Nearest neighbour: a test to see if data points attract each other, repel each other or are randomly distributed

In this note the Nearest Neighbour Index is investigated in three cases, linear, 2-dimensional and 3-dimensional. In each case the formula is investigated and the numerical values for the data points to be viewed as attracting each other, repelling each other or being randomly distributed are justif...

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Bibliographic Details
Published inInternational journal of mathematical education in science and technology Vol. 39; no. 3; pp. 371 - 383
Main Author Belcher, P.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 15.04.2008
Taylor & Francis, Ltd
Subjects
1,2 and 3-dimensional model
attracting, avoiding or random
Demonstrations (Educational)
Geographic Distribution
Mathematical Formulas
Mathematics Education
Multidimensional Scaling
nearest neighbour index
Probability
Regression (Statistics)
Statistical Distributions
Statistical Significance
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Summary:In this note the Nearest Neighbour Index is investigated in three cases, linear, 2-dimensional and 3-dimensional. In each case the formula is investigated and the numerical values for the data points to be viewed as attracting each other, repelling each other or being randomly distributed are justified. Also, in each of the three cases mentioned above, when we have a random distribution of data points we have created an approximate (exact in the linear case) probability density function for D, the distance from a point to its nearest neighbour, and obtained its mean and variance. In each case a rough statistical test is devised to be able to conclude if the data points are clustered, avoiding or randomly distributed.
ISSN:0020-739X
1464-5211
DOI:10.1080/00207390701607315