# [S] Spearman's

Steve Bousquin (sbous@lamar.colostate.edu)
Sat, 07 Mar 1998 18:57:26 -0700

A while back I sent an inquiry about a function to obtain a confidence
interval for Spearman's correlation coefficient. I am now trying to
write several versions of a function to do this and I have some
questions related to two different suggestions that were offered for
doing this. I thought I might try to wrangle some further advice:

1. FISHER'S Z: Using the formula for Fisher's z transformation, I am
able to estimate the limits for the expected values nicely. However, I
am unable to transform these back to limits for the actual interval for
the estimate. This part of the function would need to perform the same
task as Table B.8 in Neter, Kutner, et al. 4th ed. (Applied Linear Stat.
Models) where one transforms from z-prime to r as described on page
643. Applying the (rearranged) Fisher's z formula for this is not
working for negative values of the correlation statistic because of the
logs and *I was hoping someone someone might be willing to help me with
the math* (I'm fairly sure this is a mathematical problem). *Or is
there an S-Plus function somewhere that will do this?* I would like
this to be done within the function, although of course I could do the
transformation using the abovementioned table.

2. BOOTSTRAPPING: Patrick Burns suggested "bootstrapping the statistic."

```--

*First, would bootstrapping Pearson's result in a robust estimate
similar to Spearman's, or should bootstrap be applied to Spearman's?
(cor will not produce Spearman's; bootstrap will not work on cor.test
because it does not give a vector - I can work this out if necessary).*

*Second, and most important, I am having problems deciding how I can use
the bootstrap results to calculate intervals -- I have not yet got the
references mentioned in the Splus manual, but I am the impatient type.*

==============================================
Steve Bousquin

Department of Rangeland Ecosystem Science/GDPE
NR209
Fort Collins, CO 80523
USA

sbous@lamar.colostate.edu
==============================================

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