An example of functional relationship fitting in analytical science. Comment on ‘Modification of Winkler's method for determination of dissolved oxygen concentration in small sample volumes’ by A. Shriwastav, G. Sudarsan, P. Bose and V. Tare

Abstract

In a recent issue of Analytical Methods, Shriwastav et al. (Anal. Methods, 2010, 2, 1618) compared the performance of a modified method for determining dissolved oxygen in water with the standard Winkler's method. They wisely avoided using simple regression for comparing the results as a whole, but some may believe they missed an opportunity for using functional relationship fitting, a method that addresses bivariate data with error on both variables.

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In a paper published in this journal, Shriwastav et al.,¹ compared the performance of a modified method for determining dissolved oxygen in water with the standard Winkler's method. They analysed 33 samples of water, in replicate, by both methods. They conducted separate two-sample t-tests on the results for each sample and concluded overall that the modified method was an acceptable substitute for the standard method under all circumstances. They wisely avoided using simple regression for comparing the results as a whole, but missed an opportunity for using functional relationship fitting, a method that addresses bivariate data with error on both variables.² Software for this method in the form of an Excel add-in can be downloaded gratis from the AMC Website.³ The dataset also can be downloaded via the AMC Website.⁴ (Ref. 2–4 can be accessed viawww.rsc.org/amc.)

When used to summarise the substantial dataset provided in the paper, functional relationship fitting confirmed a tendency suggested by Fig. 2 of the paper,¹ namely that the new proposed method showed a small positive bias, giving results that were on average about 4% higher than the reference method. The relevant statistics and their standard errors [se(.)] were: intercept a = 0.089, se(a) = 0.061; slope b = 1.043, se(b) = 0.017, with no significant lack of fit. The slope was significantly greater than unity with a p-value of 0.008. (The above statistics were obtained after deleting the summary statistics for one sample that, because of its high concentration, exerted undue leverage on the calculation.)

This example serves to remind experimenters that functional relationship fitting is both a valuable tool and readily-available.

References

1. A. Shriwastav, G. Sudarsan, P. Bose and V. Tare, Anal. Methods, 2010, 2, 1618–1622.
2. AMC Technical Briefs, 2002, No 10, download from http://www.rsc.org/images/brief10_tcm18-25920.pdf.
3. AMC Software, http://www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/Software/FREML.asp.
4. AMC Datasets, http://www.rsc.org/images/Dissolvedoxygen_tcm18-194855.txt.

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