14.7: Chapter Summary and Key Terms

Chapter Summary

One of the goals of analytical chemistry is to develop new analytical methods that are accepted as standard methods. In this chapter we have considered how a standard method is developed, including finding the optimum experimental conditions, verifying that the method produces acceptable precision and accuracy, and validating the method for general use.

To optimize a method we try to find the combination of experimental parameters that produces the best result or response. We can visualize this process as being similar to finding the highest point on a mountain. In this analogy, the mountain’s topography corresponds to a response surface, which is a plot of the system’s response as a function of the factors under our control.

One method for finding the optimum response is to use a searching algorithm. In a one-factor-at-a-time optimization, we change one factor while holding constant all other factors until there is no further improvement in the response. The process continues with the next factor, cycling through the factors until there is no further improvement in the response.

This approach to finding the optimum response often is effective, but usually is not efficient. A searching algorithm that is both effective and efficient is a simplex optimization, the rules of which allow us to change the levels of all factors simultaneously.

Another approach to optimizing a method is to develop a mathematical model of the response surface. Such models can be theoretical, in that they are derived from a known chemical and physical relationship between the response and its factors. Alternatively, we can develop an empirical model, which does not have a firm theoretical basis, by fitting an empirical equation to our experimental data. One approach is to use a 2^k factorial design in which each factor is tested at both a high level and a low level, and paired with the high level and the low level for all other factors.

After optimizing a method it is necessary to demonstrate that it can produce acceptable results. Verifying a method usually includes establishing single-operator characteristics, the blind analysis of standard samples, and determining the method’s ruggedness. Single-operator characteristics include the method’s precision, accuracy, and detection limit when used by a single analyst. To test against possible bias on the part of the analyst, he or she analyzes a set of blind samples in which the analyst does not know the concentration of analyte. Finally, we use ruggedness testing to determine which experimental factors must be carefully controlled to avoid unexpectedly large determinate or indeterminate sources of error.

The last step in establishing a standard method is to validate its transferability to other laboratories. An important step in the process of validating a method is collaborative testing, in which a common set of samples is analyzed by different laboratories. In a well-designed collaborative test it is possible to establish limits for the method’s precision and accuracy.

Key Terms

2^k factorial design blind analysis dependent empirical model Fisher’s least significant difference independent response searching algorithm theoretical model within-sample variance

analysis of variance central composite design effective factor fixed-size simplex optimization local optimum response surface simplex validation

between-sample variance collaborative testing efficiency factor level global optimum one-factor-at-a-time optimization ruggedness testing standard method variable-sized simplex optimization