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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. 2 ( x x) s2 = 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