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 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
[4] 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. ne.jphomeOpen ↗
