# Likelihood Distance Test

Posted in Statistics, Total Reads: 900

## Definition: Likelihood Distance Test

Likelihood distance test finds a wide application in cluster analysis or classification analysis or numerical taxonomy. This in turn helps in i) market segmentation ii) understanding buyer behavior iii) identifying new product opportunities iv) selecting test markets. To measure the similarity or likelihood of observations often a distance measure is needed. With a single variable, the distance measure can be simple and straightforward.

For example, two individuals can be considered similar if they have similar income levels. The dissimilarity increases as the gap in the income or the distance increases. For multiple variables, an aggregate distance measure is used to measure the likelihood. The most well-known measure of distance used is the Euclidean distance. Let us consider that the dataset is characterized by a set of numbers.

Data 1: (x11, x12… x1n)

Data 2: (x21, x22… x2n)

Data 3: (x31, x32… x3n)

…….

Data p: (xp1, xp2… xpn)

Distance: Euclidean distance, dij,

Dij: = √ ((xi1-xj1)^2 + (xi2-xj2)^2 + ….. + (xin-xjn)^2)

The test finds wide application because of its robustness and simplicity. Diiferent algorithms can be used in conducting the test on a set of clusters. These include

• Ward algorithm

• centroid method

These algorithms do not follow hierarchy and produce a single partition. Algorithms vary according to the way the distance between two clusters is defined.

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