Re: Testing to see if there is a significant change in crime figures over time?

On Nov 5, 2:43 am, Richard Ulrich <Rich.Ulr...@xxxxxxxxxxx> wrote:
On Sat, 03 Nov 2007 12:10:55 -0700, KevinC <kevincre...@xxxxxxxxxxx>
wrote:





Hi all,

Apologies if my terminology is incorrect here - its been a while since
I did any true statistics.

I have a set of crime counts for a particular area covering a three
year period (crime counts are for each day).

I have plotted these crimes on a graph (aggregated for each month) and
have found that a trend line appears to shows me that the number of
crimes appears to be increasing over time. While the graph is useful
I was wondering if there is a significance test or quantitative way
that I could test to see if this change is significant.

I will be likely to run this same process every financial quarter so
would like to have a way of testing how things are changing (if indeed
they are at all).

You might have a choice here between "simple" and
"formally correct."

Crimes like burglary probably have serial correlation
because they reflect how many highly-busy burglars
are operating at one time. That can be awkward to
account for statistically, or to explain to a lay audience..

When I look at the newspaper and want to extrapolate
whether a trend is changing, I look at the previous
number as long-term number that is "fixed". Then I
can compare a Poisson variable to a fixed rate, which
is simple-dimple -- Take the square root of both numbers.
(For example: new monthly incidence, and average of monthly
incidence up to now, or maybe, up to a year ago.)

The standard deviation of the square root of a Poisson
is 0.5. So, if the two square roots differ by less than 1.0,
which is a t=2.0, there is no chance that they are 'significantly
different.' If they differ by more than one, they are 'nominally
significant'. That is enough for my usual, personal purposes.
If I was giving the numbers to someone else, I would mention
that the assumption of independence was not met, and I might
offer a more precise Poisson comparison of two (not-fixed)
groups, or I might offer the 1% test as an alternative that is
probably conservative as a 5% test. All of these are on the
"less formal" side, and are pretty easy to explain, and will give
pretty good results.



I realise that I could be on the wrong track here and that perhaps I
should be taking a different approach all together, so please let me
know if you think I should try something else!

Any help would be much appreciated.

--
Rich Ulrich, wpi...@xxxxxxxxxxxx://www.pitt.edu/~wpilib/index.html- Hide quoted text -

- Show quoted text -

Hi Richard,

Thanks ever so much for replying. I wonder if you could provide a
little more direction on this.

Regarding your comments I created this small worked example from
fictional data (however I am not sure of my methods are correct).

Time Period Crimes
1 2701
2 2705
3 2699
4 2805
5 2850
6 2917
7 3002
8 3025
9 3070
10 3104
11 3158
Mean: 2912.363636
Sqr Root: 53.96631946


Current Period Count: 3214
Sqr Root: 56.69215113

As 56.69215113 - 53.96215113 = 2.725832 there is a significant
difference.

Have I interpreted this correctly? Also what does "t" represent in
your example above?

Thanks for any additional comments you can give!

Regards,

Kevin

.

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