The old Google Groups will be going away soon, but your browser is incompatible with the new version.
Message from discussion Narrow Cycle Lanes?

From:
To:
Cc:
Followup To:
Subject:
 Validation: For verification purposes please type the characters you see in the picture below or the numbers you hear by clicking the accessibility icon.

More options Jun 14 2003, 8:30 am
Newsgroups: cam.transport
From: Chris <ch...@x.invalid>
Date: Sat, 14 Jun 2003 13:30:37 +0100
Local: Sat, Jun 14 2003 8:30 am
Subject: Re: Narrow Cycle Lanes?

Tim Ward wrote:
> Let's see a proof of that, please? Based on the actual figures for the
> year we've seen posted here earlier (complete gibberish, that, as no area
> with 0.2 accidents per year would get anywhere near the top of the priority
> list so the statistical significance in fluctuations of samples with an
> average of 0.2/pa are of no relevance whatsoever)

OK. Let's consider a site with an intrinsic accident rate
of 10/year. (This isn't far off the Mitcham's Corner
statistics, which have led to extensive works.) Some
traffic work is done which increases the intrinsic rate
to 15/year. Here's a possible accident history:

Accidents before, by year:
5  11   6  13  15  11  14   9  13  12   7  11  16  11  15  11   6 *19*  6   8
22  30  34  39  40  34  36  34  32  30  34  38 *42* 37  32  36  31  33   3 year total

Accidents after, by year:
11  15  14  20  24  21  14  15  15  12  14   8  18  12  18  18  20  13  12  13
40  49  58  65  59  50  44  42  41  34  40  38  48  48  56  51  45  38   3 year total

Suppose that some work is done following the year in
which 19 accidents occured. What is the probability that
the following year will see fewer than 19 accidents?

n P(n, before)       P(n, after)
cumul.             cumul.
-- -------- --------  -------- --------
15 0.034718 0.951260  0.102436 0.568090
16 0.021699 0.972958  0.096034 0.664123
17 0.012764 0.985722  0.084736 0.748859
18 0.007091 0.992813  0.070613 0.819472 <----
19 0.003732 0.996546  0.055747 0.875219

This is pretty disastrous. But don't worry, apparently in
reality three-year totals are used.

What about in the three year case? Let's say changes are
implemented in the case where 42 accidents occur in a
three-year interval. What is the probability that fewer
will take place in the next three years?

n P3(n, before)      P3(n, after)
cumul.             cumul.
-- -------- --------  -------- --------
38 0.024169 0.935156  0.036333 0.166459
39 0.018591 0.953747  0.041923 0.208382
40 0.013943 0.967690  0.047163 0.255545
41 0.010203 0.977893  0.051765 0.307310 <----
42 0.007288 0.985180  0.055462 0.362772

This is a bit better -- by comparison. But note that if you
were to apply this process to a bunch of sites with an
accident rate of 10/year, then you'd still fail to spot your
mistakes on approximately one in three occasiouns.

--
Chris Lightfoot, chris at ex dash parrot dot com; http://ex-parrot.com/~chris/
I don't care who the audience picks/
I'd rather be killed with a big sharp stick....
(`How'd The Date End?', The Mr. T Experience)