Monte Carlo research has demonstrated that there are many applications of the rank transformation that result in an invalid procedure. Examples include the two dependent samples, the factorial analysis of variance, and the factorial analysis of covariance layouts. However, the rank transformation has been shown to be a valid and powerful test in the two independent samples layout. This study demonstrates that the rank transformation is also a robust and powerful alternative to the Hotellings T2 test when the data are on a Likert scale.
Nanna, Michael J.
"Hotelling's T2 VS. The Rank Transform With Real Likert Data,"
Journal of Modern Applied Statistical Methods: Vol. 1
, Article 12.
Available at: http://digitalcommons.wayne.edu/jmasm/vol1/iss1/12