[R] Multiple comparisons in a non parametric case

Marco Chiarandini machud at intellektik.informatik.tu-darmstadt.de
Tue Sep 7 22:26:09 CEST 2004

Dear all,

I am conducting a full factorial analysis. I have one factor consisting
in algorithms, which I consider my treatments, and another factor made
of the problems I want to solve. For each problem I obtain a response
variable which is stochastic. I replicate the measure of this response
value 10 times.

When I apply ANOVA the assumptions do not hold, hence I must rely on non
parametric tests.

By transforming the response data in ranks, the Friedman test tells me
that there is statistical significance in the difference of the sum of
ranks of at least one of the treatments.

I would like now to produce a plot for the multiple comparisons similar
to the Least Significant Difference or the Tukey's Honest Significant
Difference used in ANOVA. Since I am in the non parametric case I can
not use these methods.

Instead, I compare graphically individual treatments by plotting the sum
of ranks of each treatment togehter with the 95% confidence interval. To
compute the interval I use the Friedman test as suggested by Conover in
"Practical Nonparametric statistics".

I obtain something like this:

Treat. A                |-+-|
Treat. B              |-+-|
Treat. C                   |-+-|
Treat. D           |-+-|

The intervals have all the same spread because the number of
replications was the same for all experimental units.

I would like to know if someone in the list had a similar experience and
if what I am doing is correct. In alternative also a reference to
another list which could better fit my request is welcome.

Thank you for the help,


Marco Chiarandini, Fachgebiet Intellektik, Fachbereich Informatik,
Technische Universität Darmstadt, Hochschulstraße 10,
D-64289 Darmstadt - Germany, Office: S2/02 Raum E317
Tel: +49 (0)6151 16-6802 Fax: +49 (0)6151 16-5326
email: machud at intellektik.informatik.tu-darmstadt.de
web page: http://www.intellektik.informatik.tu-darmstadt.de/~machud

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