Many testing methods require the selection of a set of paths on which tests are to be conducted. Errors in arithmetic expressions within program statements can be represented as perturbing functions added to the correct expression. It is then possible to derive the set of errors in a chosen functional class which cannot possibly be detected using a given test path. For example, test paths which pass through an assignment statement "X := f(Y)" are incapable of revealing if the expression "X -f( Y)" has been added to later statements. In general, there are an infinite number of such undetectable error perturbations for any test path. However, when the chosen functional class of error expressions is a vector space, a finite characterization of all undetectable expressions can be found for one test path, or for combined testing along several paths. An analysis of the undetected perturbations for sequential programs operating on integers and real numbers is presented which permits the detection of multinomial error terms. The reduction of the space of (potential undetected errors is proposed as a criterion for test path selection.