R help - Sep 2008 - Unexpected behaviour when testing for independence with multiple factors

Hi, I'm a new user of R. My background is Electrical Engineering, so
please bear with me if this is a silly question.

I'm trying to assess whether the results of an experiment satisfy the
hypothesis of homoscedasticity (my ultimate goal is to use ANOVA).

The result of the experiment is mean delay (dT), which depends on
three factors, topology, drift, and lambda. The first two factors are
categorical (with 4 levels each) and the last one is numerical, with
two levels.

A sample of my data is as follows:

dT	 Topology	 Drift	 lambda
258.789	 Tree	 b1	 .43
244.195	 Tree	 b1	 .43
115.961	 Tree	 b2	 .3
115.183	 Tree	 b2	 .3	

I would like to separate dT in the 32 samples (4x4x2), and test if the
variance of each sample is equal to the other 31 samples.
I tried using fligner.test and bartlett.test, but either test seems to
only work for one factor:
> fligner.test( dT ~ Topology + Drift + lambda)
        Fligner-Killeen test of homogeneity of variances

data:  dT by Topology by Drift by lambda
Fligner-Killeen:med chi-squared = 15.4343, df = 2, p-value = 0.0004451
> fligner.test( dT ~ Topology )
        Fligner-Killeen test of homogeneity of variances

data:  dT by Topology
Fligner-Killeen:med chi-squared = 15.4343, df = 2, p-value = 0.0004451

As I see from the previous two outputs, fligner.test only takes into
account the first factor. Similar results are obtained for
bartlett.test.

At this point I don't know if I'm using the test incorrectly or
something else. I would really appreciate any help. I'm using R
version 2.7.2 (2008-08-25) in Windows XP.

Many thanks in advance
Javier

----------------------------------------------------
Javier Acuna
Electrical Engineering Grad Student
Universidad de Chile
javier.acuna.o at gmail.com

Javier Acu?a <javier.acuna.o <at> gmail.com> writes:
> 
> Hi, I'm a new user of R. My background is Electrical Engineering, so
> please bear with me if this is a silly question.
> 
> I'm trying to assess whether the results of an experiment satisfy the
> hypothesis of homoscedasticity (my ultimate goal is to use ANOVA).
> 
> The result of the experiment is mean delay (dT), which depends on
> three factors, topology, drift, and lambda. The first two factors are
> categorical (with 4 levels each) and the last one is numerical, with
> two levels.
> 
> A sample of my data is as follows:
> 
> dT	 Topology	 Drift	 lambda
> 258.789	 Tree	 b1	 .43
> 244.195	 Tree	 b1	 .43
> 115.961	 Tree	 b2	 .3
> 115.183	 Tree	 b2	 .3	
> 
> I would like to separate dT in the 32 samples (4x4x2), and test if the
> variance of each sample is equal to the other 31 samples.
> I tried using fligner.test and bartlett.test, but either test seems to
> only work for one factor:
> 
> > fligner.test( dT ~ Topology + Drift + lambda)
> 
>         Fligner-Killeen test of homogeneity of variances
> 
> data:  dT by Topology by Drift by lambda
> Fligner-Killeen:med chi-squared = 15.4343, df = 2, p-value = 0.0004451
> 
> > fligner.test( dT ~ Topology )
> 
>         Fligner-Killeen test of homogeneity of variances
> 
> data:  dT by Topology
> Fligner-Killeen:med chi-squared = 15.4343, df = 2, p-value = 0.0004451
> 
> As I see from the previous two outputs, fligner.test only takes into
> account the first factor. Similar results are obtained for
> bartlett.test.

  I would try 

fligner.test(dT ~ Topology:Drift:lambda)

  there's also lots of advice floating around in the
archives about not taking these homogeneity of variance
tests *too* seriously: for small data sets they are
underpowered, for large data sets they are overpowered
(i.e., they will detect departures from normality that
are not actually a problem for ANOVA results).

  good luck,
   Ben Bolker

At 16:03 17/09/2008, Javier Acu?a wrote:
>Hi, I'm a new user of R. My background is Electrical Engineering, so
>please bear with me if this is a silly question.
For future reference you might find
?interaction
helpful as another tool in your box.

>I'm trying to assess whether the results of an experiment satisfy the
>hypothesis of homoscedasticity (my ultimate goal is to use ANOVA).
It is hard to resist quoting Box (1953, 
Biometrika, 40, p333) that these tests are '... 
like putting to sea in a rowing boat to find out 
whether conditions are safe for an ocean liner to leave port'
>The result of the experiment is mean delay (dT), which depends on
>three factors, topology, drift, and lambda. The first two factors are
>categorical (with 4 levels each) and the last one is numerical, with
>two levels.
>
>A sample of my data is as follows:
>
>dT      Topology        Drift   lambda
>258.789 Tree    b1      .43
>244.195 Tree    b1      .43
>115.961 Tree    b2      .3
>115.183 Tree    b2      .3
>
>I would like to separate dT in the 32 samples (4x4x2), and test if the
>variance of each sample is equal to the other 31 samples.
>I tried using fligner.test and bartlett.test, but either test seems to
>only work for one factor:
>
> > fligner.test( dT ~ Topology + Drift + lambda)
>
>         Fligner-Killeen test of homogeneity of variances
>
>data:  dT by Topology by Drift by lambda
>Fligner-Killeen:med chi-squared = 15.4343, df = 2, p-value = 0.0004451
>
> > fligner.test( dT ~ Topology )
>
>         Fligner-Killeen test of homogeneity of variances
>
>data:  dT by Topology
>Fligner-Killeen:med chi-squared = 15.4343, df = 2, p-value = 0.0004451
>
>As I see from the previous two outputs, fligner.test only takes into
>account the first factor. Similar results are obtained for
>bartlett.test.
>
>At this point I don't know if I'm using the test incorrectly or
>something else. I would really appreciate any help. I'm using R
>version 2.7.2 (2008-08-25) in Windows XP.
>
>Many thanks in advance
>Javier
>
>----------------------------------------------------
>Javier Acuna
>Electrical Engineering Grad Student
>Universidad de Chile
>javier.acuna.o at gmail.com
Michael Dewey
http://www.aghmed.fsnet.co.uk