2. DEFINITION
The accuracy of a determination may be defined as the concordance
between the data and the true or most probable value
• It is the agreement between the data and true value .
• it refers to the closeness of a single measurement to its true value.
• it is usually expressed in terms of error.
Although the true value is usually not known, the mean calculated from
results obtained from several different analytical methods which are
very precise and in close agreement with one another may be
considered the true value in a practical sense.
3. ABSOLUTE ERROR
The difference between the mean and the true value is known as
the Absolute error.
RELATIVE ERROR
The relative error is found by dividing the absolute error by the
true value.Relative error is usually reported on a percentage basis
by multiplying the relative error by 100 or on a parts per 1000
basis by multiplying the relative error by 1000.
For Analytical methods these are two possible ways of
determining the accuracy. They are
1.Absolute method
2.Comparative method
4. 1.Absolute method
A synthetic sample containing known amounts of the
constituents in question is used.
These substances, primary standards, may be available
commercially or they may be prepared by the analyst and
subjected to rigorous purification by recrystallization, etc. The
substances must be of known purity.
5. • The test of the accuracy of the method under consideration is
carried out by taking varying amounts of the constituent and
proceeding according to specified instructions.
• The amount of the constituent must be varied, because the
determinate errors in the procedure may be a function of the
amount used.
• The difference between the mean of an adequate number of
results and the amount of the constituent actually present,
usually expressed as parts per thousand, is a measure of
accuracy of the method in the absence of foreign substance.
6. 2.Comparative Method:
Sometimes, as in the analysis of a mineral it may be impossible
to prepare solid synthetic samples of the desired composition.
It is then necessary to resort to standard samples of the material in
question (mineral, ore, alloy, etc) in which the content of the
constituent sought has been determined by one or more supposedly
"accurate" methods of a analysis.
This comparative method, involving secondary standards, is
obviously not altogether satisfactory from the theoretical
standpoint, but is nevertheless very useful in applied analysis.
Standard samples are issued by CDL.
8. DEFINITION
• Precision may be defined as the concordance of a series of
measurements of the same quantity.
• The mean deviation or the relative mean deviation is a measure
of precision.
• Precision is a measure of reproducibility of data within a series
of results. Results within a series which agree closely with one
another are said to be precise.
• Precise results are not necessarily accurate, for a determinated
error may be responsible for the inaccuracy of each result in a
series of measurements. Precision is usually reported as the
average deviation, standard deviation, or range.
9. Precision is independent of accuracy. Precision is sometimes separated into:
1) Repeatability
The variation arising when the conditions are kept identical and repeated
measurements are taken during a short time period.
2)Reproducibility
The variation arising using the same measurement process among different
instruments and operators, and over longer time periods.
• Precision is a measure of the agreement among the values in a group of data,
while accuracy is the agreement between the data and true value.
• In quantitative analysis the precision of measurements rarely exceeds 1 to 2
parts per thousand. Accuracy expresses the correctness of a measurement and
precision the reproducibility of a measurement. Precision always accompanies
accuracy, but a high degree of precision does not imply accuracy.
10. PRECISION MEASURES
a) Ruggedness Tests
Ruggedness tests describes the influence of small but
reasonable alterations in the procedures of the quality of
analysis.
Examples of these minor variations are source and age of
reagents, concentration and stability of solution and reagents,
heating rate, thermometer errors, column temperature,
humidity, voltage, fluctuation, variations of column to column,
plate to plate, analyst to analyst and instrument to instrument
and many others.
11. Arithmetic Mean
• The arithmetic mean is obtained by adding together the results of the
various measurements and dividing the total by the number N of the
measurements.
• In mathematical notation, the arithmetic mean for a small group of
value is expressed as
in which ∑ standing for the sum of X1. X1 is the individual
measurement of the group, and N is the number of values.
Median
• It is the central value of all the observations arranged from the lowest
to highest.
The Median is a value about which all the other are equally distributed.
Half of the values are smaller and other half are larger than median value.
The mean and median may or may not be the same.
12. Accuracy Precision
Accuracy refers to the level of agreement
Precision implies the level of
variation that lies in the values of
between the actual measurement and the
several measurements of the same
absolute measurement.
factor.
Represents how closely the results agree with Represents how closely results agree
the standard value with one another
Single-factor or measurement multiple measurements or factors are
needed
Results can be precise without being
it is possible for a measurement to be accurate
on occasion as a fluke. For a measurement to
accurate. Alternatively, the results
be consistently accurate, it should also be
can be precise and accurate.
precise.
DIFFERENCE BETWEEN ACCURACY AND PRECISION
13.
14. DEFINITION
The number of significant figures is the minimum number
of digits needed to write a given value in scientific notation
without loss of accuracy.
16. Addition and Subtraction
• For addition and subtraction, the number of significant figures is
determined by the piece of data with the fewest number of decimal
places.
• For example, 100 (assume 3 significant figures) + 23.643 (5
significant figures) = 123.643, which should be rounded to 124 (3
significant figures).
17. Multiplication and Division
For multiplication and division, the number of significant
figures used in the answer is the number in the value with the
fewest significant figures.
For example, 3.0 (2 significant figures ) 12.60 (4 significant
figures) = 37.8000 which should be rounded off to 38 (2
significant figures).
18.
19.
20. Logarithms and Antilogarithms
It is made of two parts:
1) whole numbers ( charecteristics) not considered as significant
figures
2) fractions ( mantissa) considered as significant figures
