Use of regression lines for comparing analytical methods

The level of phytic acid in 20 urine samples was determined by a new catal)d ic fluorimetric (CF) method, and the results were compared with those obtained using an established extraction photometric (EP) technique. The following data were obtained (all the results, in mg 1 are means of triplicate measurements). 

This set of data shows why it is inappropriate to use the paired t-test, which evaluates the differences between the pairs of results, in such cases (Section 3.4). The range of phytic acid concentrations (ca. 0.14-3.50 mg 1 ) in the urine samples is so large that a fixed discrepancy between the two methods will be of var5dng significance at different concentrations. Thus a difference between the two techniques of 0.05 mg 1 would not be of great concern at a level of ca. 3.50 mg 1 , but would be more disturbing at the lower end of the concentration range. 

Two further points maybe mentioned in connection with this example. Firstly, the literature of analytical chemistry shows that authors frequently place great stress on the value of the correlation coefficient in such comparative studies. In the above example, however, it played no direct role in establishing whether or not systematic errors had 

Multiple R 0.9966 R square 0.9933 Adjusted R square 0.9929 Standard error 0.0829 Observations 20  

When the assumption of error-free x-values is not valid, either in method comparisons or, in a conventional calibration analysis, because the standards are unreliable (this problem sometimes arises with solid reference materials), an alternative comparison method is available. This technique is known as the functional relationship by maximum likelihood (FREML) method, and seeks to minimize and estimate both x- and y-dlrection errors. (The conventional least squares approach can be regarded as a special and simple case of FREML.) FREML involves an iterative numerical calculation, but a macro for Minitab now offers this facility (see Bibliography), and provides standard errors for the slope and intercept of the calculated line. The method is reversible (i.e. in a method comparison it does not matter which method is plotted on the x-axis and which on the y-axis), and can also be used in weighted regression calculations (see Section 5.10). 

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Use of regression lines for comparing analytical methods 129 Table 5.1 Excel output for Example 5.9.1... 

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