SIGNIFICANCE TESTING OF LANTHANIDE SHIFT-REAGENT DATA

The mathematical model which underlies Hamilton's R-factor ratio test is shown to be inappropriate for determining molecular structure by lanthanide shift reagents for the following reasons. There is uncertainty in the degrees of freedom associated with the hypothesis to be tested because the observational equations are not linear, and, for certain problems, the dimension of the hypothesis to be tested is ill-defined. Two simple alternative tests are proposed. One is based on a jackknife test, the other on the Kendall τ statistic. Re-analysis of Sullivan's data (J. Am. Chem. Soc. 98, 7162 (1976)) shows that both of these tests give similar results and both are able to distinguish between closely related structures. © 1979.