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

Javier Acuña javier.acuna.o at gmail.com
Sun Sep 21 23:01:18 CEST 2008

```>Ben Bolker <bolker <at> ufl.edu> writes:
>
>I would try
>
>fligner.test(dT ~ Topology:Drift:lambda)
>
>in response to:
>
>Javier Acuna <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 tried what you suggested Ben, but I'm still puzzled by the output.
In this case, I obtain different results with different ordering of
the factors:

> fligner.test( dT ~ Dims : Topology :Drift )

Fligner-Killeen test of homogeneity of variances

data:  dT by Dims by Topology by Drift
Fligner-Killeen:med chi-squared = 195.2067, df = 1, p-value < 2.2e-16

> fligner.test( dT ~ Topology :Drift:Dims  )

Fligner-Killeen test of homogeneity of variances

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

I don't know what to do now, any help would be reaaally appreciated.

Best Regards
Javier

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

```

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