R help - May 2003 - Test for trend?

Hello R community,

I would like to test for learning effects by subjects in my experiment. Each
subject participates in six consecutive auction rounds of the same treatment.
The response variable is the efficiency of an auction outcome measured by a real
number. Since the efficiency increases over the six rounds, I suppose that
subjects learn about the rules of the auction institution, but I would like to
test for that conjecture.

The prop.trend.test does not seem to be right, because the treatment does not
change between the rounds, i.e. the number of trials (n) is not available. A
linear regression shows a positive slope and the 99%-confidence interval shows a
significant deviation from a zero slope, but I am not able to compute the exact
p-value. The Cox-Stuart test for trend detects a trend but gives a p-value of 1.

Isn't there a distribution-free, exact test for trend which operates on the
rank-oder of the data instead of binary coded values?

Please apologize for asking a rather R-unspecific question.

Thanks in advance
Stefan
---
Stefan Strecker
Universitaet Karlsruhe (TH)
Department of Economics and Business Engineering
Chair for Information Management and Systems
Englerstrasse 14
D-76131 Karlsruhe, Germany
T: +49 721 608 8374
F: +49 721 608 8399
M: +49 179 69 29 746
http://www.iw.uni-karlsruhe.de
DH PGP Key available upon request

I think this depends on what you mean by "trend." What I would mean is
"effect of successive trials that is very unlikely to be spurious,"
which
is a good lay definition of statistical significance.

Given that these are multiple trials on the same subjects over time, it
seems like a mixed-effects model might be in order. Take a look at the
nlme pacakge, as well as Pinheiro and Bates' excellent treatment:

http://cm.bell-labs.com/cm/ms/departments/sia/project/nlme/MEMSS/index.html

...and John Fox's different (but also excellent) discussion:

http://www.socsci.mcmaster.ca/jfox/Books/Companion/appendix-mixed-models.pdf

Best,
Andy Perrin

----------------------------------------------------------------------
Andrew J Perrin - http://www.unc.edu/~aperrin
Assistant Professor of Sociology, U of North Carolina, Chapel Hill
clists at perrin.socsci.unc.edu * andrew_perrin (at) unc.edu


On Wed, 28 May 2003, Strecker, Stefan wrote:
> Hello R community,
>
> I would like to test for learning effects by subjects in my experiment.
Each subject participates in six consecutive auction rounds of the same
treatment.
> The response variable is the efficiency of an auction outcome measured by a
real number. Since the efficiency increases over the six rounds, I suppose that
subjects learn about the rules of the auction institution, but I would like to
test for that conjecture.
>
> The prop.trend.test does not seem to be right, because the treatment does
not change between the rounds, i.e. the number of trials (n) is not available. A
linear regression shows a positive slope and the 99%-confidence interval shows a
significant deviation from a zero slope, but I am not able to compute the exact
p-value. The Cox-Stuart test for trend detects a trend but gives a p-value of 1.
>
> Isn't there a distribution-free, exact test for trend which operates on
the rank-oder of the data instead of binary coded values?
>
> Please apologize for asking a rather R-unspecific question.
>
> Thanks in advance
> Stefan
> ---
> Stefan Strecker
> Universitaet Karlsruhe (TH)
> Department of Economics and Business Engineering
> Chair for Information Management and Systems
> Englerstrasse 14
> D-76131 Karlsruhe, Germany
> T: +49 721 608 8374
> F: +49 721 608 8399
> M: +49 179 69 29 746
> http://www.iw.uni-karlsruhe.de
> DH PGP Key available upon request
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>