Introduction error, accuracy, precision Source of Errors Types of Errors Methods of minimizing errors Test for rejection of data Significant Level Rounding of Figures References

1. ERRORS
Prepared by
G. Nikitha, M.Pharmacy
Assistant Professor
Department of Pharmaceutical Chemistry
Sree Dattha Institute Of Pharmacy
Hyderabad
Subject: Pharmaceutical Inorganic Chemistry
Year: Pharm-D 1st Year
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2. CONTENTS
 Introduction
 error, accuracy, precision
 Source of Errors
 Types of Errors
 Methods of minimizing errors
 Test for rejection of data
 Significant Level
 Rounding of Figures
 References
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3. INTRODUCTION
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4. INTRODUCTION
 It has been said that reliability, reproducibility and accuracy are the basis of
analytical chemistry, the task of the analytical chemist will be to device methods
which give results that are reliable, reproducible and accurate.
 But every measurement made no matter how systematically and carefully is
subject to some degree of uncertainty or error.
 Unfortunately the magnitude of uncertainty or error is a difficult quantity to be
determined.
 This is not due to any handicap on the part of the analytical chemist. It is due to
the fact that magnitude of error in a measurement which is equal to the
measured value minus the true value is not really determinable, since the true
value of the measured property may not be known at all.
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5.  The true value of the property is really an elusive philosophical quantity
something that man perhaps is not destined to know. All that one can aspire is to
decrease the margin of uncertainty so that the results become sufficiently
accurate to an acceptable level. Error, accuracy, etc are relative terms and can
have different meanings when used in different contexts.
 For example an industrial analyst may tolerate a higher margin of error and
accept a particular result as accurate. But the same result may be considered as
highly inaccurate by a research worker. What is acceptable to the industrial
analyst may be totally unacceptable to the research worker because their aims of
analysis are different.
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6. ERROR, ACCURACY, PRECISION
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7. ERROR, ACCURACY, PRECISION
Error: The difference between the experimental mean and a true value is termed as
Absolute error. Absolute error may be positive or negative. Often a term
Relative error is used. The relative error refers to the value found by dividing
the absolute error by the true value.
 The relative error is generally expressed as per cent by multiplying the relative
error by 100 or by expressing it as parts per thousand by multiplying the relative
error by 1000.
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8. Example: A chemist prepared a buffer solution of pH 4.62. When an analyst made
replicable measurement of the pH of the solution by a PH meter the following
values are obtained 4.59, 4.63 and 4.60. Calculate the absolute error and relative
error for each of these values.
Solution
Here the true value X is 4.62
Absolute error
4.59-4.62 = -0.03
4.63-4.62 = 0.01
4.60-4.62 = -0.02
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Relative Error Relative Error
(per cent)
Relative Error
(ppt)
i.-0.03/4.62=
-0.0065
-0.0065x100=
-0.65
-0.0065
x1000=-6.5
ii.0.01/4.62=
0.002
0.002x100=
0.20
0.002
x1000=2.0
iii.-0.02/4,62=
-0.0043
-0.0043x100=
-0.43
-0.0043
x1000=-4.3

9. Accuracy: (near to the true value). The term accuracy refers to the agreement of
experimental result with the true value and it is usually expressed in terms of
error. In scientific experiments, it is known that true value is not known. It is
simply the value that has been accepted and is usually a mean calculated from
the results of several determinations from many laboratories employing
different techniques.
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10. Example 1:
True value is 30
A has nearest value
B has moderate accurate value
C has less accurate value
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11. Example-2:
There are two analyst X and Y who determining the % of the Paracetamol.
Standard value of paracetamol in that tablet is 100% and observation are given
below
X= 99.80, 99.90, 100.00, 99.30
Y= 98.75, 98.75, 98.80, 98.80
Who has done more accurate analysis?
Solution
X= Average value
Error
100-99.75= 0.25%
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12. Y= Average value
Error
100-98.775= 1.225%
Error of X is less than Y. X has more accurate analysis.
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13. Precision: (Repeatability of values) Precision may be defined as the degree of
agreement between various results of the same quality. That is it refers to the
reproducibility result. Good precision are not necessary. An analytical chemist
always attempts for reproducible results to assure the highest possible accuracy.
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14. Example 1:
True value = 30
A has more accurate value and repeatability
B has less accurate and no repeatability
C has less accurate and repeatability
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15. Example 2:
Two analysts’ done the analysis and estimated value is 100 and observations are
given below
A= 97,96,99,96
B= 92,91,93,92
Who has done more précised value??
Solution
Standard Deviation formula for total population
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16. Standard Deviation formula for total sample
In this problem we are selecting Standard Deviation formula for total sample
formula i.e
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17. 17
- mean value

18. A= B=
18
X ( ) 2
97 97-97=0 0
96 96-97=-1 1
99 99-97=2 4
96 96-97=-1 1
total= 6
X ( )2
92 92-92=0 0
91 91-92=-1 1
93 93-92=1 1
92 92-92=0 0
total= 2

19. 19
A= 1.414
B= 0.816
Less standard value means more Precision value
So B has less standard value and more Precision value

20. DIFFERENCE BETWEEN ACCURACY AND
PRECISION
Accuracy Precision
1. Accuracy indicates how close a
measurement is to the correct or
accepted value
1. Precision indicates the closeness of
two more Measurements to each other.
2. Your measurement will be close to
the standard measurement
2. Your measurement will be similar
every time you measurement
3. Accuracy is not dependent on
Precision
3. Precision is not dependent on
Accuracy
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21. SOURCE OF ERRORS
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22. SOURCE OF ERRORS
The errors in the result in an analysis can be resulted from various sources. Some
major sources of errors in pharmaceutical analysis are described here under:
1. Human Source: The qualification and experience of an analyst performing the
analysis has major impact in results. If an experiment is performed by in
experiment person the chances of error are mores compared to same experiment
performed by the experience analyst.
2. Instrumental, apparatus and glassware: If the instrument, glass ware as well
as apparatus used in analysis is of low quality and un calibrated the chances of
error are increased at significant extent.
3. Experimental conditions: If the analysis is carried out in the conditions which
are unfavorable for particular experiment or analysis the desirable result will not
obtained.
4. Constitutes used in analysis: If various constituents like standards, solvents,
reagents etc used in analysis are not of desired quality and purity the results will
be obtained with errors.
5. Procedure: If the analytical procedure used in analysis is not validated and if
validated but not fallowed carefully the errors on the results will be obtained.
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23. TYPES OF ERRORS
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24. TYPES OF ERRORS
Two main types of errors can affect the accuracy or Precision of a measured
quantity. These are:
a. Determinate errors b. indeterminate errors
a. Determinate errors: Determinate errors are those that as the name implies are
determinable and that presumably can be either avoided or corrected. They may
be constant as it the case of an uncalibrated weight that is used in all weighings
or may be variable but of such a nature that they can be accounted for any
correction. The determine errors can be classified as
i. Instrumental errors
ii. Operative errors
iii. Errors of methods
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25. i. Instrumental errors: These errors are common to all instruments as each one
has a limited accuracy. The manufacturer of the instrument generally provides
the tables quoting the reliability of the results in the respective ranges. It should
be kept in mind that the calibration of the instrument in one range may not be
valid for the entire range. In the case of volumetric analysis the glass apparatus
like burette, pipette and measuring flask are calibrated to provide or contain a
specific volume at certain temperature. If the working temperature is different
the volume delivered or measured may be incorrect. The chemist has to
consider all these errors which are introduced during experiments.
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26. ii. Operative errors: These include personal errors and can be reduced by
experience and in case of the analyst in the physical manipulations involved.
Operations in which these errors may occur include transfer of solutions,
effervescence, incomplete drying of samples, etc. These are difficult to correct
for personal errors which may also be introduced due to physical disability like
colour blindness which may make incorrect judgment of colour. Other personal
errors include mathematical errors in calculations.
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27. iii. Errors of methods: These are most serious errors of an analyst. Most of the
errors discussed above can be minimized or corrected for but errors that are
inherent in the method cannot be changed. Thus the kjeldahl’s method used for
the determination of nitrogen compounds the digestion with concentrated
sulfuric acid may not completely convert the nitrogen ring to ammonium
sulphate. This is particularly true in case of pyridine compounds in which the
result of nitrogen determinations are low. Some other sources of methodic
errors include precipitation of impurities, side reaction, slight solubility of
precipitation, impurities in reagents etc.
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28. b. indeterminate errors: The second type of error includes the indeterminate
errors generally called accidental or random errors. They are revealed by small
differences in successive measurements made by the same analyst under
virtually identical conditions. These errors cannot be predicted or determined.
These accidental errors will follow a random distribution thus a mathematical
law of probability can be applied to arrive at some conclusion regarding the
most probability can be applied to arrive at some conclusion regarding the most
probable series of measurements. To give a simple example an analyst reads
incorrectly the instrument panel reading in pH meter or spectrophotometer. He
notes down this reading which is used in calculations based on in pH meter or
spectrophotometer. He notes down these reading which is used in calculations
based on this reading.
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29. METHODS OF MINIMIZING ERRORS
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30. METHODS OF MINIMIZING ERRORS
The error is in differentiating part of any analytical operative analytical chemistry
his best to minimize the error as much as possible errors can be minimized by
applying following methods.
1. Calibration of instruments, apparatus and applying conditions
By calibration of instruments like UV spectrophotometer, Ph meter, potentiometer
etc and glass ware like burette, measuring cylinder etc performing analysis one
can eliminate errors to very much extension error can also minimized by
applying necessary corrections of the source of error is known.
2. By running control determination
By running a control determination parallely to the sample by taking standard
under same experimental conditions the error can reduce at very possible extent.
However a standard should contain same weight of the constituent present in
unknown sample. The weight of the constituent of unknown sample can be
calculated as fallows
Where X = weight of constituent in unknown solution.
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31. 3. By running blank determination
Blank determination is the determination under the same experiment conditions
which are used for sample analysis but in this case the sample is excluded. The
aim of blank determination is know the effect of impurities introduced by
reagents on results. From the readings obtained from the blank determination
one can eliminate the error at very much extent.
4. By using standard addition
In this method small amount of standard of constituent present in sample is
analyzed for the total amount of constituent present. The difference in the
results from samples with and without added standard is calculated.
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32. TEST FOR REJECTION OF DATA
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33. TEST FOR REJECTION OF DATA
In replicate measurement a situation encountered is that few values in a set of
values deviate significantly from the rest and therefore there is a tendency to
reject such values. This becomes a dilemma for e scientist to reject or not to
reject the doubtful value. Retaining such values will give rise to an error in the
mean while rejection may lead to discarding a rightful value. The Q test
described by Dean and Dixon is quite often used for deciding whether to retain
a particular vale or reject it. With the help of the Q test a doubtful vale can be
retained or rejected with a 90% confidence level. The only drawback of this test
is that with a small number of measurements the test indicates the rejection of
those values which are in gross error, but does not eliminate the chances of
retaining values which appear less suspicious.
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34. The Q test is applied as fallows.
1. Arrange the measured vales in a set in ascending order.
2. Calculate the spread or the range of the vales thus arranged.
3. Find the difference between the doubtful vale and its nearest neighbour.
4. Divide the difference found in step 3 by the spread or the range. This gives the
rejection quotient Q.
5. Compare the calculated value of Q with those given in table below. If calculated
Q is greater than the one in the table for the particular number of measurements
then reject the experimental value.
Value of rejection Quotient, Q (90%)
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35. Number of Observations Q crit (90% confidence
limit)
2 _
3 0.94
4 0.76
5 0.64
6 0.56
7 0.51
8 0.47
9 0.44
10 0.41

36. Example:
In the analysis of sulphur content of a sample the following values were reported
sulphur content % : 0.47, 0.48, 0.47 and 0.50
Find whether the value 0.50 can be retained or rejected on the basis of the Q test.
Solution:
1. Arrange the vales in ascending order
0.47, 0.47, 0.48, 0.50
2. Spread= 0.50-0.47= 0.03
3. The difference between 0.50 and its nearest neighbour
= 0.50-0.48 = 0.02
4. Q= 0.02/0.03 = 0.667
5. The Q value for the measurements from above table is 0.76.
Since Q calculated is less than the value of Q in the table, the value 0.50 can be
retained with 90 % confidence level.
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37. SIGNIFICANT LEVEL
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38. SIGNIFICANT LEVEL
Significant figures of a number are those digits which carries meaning contributing to
its measurements resolution.
Rules
1. It should be in decimal system.
2. All non zeros are significant.
Example: 123- significant value is 3.
3. All leading zeros are non significant.
Example: 1. 0.077- significant value is 2.
2. 0.00032- significant value is 2.
4. If any zero is coming in between the two non zero values then considered as
significant values.
Example: 1. 2008- significant value is 4.
2. 3.002- significant value is 4.
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39. 5. Trailing zero rule or Zeros coming after the non zero values present in two forms
i. In decimal values considered as significant.
Example: 1.2.70-significant value is 3
2. 2.700- significant value is 4
ii. Without decimal considered as non significant.
Example: 1. 270-significant value is 2.
2. 2700-sigsificant value is 2.
6. If any value is present as 10n or 10-n considered as non significant.
Example: 1.3x10-3- significant value is 2.
2. 2.3x103 –significant value is 2.
7. Significant figure of the measurement of any instrument should not greater than
the instrument limit.
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40. ROUNDING OF FIGURES
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41. ROUNDING OF FIGURES
The rounding of the figures is essential to curtail length and tedious calculations.
The following rules are kept in view in rounding of figures.
1. Data or results should be so reported as not to contain more than one uncertain
digit.
2. In rounding of numbers to the correct figures if the last digit which is rejected is
5, the previous digit if odd is increased by one and even left unchanged, if the
last digit is less than 5, leave the previous digit unchanged and if the last digit is
greater than 5, increase the previous digit by one. Thus
i. 3.15 is rounded off to 3.14; digit retained is odd (3) and digit rejected is 5.
ii. 3.145 is rounded off to 3.14: digit retain is even (4) and digit rejected is 5.
iii. 3.134 is rounded off to 3.13: digit rejected is < 5
iv. 3.128 is rounded off to 3.13: digit rejected is > 5.
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42. 3. In addition or subtractions retain in each term an in the result figures only to the
decimal place that is present in the term having the least number of decimal
places.
Thus,
i. 3.145+10.08+ 15.4 becomes
3.1+10.1+15.4 = 28.6
4. In multiplication and division each term and the result are reported to contain
significant figures so that the relative precision is as great as that of the least
precise term. Thus,
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43. REFERENCE
 Pharmaceutical Chemistry -Inorganic Volume-1 by G. R. Chatwal.
 Essentials of Inorganic Chemistry by Katja A. Strohfeldt.
 Indian Pharmacopoeia.
 M.L Schroff, Inorganic Pharmaceutical Chemistry.
 P. GunduRao, Inorganic Pharmaceutical Chemistry, 3rd Edition
 A.I. Vogel, Text Book of Quantitative Inorganic analysis.
 Bentley and Driver's Textbook of Pharmaceutical Chemistry.
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44. THANK YOU
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