2.2.1 Errors and their causes
2.2 Measurement Error
Error
2.2.1 Errors and their causes
2.2.2 The expression of Errors
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2.2.1 Errors and their causes
①method: imperfection of methods, e.g
e.g,, incorrect
indicators
indicator in titrametry or incomplete
precipitation in gravimetry
error: measured value subtracted from true value
①systematic error
②random error
1. Classification
③gross error
2. systematic error
errorss are biases in measurement which
lead the situation where the mean of many separate
measurements differs significantly from the actual value
of the measured attribute. Sources of them may be
imperfect calibration of instruments, imperfect methods
of observation, or changes in the environment which
interfere with the measurement process.
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2.2.1 Errors and their causes
Incorrect calibration of volumetric
flask or pipette
precipitation
②instrument
instrument::
Incorrect calibration
E.g., corrosion of weight or balance
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2.2.1 Errors and their causes
Characterization of systematic errors
①exhibit same direction and magnitude
②relatively constant in repeated measurements
measurements;;
③ “measurable
measurable”” and reducible (determinate)
3.random error
random error is caused by random reasons, such as
variations in temperature, pressure or humidity of
Lab. And it is difficult to identify the specific
reason for it. Therefore random error may change
direction and magnitude randomly (indeterminate)
(indeterminate),,
but it follows the normal distribution.
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pipette
③reagent
reagent::
deionized or distilled water is contaminated
④ personal reason
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2.2.1 Errors and their causes
Statistical characteristics
① equal probability for positive and negative errors
② Probability is inversely proportional to its magnitude
4. gross error:
5. How to avoid the errors
(1)systematic error:
blank test
conduct same measurement procedure without sample
check test
conduct same measurement procedure with a standard
or a sample of “known
known”” content
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1
2.2.1 Errors and their causes
(2) random error:
increase the measurement time
(3) gross error::
carefulness and good habit (professional)
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2.2.2 Error expression
absolute error:
Ea = x − xT
relative error:
Er =
Ea
xT
note: error can be positive or negative
2.2.2 Error expression
1. Accuracy and errors:
Accuracy is a measure of how close a measure of
central tendency is to the true, or expected value, xT.
Accuracy is usually expressed as either an absolute
error E a or a percent relative error, Er .
true value
value:: theoretical value or value agreed by
authority, different labs
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E1: Two samples A and B are weighed to be 1.5268g and
0.1526g respectively by using an electronic balance. If
the true weights of A and B are 1.5267g and 0.1525g,
please work out the Ea and Er .
EaA = 1.5268 - 1.5267
= +0.0001g
EaB = 0.1526 - 0.1525
= +0.0001g
balance
ErA = +0.0001/1.5267
= +0.006%
ErB = +0.0001/0.1525
= +0.06%
What you can conclude from the calculations?
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E2: It is known that the reading error of a burette could be
±0.01mL. To keep the relative error of a burette within 0.1%,
then at least how much of titrant volume should be used?
∵Ea = 0.01
To obtain a volume, two times of reading are needed,
burette
Therefore, Ea = 0.02mL.
burette
And ∵Er ≤0.1%.
Er =
Ea
xT
∴V = 0.02/0.1%
= 20mL
Conclusion?
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E3
E3:: If titrant consumption is controlled at around 25mL, and
reading error of an electronic balance is ± 0.0001g. To
standardized 0.2mol
0.2mol·· L-1 NaOH both (A) potassium hydrogen
phthalate (MA = 204) and (B) oxalate acid (MB = 126) can be
used as the primary standard. Please compare the relative
errors caused by using different standards.
①nNaOH = nA
mA = 0.2×25×10-3×204 = 1g
∴Er A = 0.0002/1 = 0.02%
∵H 2C2O4 + 2OH- = C2O 42- + H2O
②∵
nNaOH = 2nB
mB = 0.2×25×10-3×126/2 = 0.3g
∴Er B = 0.0002/0.3 = 0.07%
Conclusion?
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2
2.2.2 Error expression
2.2.2 Error expression
2. Precision and deviation
Precision is a measure of the spread of data about a
central value and may be expressed as the range,
the deviation, the standard deviation, or the
variance.
Deviation can also be expressed in an absolute or
relative way
Precision is commonly divided into two categories: repeatability
and reproducibility. Repeatability is the precision obtained
when all measurements are made by the same analyst during a
single period of laboratory work, using the same solutions and
equipment. Reproducibility is the precision obtained under any
other set of conditions,including that between analysts, or between
laboratory sessions for a single analyst.
The relationship between accuracy and precision:
Note
Note that
that there
there are
are no
no direction
direction notations
notations for
for deviation
deviation
Systematic errors decide the error of an analysis, while random
errors decide the precision. If systematic errors are not excluded,
than the accuracy can not be assured even with a good precision
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E4. Shooting results of 4 students (A, B, C and D)
A
B
C
D
Conclusion
Conclusion:: precision is the premise of accuracy,
but good precision can not guarantee a satisfactory
accuracy
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