# 5: Standardizing Analytical Methods

The American Chemical Society’s Committee on Environmental Improvement defines standardization as the process of determining the relationship between the signal and the amount of analyte in a sample.^{1} In Chapter 3 we defined this relationship as

\[S_{\large{\textrm{total}}}=k_{\large{\textrm A}}n_{\large{\textrm A}}+S_{\large{\textrm{reag}}}\hspace{5mm}\textrm{or}\hspace{5mm}S_{\large{\textrm{total}}}=k_{\large{\textrm A}}C_{\large{\textrm A}}+S_{\large{\textrm{reag}}}\]

where \(S_{total}\) is the signal, \(n_A\) is the moles of analyte, \(C_A\) is the analyte’s concentration, \(k_A\) is the method’s sensitivity for the analyte, and \(S_{reag}\) is the contribution to \(S_{total}\) from sources other than the sample. To standardize a method we must determine values for \(k_A\) and \(S_{reag}\). Strategies for accomplishing this are the subject of this chapter.

*Thumbnail: Illustration showing the evaluation of a linear regression in which we assume that all uncertainty is the result of indeterminate errors affecting y. The points in blue, y _{i}, are the original data and the points in red, ŷ_{i}, are the predicted values from the regression equation, ŷ = b_{0} + b_{1}x. The smaller the total residual error (equation 5.16), the better the fit of the straight-line to the data*