Richard,
I'm going to play Devil's advocate for a change. :)
richard wrote:So far, it has been involved in 1,139 projects, contrasting with Ireland (with about the same population and an EU member), which has significantly less input than Norway, contributing to 1,079 projects.
The word '
significantly' triggered an autonomic reflex. But is the
funding number itself really
significantly less I wondered? I thought maybe I should check. So I did. OK, that wasn't exactly your point here but it's kind of related.
Assuming funded projects 'rain down' at random and generally evenly in proportion to population, is the difference in the two numbers significant if the populations are the same? A back of the envelop calculation says no.
Taking the worst case figure of incidence (1079) and assuming that it reflects the average rate of project 'rain' then what are the chances of it having been 1139 instead? Random 'rain' like this has pretty much a
normal (Gaussian) distribution, the standard deviation of which is about √(what you see)*: in this case, √1079 ~= 33. In most studies, statistical significance is taken at the 5% level. For a Gaussian distribution this means falling outside two standard deviations from the expected average, which, for a two-tailed test, means a 2.5% chance at either end of falling outside. Actually 2 standard deviations gives 2.3% at either end but 2 sds is good enough (the strict figure is 1.96 sds).
Norway's excess is 1139 -1079 = 60, so it's just
inside the 2-standard deviation mark, making it not significant.
Then I wondered about the populations sizes exactly. Googling gives ROI 4.58 million and Norway 5.03 million, about 9.8% larger. But the number of Norway's funded projects is only 5.6% more than ROI's. So ROI gets more per capita!
But not
significantly more. :)
I would have liked to have done this in more excruciating detail and really dragged it out but just after I started I happened to notice that my left shoelace needed urgent attention. Inexplicably the knot has lost all symmetry! Gotta rush — emergency adjustment needed. I must remain calm. Pffff!
* From the binomial approximation to the Gaussian, and a very good one it generally is too in cases like this.
P.S. So no one's murdered Paul Nurse yet? How disappointing!
Edited by user 28 January 2013 04:45:31(UTC)
| Reason: Asterisk AWOL. Now sorted. Shoe lace doing well.