Hello.

I have computed a distance matrix for a set of n protein structures from the PDB. I know the CATH classification for each protein structure on the Class level (three possible classes: alpha, beta, or alpha/beta).

For each class, I have computed the average distance to members of all classes (i.e., I now have a 3x3 matrix of average distances). The classes have the same number of members (n/3 each). Here is an example distance matrix:

```
=====================
class | a b ab
---------------------
a | 16 51 34
---------------------
b | 53 22 34
---------------------
ab | 33 34 26
=====================
```

I would like to test whether the score differences are statistically significant between the groups.

E.g., the average distance within the alpha proteins is 16. The average distance of an alpha protein to a beta protein is 51. Which test or method should I use to determine whether this difference is significant?

Is the t.test() function in GNU R suitable for this? Or ANOVA?

EDIT: It seems I have to do multiple t-tests or ANOVA. The disadvantage of multiple t-tests seems to be accumulating errors. It also seems that there was no need to compute the averages, most software wants the raw data as input.