Limitations of Analytical
Methods
 The function of the analyst is to obtain a result as near to the true value as possible by the correct application of the analytical procedure employed.

Limitations of Analytical
Methods
 The level of confidence in the results will be very small unless there is a knowledge of the accuracy and precision of the method used as well as being aware of the sources of error in the measurement.

Data Handling
 Accuracy and Precision
 Statistics
 Errors
 Calibration Curves

Data Handling
 Accuracy
 The accuracy of a determination may be defined as the concordance between it and the true or most probable value.

Data Handling
 Accuracy: Two possible ways of determining the accuracy.
 Absolute Method: Using a synthetic sample containing known amounts of the constituents to be determined.
 Comparative Method: Using a standard sample of the material in question.

Data Handling
 Precision
 Precision may be defined as the concordance or reproducibility of a series of measurements of the same quantity.

Data Handling
 Precision
 This definition can be further refined to take account the timing of the experiment.
 Thus there is a distinction between a series of measurements made by one analyst on one day;
REPEATABILTY , and measurements made by a number of analysts over several days;
REPRODUCIBILTY .

Data Handling
 Precision
 Precision always accompanies accuracy, but a high degree of precision does not imply accuracy.

Data Handling
 Inaccurate and Imprecise

Data Handling
 Accurate but Imprecise

Data Handling
 Accurate and Precise

Data Handling
 Inaccurate but Precise

Data Handling
 Statistics
 The true or absolute value of a quantity cannot be established experimentally, so that the observed value must be compared with the most probable value.
 Statistics provide a means of quantifying the precision of a set of measurements.

Data Handling
 Mean
 It is found that the results of a series of determinations will vary slightly.
 The average value is accepted as the most probable.
x =
 x n

Data Handling
 Estimates of Precision
 Standard Deviation
 Variance
 Relative Standard Deviation
 Coefficient of Variation

Data Handling
 Standard Deviation
 Defined as the square root of the sum of the squares of the deviation from the mean.

Data Handling
 Standard Deviation s =

( x - x) 2 n - 1

Data Handling
 Standard Deviation s
=

( x - x) 2 n

Data Handling
 Variance
 Is the square of the standard deviation.
s 2 =

( x - x) 2 n - 1

Data Handling
 Relative Standard Deviation
 A further measure of precision is known as the Relative Standard
Deviation (R.S.D.).
R.S.D. = s / x

Data Handling
 Coefficient of Variation
 This measure is often expressed as a percentage as the coefficient of variation (C.V.)
R.S.D. = 100s / x