Combining nonoverlap and trend for single-case research: Tau-U

Behav Ther. 2011 Jun;42(2):284-99. doi: 10.1016/j.beth.2010.08.006. Epub 2011 Feb 3.


A new index for analysis of single-case research data was proposed, Tau-U, which combines nonoverlap between phases with trend from within the intervention phase. In addition, it provides the option of controlling undesirable Phase A trend. The derivation of Tau-U from Kendall's Rank Correlation and the Mann-Whitney U test between groups is demonstrated. The equivalence of trend and nonoverlap is also shown, with supportive citations from field leaders. Tau-U calculations are demonstrated for simple AB and ABA designs. Tau-U is then field tested on a sample of 382 published data series. Controlling undesirable Phase A trend caused only a modest change from nonoverlap. The inclusion of Phase B trend yielded more modest results than simple nonoverlap. The Tau-U score distribution did not show the artificial ceiling shown by all other nonoverlap techniques. It performed reasonably well with autocorrelated data. Tau-U shows promise for single-case applications, but further study is desirable.

MeSH terms

  • Humans
  • Models, Theoretical
  • Research Design*
  • Statistics, Nonparametric