Application of rank correlation to lanthanide induced shift data

Abstract

Spearman's rank correlation method is suggested as an alternative procedure for the treatment of lanthanide induced shift data. When this method is applied to Sullivan's data [J. Am. Chem. Soc. 98,7162 (1976)], the results are similar to those obtained by the jack-knife and Kendall techniques, which were introduced in a previous article. All three methods are able to distinguish between closely related structures. Among these three non-parametric methods, the Spearman procedure is probably the simplest.In a previous paper,' Hamilton's R-factor ratio test was shown to be inapplicable for determination of molecular structures by lanthanide shift reagents. Instead, two alternative tests were proposed; one was based on a jack-knife test,* the other on the Kendall 7 stati~tic.~ When both tests were applied to Sullivan's lathanide induced shift (LIS) data,4 they yielded similar results and both were able to distinguish between closely related structures.In this note another relatively simple statistical procedure, Spearman's rank correlation m e t h~d ,~ is proposed for the treatment of LIS data. A brief description of the procedure is given in the next section. In the final section the test is again applied to Sullivan's data4 and the results are compared with those obtained by Hamilton's test, the jack-knife test and Kendall's procedure. A summary of the results of treating Sullivan's data with Hamilton's R-factor ratio test is, however, first given.After obtaining the LIS for 4-amino-1,7,7-tri- (1) w k ( 6 k " ) 2 where 6," and 6,' are the observed and calculated LIS for the k-th nucleus, respectively, and wk is the weighting factor. It is obvious that the lower the R-factor the better the agreement between observed and calculated LIS. For the LIS observed for 1, Sullivan found three distinct conformations, called models A, B and C in this note, having minimum R values of 3.47, 3.71 and 4.50%, respectively. Use of Hamilton's test6 of significance indicated that the three R values, and hence the three models, were not statistically different, i.e. none of the three conformations could be rejected.In another calculation, using the observed LIS val-* Author to whom correspondence should be addressed. showed that the five models generated so far were not statistically different. Thus, Sullivan concluded that the use of LIS data failed to distinguish between diastereomers 1 and 2. Since structural differences in 1 and 2 might be somewhat subtle, Sullivan tested whether LIS data could be used to detect more drastic structural changes. To do this, the calculated conformation was 0 Heyden

Exceptionally Monotone Models -- The Rank Correlation Model Class for Exceptional Model Mining

“…Rank correlation has been employed on an eclectic variety of domains, including bioinformatics (Balasubramaniyan et al, 2005), information retrieval (Yilmaz et al, 2008), recommender systems (Breese et al, 1998), and determining molecular structure by lanthanide shift reagents (Li and Lee, 1980). Finding coherent subgroups of the dataset at hand displaying exceptional interaction between two targets, as measured through rank correlation, should be interesting to practitioners in these fields.…”