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

Ben Bolker bolker at ufl.edu
Wed Sep 17 22:41:58 CEST 2008

```Javier Acuña <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

```