A Geometric Interpretation of Inferences Based on Ranks in the Linear Model

12 On the use of rank tests and estimates in the linear model

“…In 1983 the Minitab statistical computing system will contain a command that will produce in its output the rank estimate B and the test statistic W. There is further discussion of computation in Section 3. (3) With the exception of the small unpublished simulation by Hettmansperger and McKean (1981) Finally, it should be emphasized that the use of T* requires the assumption of symmetry of the error distribution. The estimate T does not require symmetry.…”

“…asymptotically it makes no difference. In a small, unpublished study, Hettmansperger and McKean (1981) find that in testing for parallelism, the simulated levels of A were more erractic than the levels of the other tests discussed below. Further, there was some indication that the presence of good design points with moderate leverage can make A extremely conservative.…”

“…3There are no published studies on small-sample power of A. In the unpublished report by Hettmansperger and McKean (1981) Section 3 we discuss the computational problems that must be overcome to be able to implement the Wald test. By 1983 there will be a rank-regression command in the Minitab statistical computing system which will provide all of the necessary computations.…”

Robust multiple classification of known signals in additive noise-an asymptotic weak signal approach

“…Since the R-distance is scale equivariant, there is no need for a preliminary estimate of scale, as for the M-distance. For an account of R-distances, see [6]. Remark: We close the section by remarking that our signal model can be imbedded into a linear regression model,…”

Did Divorces Decline After the Attacks on the World Trade Center?1

“…To examine the effects of the WTC attack in the context of a simpler analytic approach, we also defined a pre‐/post‐ nonequivalent control group design comparing the average divorce rate within each county for the 10 years before the WTC attack to the average divorce rate during the 4 years after the WTC attack. Hettmansperger–McKean's aligned‐rank test (Hettmansperger & McKean, 1983), which is the nonparametric equivalent of the parametric ANCOVA, was run in which the average post‐WTC attack divorce rate was the dependent variable, the average pre‐WTC attack divorce rate was the covariate, and the manipulation (New York City county vs. non‐New York City county; or metropolitan county versus nonmetropolitan county) was added to the independent variables as a dummy variable. Hettmansperger–McKean's aligned‐rank test was used because of the violation of conditional normality.…”