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

Michael Dewey info at aghmed.fsnet.co.uk
Thu Sep 18 14:32:20 CEST 2008

```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