What could “directional mean” be in this context?

I have some reasonable idea of what directional means are in the context of spatial statistics, but I am stumped by this use of the term in the methods section of this computational biology paper (emphasis mine):

The raw ES values were normalized to account for variable numbers of shRNAs across different genes by dividing the raw ES by the directional mean of a size-matched null distribution generated by 100,000 random permutations of a hairpin set of the same size.

To sum up the relevant part: one is supposed to compute the directional mean of a distribution obtained from a set of scores (no vectors involved).

How would one go about getting a directional mean from a set of values (or associated density function)?

Edit: one piece of information that could be relevant: the score values whose distribution is being plotted and whose "directional mean" is supposed to be extracted, are obtained through a goodness-of-fit test applied to a subset of values ("the hairpin set") out of the whole ranked list (the microarray data, converted to a list of differential expression values).

I also doubt the spatial aspect of the microarray data could play any role here (it's long been eliminated through pre-treatment).

• Just a guess, but "hairpin set" sounds like it could be directional. – Peter Flom Jul 20 '12 at 10:13
• I looked at the article. Although I didn't catch the specific sentence that you mentioned the data was collected on a microarray which does have a spatial aspect to it. I think Peter's guess is correct. – Michael Chernick Jul 20 '12 at 10:38
• Thanks for your comment @Peter, but "hairpin sets" here only represent a subset of probes (i.e. each key to a value in the microarray). Although you could say there's a spatial aspect to microarray, it is dealt with (and eliminated) long before, during pre-treatment of the data. I really don't think this spatiality would pop up at this stage, especially when considering a distribution of scores obtained from these (the scores are essentially a goodness-of-fit test on the subset compared to the whole array, in a ranked list of values). – Dave Jul 21 '12 at 1:40
• From my experience the best way to be certain is to email the authors – Bitwise Sep 28 '12 at 18:08
• 'directional mean' appears to be a term from spatial statistics; it's unclear if that's what's intended here. – Glen_b Jun 26 '13 at 8:41

I think it is not exactly standard terminology, hence it can mean pretty much anything. However, I have found this article which seems to be in the same genre: http://www.plosgenetics.org/article/info%3Adoi%2F10.1371%2Fjournal.pgen.1002621

This makes me suspect that directional may have been used instead of conditional.

But of course directional mean could just be mean, or absolute mean.

• You could perhaps try backtracking the use of the word by checking the sources if there are any known ones? – Dennis Jaheruddin Jul 30 '12 at 15:57