Limitations of Analytical Methods l 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 l 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 l Accuracy and Precision l Statistics l Errors l Calibration Curves

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

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

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

Data Handling l Precision v This definition can be further refined to take account the timing of the experiment. v 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 l Precision v Precision always accompanies accuracy, but a high degree of precision does not imply accuracy.

Data Handling l Inaccurate and Imprecise

Data Handling l Accurate but Imprecise

Data Handling l Accurate and Precise

Data Handling l Inaccurate but Precise

Data Handling l Statistics v 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. v Statistics provide a means of quantifying the precision of a set of measurements.

Data Handling l Mean v 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 l Estimates of Precision v Standard Deviation v Variance v Relative Standard Deviation v Coefficient of Variation

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

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

Data Handling l Standard Deviation  ( x - x) 2 n  =

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

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

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