# [R] An ANOVA test that uses a distance matrix like hierarchical cluster analysis?

From: Nick Flyger <nickflyger_at_gmail.com>
Date: Sun, 27 Apr 2008 15:24:33 +0800

I have a question which does not pertain directly to the use of R but comes from my use of R!

I have data which can be described as 3-dimensional e.g. (x,y,z), with no negative component. The suggested way to analyze this data is via multivariate techniques or by calculating what amounts to a levene's test on the data and then an ANOVA on the three components if the first test is significant or a t-test when only two groups are involved.

I do not like either of the first methods because of the case of 3 or more groups. As an example, if I had three groups each with mean distance of 5 from the origin (0, 0, 0) and a variance of 1 about that mean. Now say group A has a mean for the 3 components of (5, 0, 0), B a mean of (0, 5, 0) and C a mean of (0, 0, 5). In this case the ANOVA will find no difference between the groups because the mean difference and variances are identical. Yet we clearly see the groups are different. The t-test is valid because I can adjust the formula to accept the euclidean difference between the mean scores of two groups.

As an alternative I like to use hierarchical cluster analysis with the euclidean distance matrix and bootstrapping for p-values. In this way I don't have to prematurely collapse the data to a single value per observation and the distance matrix allows for direct distance comparison between all the observations for all the groups similar to the t-test.

However, prior to analysis I know the groups that the observations belong to and I would like to use ANOVA and post hoc tests to tease out the differences. Is there a ANOVA style of analysis that makes use of distance matrices?

Any thoughts would be appreciated as statistics is not my specialty although I am happy with programming in R, Matlab etc...

```--
Nick Flyger

Senior Biomechanist
Centre for Biomechanics,
Institut Sukan Negara Malaysia,
Komplex Sukan Negara,
Bukit Jalil, Sri Petaling
PO Box 10440, 50174 Kuala Lumpur,
MALAYSIA

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