Errors in Analysis
Content
• Error
• Types of error
• Minimizing the errors
• Accuracy, precision and significant figures
Learning
Objectives
At the end of this lecture, the student will be able to
• Define error
• Classify error
• Discuss about determinate and indeterminate error
• Explain how to minimize the error at each step
• Discuss about the different types of methods for minimizing
the errors
• Define Accuracy, precision, Significant figures
Errors
Definition: Error
is the difference between the true result (and accepted true result) and the
measured result
Expression of Errors
Errors are expressed either in absolute terms or in relative
terms
Absolute Errors: E abs = Calculated value
–True Value
Relative Error: Used
in the determination of accuracy of a measurement and is expressed in terms of
percentage
Relative Error E rel: Absolute
error/True value X100
It is also expressed in parts per thousand (ppt)
Types of
Errors:
Determinate or systematic error
Indeterminate or random error
Determinate
errors
• Determinate errors are caused by faults in the analytical
procedure or the instruments used in the analysis
• The name determinate error implies that the cause of this
type of error may be found out and then either avoided or corrected
• Determinate errors are systematic errors; that is, they are
not random
• Sometimes the determinate error is proportional to the
true result, giving rise to proportional errors
• Other determinate errors may be variable in both sign and
magnitude, such as the change in the volume of a solution as the temperature
changes
• Although this variation can be positive or negative, it can
be identified and accounted for
• Determinate errors can be additive or they can be
multiplicative
• It depends on the error and how it enters into the calculation
of the final result
• This determinate error could be the result of an
incorrectly calibrated balance
For example:
• If the balance is set so that the zero point is actually
0.5 mg too high, all masses determined with this balance will be 0.5 mg too
high
• If this balance was used to weigh any standard solution
used in the laboratory, the standard concentration will be erroneously high,
and all of the results obtained using this standard will be erroneously low
• The error is reported as the absolute error, the absolute
value of the difference between the true and measured values
How are determinate errors
identified and corrected?
• Two methods are commonly used to identify the existence of
systematic errors
Standard methods and
To run several analyses
• Standard method:
is to analyze the sample by a completely different analytical procedure that is
known to involve no systematic errors
• They have been evaluated extensively by many laboratories
and shown to be accurate and precise
• If the results from the two analytical methods agree, it
is reasonable to assume that both analytical procedures are free of determinate
errors
• The second method is to run several analyses of a reference
material of known, accepted concentration of analyte
• The difference between the known (true) concentration and
that measured by analysis should reveal the error
• If the results of analysis of a known reference standard
are consistently high (or consistently low), then a determinate error is
involved in the method
How to correct the
determinate error?
• The cause of the error must be identified and either
eliminated or controlled if the analytical procedure is to give accurate
results
• Many clinical and analytical laboratories participate in
proficiency testing programs, where “unknown” standard samples are sent to the
laboratory on a regular basis
• The results of these samples are sent to the government or
professional agency running the program
• The unknowns are of course known to the agency that sent
the test samples; the laboratory receives a report on the accuracy and
precision of its performance
Reasons for
determinate errors in analytical procedures:
• uncalibrated balances
• Improperly calibrated volumetric flasks
• Pipettes, malfunctioning instrumentation,
• Impure chemicals
• Incorrect analytical procedures or techniques
• Analyst error
The following are the
types of determinate errors may be noted:
a) Operational and personal errors
b) Instrumental and reagent errors
c) Errors of method
d) Additive and proportional errors
Determinate
Errors: a) Operational and Personal Errors
• Analyst error: The person performing the analysis causes
these errors
• They may be the result of inexperience, insufficient
training, or being “in a hurry”
• An analyst may use the instrument incorrectly, perhaps by placing
the sample in the instrument incorrectly each time
• Setting the instrument to the wrong conditions for
analysis
• Consistently
misreading a meniscus in a volumetric flask as
high (or low)
Improper use of
pipettes, such as
These are due to factors for which the individual analyst
is responsible and are not connected with the method or procedure
They form part of the ‘personal equation’ of an observer
The errors are mostly physical in nature and occur when sound
analytical technique is not followed
Examples:
• Mechanical loss of materials in various steps of analysis
• Under washing or over washing of precipitates
• Ignition of precipitates at incorrect temperatures
• Insufficient cooling of crucibles before weighing
• Allowing hygroscopic materials to absorb moisture before
and after weighing
• Allowing the volatile materials to volatile after weighing
• Maintaining incorrect temperature and time for reaction before
completion
•Burette reading properly not done
