Statistics help

[2000AD]

Wondering if anyone can help me find the right statistical test for some data.
I've got eight sets of data and in each set of data there's 4 other sets, so my table looks like this:

---X1 X2 X4 X4 X5 X6 X7 X8
Y1
Y2
Y3
Y4

Where X is a compass point and Y is a type of lichen, the data being the % of a wall a lichen covers (the compass point being the orientation of the wall)

I've got to compare the different compass orientations to see if there's any difference between them with respect to lichen coverage.

Anyone got any clue as to which test i can use?

[drachefly]

Well, I'd look at each kind of lichen separately and then compare the results. That simplifies your table considerably... and it makes the result comprehensible. "This lichen is like this other lichen"; "this lichen is unlike this one", etc.

There are all kinds of methods you could use to compare the pattern of compass readings. For example, you could just rank the compass points by the amount of lichen present (of the type in question), and then compare the lists with a Spearman Ranking or Kendall's Tau. That's good for robustness.

If it's for a class, though, the teacher might want something a bit more subtle. You might want to compare lichens' growth patterns by correlating them or getting their covariance.

[Wyrm]

What are your assumptions? Is your model something like this?

% = f(X) + h(Y) + ε

[Kuroneko]

Probably the simplest method you could use is to do the standard Pearson correlation coefficient with the mean differences X-μ(X) replaced by sin(A-μ(X)) followed by a permutation test to determine the significance of the coefficient. There are only about forty thousand permutations, so it's not hard for a computer to do through them all (or you could use a random permutation test of several thousand or so).

For more in depth treatments of this subject, there are two books by N.I.Fisher, et. al.: Statistical Analysis of Circular Data and Statistical Analysis of Spherical Data. I don't have the former, so I have no idea how good it is nor how helpful it would truly be, but it sounds exactly what you need. While I do have the latter, I have never studied it in depth (statistics does not generally interest me), but toward the end of the book there is a general but simple correlation coefficient for unit 3-vectors (spatial directions) with p-vector data. It's not quite what you have, but it is fairly obvious how to drop a dimension (or add, for that matter) and have p = 1 (only one data variable: percent coverage).