On Wed, 12 Jan 2000 16:32:14 +0000, Andrew Norreys
<[EMAIL PROTECTED]> wrote:
> Can anyone tell me whether in a series of numbers of which there are
> repeats, do the repeated numbers hold the same rank, or does the
> numbering carry directly on regardless of value?
>
> I seem to get conflicting arguments from people and by altering the way
> the ranking is done, can get a significant improvement in the calculated
> modulus/expectancy.
- where I found Weibull Modulus in some articles on-line, I did not
see any reliance on rank-methods. I have seen one posted comment
about ranking which was correct, as far as it went, which was not far
enough. Here is more, just about ranking.
The usual way of doing scoring based on ranks, these days, is to do
what the poster says -- each score in a set that is tied is replaced
with the average of the ranks. But that is an approximate method. It
preserves the old mean, without changing the SD by too much. And?
However, if there are very many ties, then it *might* be a fairly
poor method, and it might be worse than some other methods of
arbitrarily re-scoring the original set of numbers. If you get
results that are notably different according to how you score your
ranks (as you say), then that might be indicating that you have
trouble.
This is a comment about ranks, and, especially, ordered CATEGORIES --
the use of ranking is inferior to scores that were sensibly assigned
to the categories, and might be inferior to arbitrary integer counts
on the categories if they were (merely) intelligently constructed for
relevance. In the old days, another way to rank with ties was to
assign the set of rank-numbers randomly among the cases. That is, if
ranks 3-8 were tied, you assign #3 .. 8 randomly to the actual cases.
With computers on hand, that might be combined with bootstrapping, but
I have not read of anyone actually advocating a return to that style.
Again, if the outcome varies according to *how* you deal with your
ties, that suggests that your method is not nearly as robust as you
wanted it to be.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
