# RE: st: are there any statistics rules that I can apply to separate numbers into groups?

 From "Nick Cox" To Subject RE: st: are there any statistics rules that I can apply to separate numbers into groups? Date Thu, 12 Mar 2009 12:41:34 -0000

```The fact that you get the same results with -group1d- and a k-means
approach is good fortune, as k-means methods don't guarantee that an
optimum will be found.

The main point of -group1d- is that it produces classes that are
contiguous intervals in one dimension. In contrast -cluster- has no
notion of contiguity.

Your main question is about -cluster- and is best left to Ken Higbee, I
suspect.

Nick
n.j.cox@durham.ac.uk

Thanks to Nick for introducing me to this wonderful command -group1d-.
It's exactly what I was looking for.

I have some further questions - which I hope someone would help me to
understand.  I was also playing around with the -cluster kmeans-
command and find that -group1d- generates the same groupings -cluster
kmeans- with the option -measure(L2squared)- applied.

I then compare the results of -cluster kmeans- with or without the
-measure(L2squared)- option specified.  The result groupings are
different.  I don't really understand why this should be the case for
univariate clustering, because when I typed:

help measure_option  (note the underscore between the words measure
and option, without the underscore a different help file will show up)

It is explained that the default option calculates the grouping by
minimising:
requests the Euclidean distance / Minkowski distance metric
with argument 2

sqrt(sum((x_ia - x_ja)^2))

But when the option -measure(L2squared)- is specified
grouping is assigned by minimising the square of the Euclidean
distance / Minkowski distance metric with argument 2

sum((x_ia - x_ja)^2)

Here are some output generated using the same 49 observations:

. cluster kmeans var1, k(4) generate(euclid)
cluster name: _clus_5

. cluster kmeans var1, k(4) generate(euclidsq) measure(L2squared)
cluster name: _clus_1

. tab  euclid euclidsq

|                  euclidsq
euclid |         1          2          3          4 |     Total
-----------+--------------------------------------------+----------
1 |        10          0          0          0 |        10
2 |         0          0         12          0 |        12
3 |         0          4          0          6 |        10
4 |         9          0          0          8 |        17
-----------+--------------------------------------------+----------
Total |        19          4         12         14 |        49

. bys euclid: egen m_euclid=mean(var1)

. bys euclidsq: egen m_euclidsq=mean(var1)

. egen tot1euclid=total((var1-m_euclid)^2)

. egen tot1euclidsq=total((var1-m_euclidsq)^2)

. sum tot*

Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
tot1euclid |        49    712.2434           0   712.2434   712.2434
tot1euclidsq |        49    524.9169           0   524.9169   524.9169

. di sqrt(712.2434 )
26.687889

. di sqrt( 524.9169  )
22.911065

Groupings generated with the option -measure(L2squared)- applied is
superior to the one without.  This shouldn't be the case for
univariate clustering, or should it??  Have I missed something
important?

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```