Errors in Chemical Analyses
Chapter 5
Skoog, West, Holler and Crouch
8th Edition
Slide 1
Usage of the term Error
1. Error: difference
between measured
value and true value
2. Error: uncertainty in
measurement
Slide 2
1
Mean and Median
• Results of replicate measurements are
customarily reported as a mean
• Mean: estimate of the central value
• Median = middle value
In case of an even number of measurements,
the average of the central pair in the middle value
• When is it advantageous to use median rather
than the mean?
– In case of gross error
Slide 3
Median
Mean
Qtest
Qcrit
791
850
862
865
869
847.4
0.76
0.71
39.25
39.61
39.68
39.83
39.645
Slide 4
2
Accuracy
• Acurracy refers to the
closeness of the
measurement to the
true value.
• Absolute error
E = x i − xt
• Relative error
%E =
xi − xt
× 100
xt
Slide 5
Precision
• Precision refers to the closeness between
measurements of a set obtained exactly the
same way.
• Measures of Precision
– Standard deviation
– Variance
– Coefficient of variance (CV): %RSD
• Deviations from the mean
– Absolute values
Slide 6
3
Accuracy and Precision
Slide 7
Fig 5-2, p.93
Accuracy and Precision
Standardization of HCl by TRIS
Mean
M.R.
0.09531 0.09547 0.09530
0.09514 0.09546
M.R.
0.08732 0.08740 0.09094
0.08824 0.08672
M.R.
0.08757 0.08885 0.08795
0.08697 0.08797
M.R.
0.08814 0.08899 0.08828
0.08886 0.08823
0.09536
STD
0.09534
0.00012
0.08812
0.00166
0.08786
0.08786
0.00061
0.08834
0.08847
0.00036
MR indicator range: 6.0 (yellow) - 4.8 (Red)
End point: appearance of pink
pHeq ~ 4.5 (depends on concentration of TRIS in solution)
Slide 8
4
Accuracy and Precision
Determination of nitrogen
Slide 9
Fig 5-3, p.94
Types of Errors in Experimental Data
• 2 main types
• Random or indeterminate errors
– Are inherent to all measurements
– Cause symmetrical spread of data round the
mean
– Lower precision
• Systematic errors
– Lower accuracy
• (Gross errors
– Produce outliers)
Slide 10
5
Sources of Systematic errors
•
Instrumental errors
–
Examples:
•
•
•
Method errors
–
Examples:
•
•
•
faulty calibration
temperature effect on electronic equipment
use of a “bad” indicator for an acid-base titration
presence of an interferent,
Personal errors
–
Example:
•
•
Incorrect reading of a buret
bias
Slide 11
Effects of Systematic Errors
• Systematic errors can be constant or proportional
• Constant: the absolute error is independent of the
magnitude of the measured quantity, thus of the size of the
sample.
– Thus the relative error varies
– Decreases as the
– Example: titration error
The color change of a chemical indicator requires an overtitration of 0.04 mL.
Calculate the percent relative error if the total volume of the titrant is
mL
%error
0.08
50.00
25.00
0.16
10.00
0.4
40.00
0.1
Slide 12
6
• Proportional errors increase or decrease
proportionally to the size of the quantity
measured.
– Absolute error varies with size of sample
– Relative error is constant
– Example:
• the amount of an interferent increases with the
size of the sample
Slide 13
• A proportional
systematic error can
change the slope
while preserving the
linearity of the
function
Slide 14
Fig 8-10, p.195
7
Detection of Systematic Instrument and
Personal Errors
• All instruments are subject to wear and
tear
• Periodic calibration is necessary
• Personal errors….
Slide 15
Detection of Systematic Method Errors
• Analysis of standard samples such as SRMs
from NIST. Three approachesused to determine
the concentration of analytes of interest in SRMs:
– analysis using a previously validated reference
method
– Analysis by two or more independent, reliable
methods
– Analyzed by a network of cooperating laboratories
• Independent Analysis
– Use another available reliable analytical method.
– The principle of the method must differ from the
method being questioned
Slide 16
8
Detection of Systematic Method Errors
• Blank Determination
– Blank: solvent and reagents
– Blank: solvent, reagent and sample matrix
– Matrix: everything else in the sample except
analyte. A matrix can be very difficult to
mimic.
• Variation in sample size
– Constant error will be detected as a decrease
in relative error
Slide 17
Recommended Excel exercises
• Calculate mean using the SUM and Count
functions
• Calculate mean using the AVERAGE
function
Slide 18
9