# [R] Unexpected behaviour when testing for independence with multiple factors

Javier Acuña javier.acuna.o at gmail.com
Sun Sep 21 23:05:06 CEST 2008

```Michael, so you're suggesting that I should do:

aux <- interaction( Topology, Drift, lambda)
and then
fligner.test(dT~aux)

Is that correct?

On Thu, Sep 18, 2008 at 8:32 AM, Michael Dewey <info  <at>
aghmed.fsnet.co.uk> wrote:
> At 16:03 17/09/2008, Javier Acuña 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
>
>
>> 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.
>>
>> Javier
>>
>> ----------------------------------------------------
>> Javier Acuna