David Martin <[email hidden]> wrote in message news:<[email hidden]>...
Quoted message said:On 1/6/04 10:22 pm, in article
[email hidden], "James Annan"Quoted message said:No, the very basic error I was thinking of is the one they make in the
"60%" calculation. The ratio of the two numbers they calculate is
meaningless.The drop in head injuries rate according to their stats is 3.6
percentage points. This is not a 3.6% drop in head injuries but a 13%
change (3.6/27.9)! However, the number of unhelmeted cyclists only
dropped by 5.8/84 = 7%. So according to their stats, the extra helmet
wearers did not only prevent their own head injuries but also stopped
injuries in a large number of those who were not wearing helmets!I suppose you missed the point that the confounding factors are assumed to
apply to pedestrians as well and that pedestrian injuries typically act as a
good model for cyclist injuries. So comparing the change in cyclist HI with
the change in pedestrian HI, one presumes that the difference in change is
due to cyclists increased wearing of helmets.
No, I didn't miss that, which is why I used their figure for the
_extra_ gains made by cyclists, over and above that made by
pedestrians. Incidentally, none of the figures in the paper seem to
square with the data points or the regression line in the figure, but
I wasn't particularly addressing that initial part of their
calculation at all, even though it is also wrong in detail[1].
Quoted message said:
Quoted message said:
If that is not clear enough, consider a simple hypothetical: head
injury rates drop from 20% to 0% while helmet use increases from 0% to
100%. It is clear that helmet effficiency is 100% (all injuries are
prevented), and not 20/100=20% as Cook and Sheikh's method would
indicate.No. You cannot take the extreme.
Sheesh. I just dropped in a simple numerical example to show the
bogosity of their calculation.
Quoted message said:
Assume cyclist HI drop from 50 to 25 percentage points. A 50% drop
You can stop right there, since according to the method in the paper
it is clear that they would refer to this as a 25% drop (50 - 25, not
the correct 25/50). This is the error which I am referring to. Their
3.6% drop in %HI (after accounting for pedestrian gains) is a number
of percentage points, not a % fall in injury rate. Got it yet? When
calculated as a % change in injury rate, it is double the % drop in
the proportion of unhelmeted cyclists. As soon as one realises this
point, it is clear that there are other factors present which exceed
any possible benefit of helmets, and that attributing any part of this
large overall injury reduction to helmets is basically guesswork.
I see you need to work through all the numbers rather than
understanding the essence of the mistake directly. Biologists!
[snip lots of tedious calculation]
Quoted message said:the answer is so obviously bogus that it is
hard to credit the study.
So finally you agree with me. I'm happy for you. Do you understand
_why_ it is bogus, and how their 60% figure is wrong, or do I need to
go through it one more time?
Quoted message said:Quoted message said:I guess I get the prize...of writing to the journal and the authors to
explain their mistake.Don't do it, you'll be laughed out of court unless you can come up with a
much better interpretation of the data than you already have. Mine would
need to be thoroughly worked over before letting anyone near it
professionally.
Don't be such a pompous ass, their formula for the 60% calculation is
obviously bogus, and the correct conclusion from that data, which I
have already explained, is that there _must_ be substantial
confounding factors that they have not taken into account since the
overall reduction in head injury rates is twice what would be provided
by 100% effective helmets. There is no better interpretation of this
data than to point out that it is wholly inadequate for the purpose.
James
[1] Note that there is also essentially the same error in the way they
calculate an "excess" 3.6 percentage points gain for cyclists, since
the drop in ped and cyclist %HI rates should also both be normalised
by their initial values before subtracting one from the other.
However, the effect of this error is probably small, since the ped and
bike values are quite similar, and it could perhaps be defended as an
insignificant approximation. I'm only addressing the error where they
calculate the efficiency of helmets as 3.6/5.8 = 60% which is a rather
elementary mistake to make for those who presume to write statistics
textbooks.
--
If I have seen further than others, it is
by treading on the toes of giants.
http://www.ne.jp/asahi/julesandjames/home/