🚀 go-pugleaf

  A general note of thanks to all who responded to my orginal
question noted below.  No one had heard of "Ran-Anova" and my search
of _DATA SOURCES SOFTWARE_ failed to locate any program resembling
that name.
 The responses were diverse, so I leave them in their orginal form below.
The professor is planning on using the PROC MRANK from the
SUGI supplemental library.
Happy Holidays, Tom Bohman,  CCDT001@UTXVM

**********************Original question********************************
      A professor here at UT is interested in analyzing marketing
data where subjects rank 5 different alternative at 4 different
times (approx 75 subjects).  She has heard of a program called
"Ran-anova?" that does repeated-measures analysis of ranked
data.  If anyone recognizes this program and could provide information
on how to obtain it, I would appreciate it.  Alternatively, can someone
suggest either a different package or a method using  one of
the standard packages (SAS, SPSS, BMDP, etc. ).  Finally, any
references to this type of analysis would be appreciated as well.

**************************Responses************************************
FROM: PD@UTXVM

Tom,
You might refer your user to Akritas' JASA article, june 1991, v86, p457
Limitations of the Rank Transform Procedure: A Study of Repeated Measures
Design, Part I.  It is "demonstated that the [rank transform] is not a
generally applicable method for [repeated measures] design [even assuming
you have] equicorrelated errors.... The underlying reason for the failure
..is the nonlinear nature of the rank transformation.  For some hypotheses
this nonlinearity introduces additional parameters in the model for the
transformed data; thus the naive use of the RT method will reject the null
hyp. with probability higher than alpha even when the null hyp. is true.
The nonlinearity of the rank transformation can also destroy the equicorre-
lation between the errors and/or the assumption of equal covariance matrices."

In the same issue, p.410, Thompson's article A Unified Approach to Rank Tests
for Multivariate and Repeated Measures Designs covers the asymptotic distri-
butions of many rank transform tests.
=========================================================================

From: <U50161@UICVM>
         Although I have not  used  it recently I think the MRANK
procedure in the  Sugi Supplemental Library User's Guide Version
5 edition (page 361-376) may be applicable to this problem.
                                                 A. Herzog
                                                 UIC - Chicago
                                                 School of Public Health
=========================================================================

From:        R.A.Reese@hull.ac.uk
     Off the cuff answer, but I think repertory grid analysis and
multidimensional scaling addressed the type of problems you're
asking about.
=========================================================================

From: cole@waldron.stanford.edu

First, I don't know anything about "Ran-anova," so I can't
help you there. However, if you do find something out about it,
please let me (or the net) know.

As for other approaches, several possibilities exist, depending on what
kind of design your client presents.  If it's a simple one-way
repeated-measures design, Friedman's (as in Milton) test
may be what you're looking for. It's ubiquitous (available in Minitab,
SAS, BMDP), and covered in most books on nonparametric techniques.
If it's a more complex
design, a couple of possibilities exist.  One, based on an extended
Mantel-Haenszel procedure, is fairly well documented in an article by
Landis, Miller, Davis, & Koch, Statistics in Medicine, 7, 109-137 (1988).
You can implement simple versions of this procedure in SAS or BMDP (other
packages as well, I'm sure), and you could easily program more complex
versions since Landis et al. provide formulas for the estimators and test
statistics.
    Lots of smart people have argued that there is no real problem
simply submitting the rank data to the standard analysis, particularly if
the number of items ranked is reasonably large (say, greater than 3).  I
think there's a recent (like, within the last 5 years) article in
Psychological Bulletin basically advocating this position (by a well-known
nonparametric theorist whose name escapes me at the momen), though not
specifically for the repeated-measures problem.  Finally, a popular
approach for categorical data involves weighted least squares
prediction of cell counts (this is also covered in the Landis et al.
article mentioned above).  As that procedure is implemented in SAS,
I don't believe it takes advantage of the ordinal information
contained in  rank data, but you might be able to reformat the problem in
terms of cumulative logits in order to incorporate the
ordinal information.