Descriptive statististical method
– for analysing the amalgamation of Danish municipalities

Lars J. Ravn-Jonsen, June 2005

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The object of the paper is to explain some descriptive statistical methods usable to analyse the distributional consequences of the coming merger among Danish municipalities. The methods used are box plots and calculation of the expected mean error, average and gini-coefficients as expressed in some test numbers.

The paper explains how the concept of homogenizing can be interpreted statistically: as a change from a cluster distribution towards a random distribution and further towards a systematic distribution. A cluster distribution can also be described by a positive correlation between the individuals, a random distribution by nil correlation between the individuals and a systematic distribution by a negative correlation between the individuals; consequently homogenizing can be interpreted as a decrease in correlation. A homogenizing will be expressed as a decrease in the mean error of the average, too. By the merger of smaller municipalities to fewer, but bigger municipalities, the municipal distribution of the properties will change. How this change in the distribution can be observed in box plots and test numbers is described and related to the notion of random, correlated and thereby to cluster and systematic.

In Christoffersen and Ravn-Jonsen (2005) the described methods are applied for analysing of different aspects related to the in 2007 planned fusion of the Danish municipalities. The report illustrates the potential that the graphical methods of this paper have in explaining and analysing otherwise hard accessible material by the mean of illustrations.

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