usually discarded when assessing data.

 The "Q-Test" (discussed later) is a systematic way to determine if a
data point should be discarded.
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Gross errors
 These differ from indeterminate & determinate errors.

They usually occur only occasionally, are often
large, and may cause a result to be either high or
low.

They are often the product of human errors.

Can lead to outliers, results that appear to differ
markedly from all other data in a set of replicate
measurements.
summary
 Errors are caused by



faulty calibrations or
standardizations or
by random variations and uncertainties in results.
 Frequent calibrations, standardizations, and analyses
of known samples can sometimes be used to lessen
all but the random errors
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