Re: Testing to see if there is a significant change in crime figures over time?
- From: dave@xxxxxxxxxxx
- Date: Wed, 07 Nov 2007 04:48:28 -0800
On Nov 6, 11:12 am, KevinC <kevincre...@xxxxxxxxxxx> wrote:
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- Hide quoted text -
- Show quoted text -
Kevin,
The question is "What do you precisely mean by "SIGNIFICANT CHANGES IN
CRIME FIGURES OVER TIME"
I took your fictitious data and obtained
MODEL COMPONENT LAG COEFF STANDARD P
T
# (BOP) ERROR VALUE
VALUE
Differencing 1
1CONSTANT 45.7
[(1-B**1)]Y(T) = 45.700 + [A(T)]
TIME DATE LOWER 95% UPPER 95% FORECAST ACTUAL
RESIDUAL %
(T) LIMIT LIMIT (IF KNOWN)
ERROR
12 2001 3136. 3271. 3204.
13 2002 3154. 3345. 3249.
14 2003 3199. 3391. 3295.
9489. 0.1001E+05 9748.
The equation suggests ( since there are no significant outliers/
inliers) that the pattern has not changed in the 11 years.
Clearly the mean of the M most recent is DIFFERENT from the earlier 11-
M values .
Thus the MEAN HAS CHANGED but .... THE PATTERN (EQUATION) HAS NOT.
Your Call !
Dave Reilly
Automtic Forecasting Systems
http://www.autobox.com
215-675-0652
.
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