Reply to Dennis Edinger 28 May 2001:
<<I wonder if you could tell me why 6 and (less often) 12 show up so
often in non-parametric statistics as constants in that special field
of statistics?>>
For 12: The variance of any set of consecutive integers, 1 through N,
as in rank ordering, will be equal to
[(N^2)-1]/12
For 6: The sum of the squares of any set of consecutive integers, 1
through N, will be equal to
[N(N+1)(2N+1)]/6
Also for 6, as in rank-order correlation: The minimum possible value
of sum(D^2), occurring in the case of perfect positive correlation,
is zero. The maximum possible value, occurring in the case of perfect
negative correlation, is
{N[(N^2)-1]}/3
The ratio of observed sum(D^2) to maximum possible sum(D^2) is therefore
[obs.sum(D^2)]/[{N[(N^2)-1]}/3]
which is equal to
3[obs. sum(D^2)]/{N[(N^2)-1]}
Double this latter ratio, subtract it from 1, and you have the
standard computational formula for the Spearman rank-order
correlation coefficient:
1-[6[obs.sum(D^2)]/{N[(N^2)-1]}]
Hope this helps.
--Richard Lowry
--
__________________________________
Richard Lowry
Professor of Psychology
Jacob P. Giraud Professor of Natural History
Vassar College
Poughkeepsie, NY 12604-0396 USA
office: (845)437-7381
fax: (845)437-7538
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