Abstract
Based on an interval distance, three functions are given in order to quantify similarities between one-dimensional data sets by using first-order statistics. The Glass Identification Database is used to illustrate how to analyse a data set prior to its classification and/or to exclude dimensions. Furthermore, a non-parametric hypothesis test is designed to show how these similarity measures, based on random samples from two populations, can be used to decide whether these populations are identical. Two comparative analyses are also carried out with a parametric test and a non-parametric test. This new non-parametric test performs reasonably well in comparison with classic tests.
Highlights
Today, in many tasks in which data sets are analysed, researchers strive to achieve some way of measuring the features of data sets, for instance, to distinguish between informative and non-informative dimensions
This study aims to use first-order statistics to explain the similarity between data sets
Several similarity measures between one-dimensional data sets have been developed which can be employed to compare data sets, and a new hypothesis test has been designed. Two comparisons of this test with other classic tests have been made under the null hypothesis that two populations are identical
Summary
In many tasks in which data sets are analysed, researchers strive to achieve some way of measuring the features of data sets, for instance, to distinguish between informative and non-informative dimensions. The similarity is established in the sense that one-dimensional data sets are similar by comparing the statistics of the variables in each data set. Other similarity measures between data sets are available (González, Velasco & Gasca 2005), for instance, those which are used in hypothesis testing. In this way, a non-parametric hypothesis test based on the proposed similarity is presented in this paper and a comparative analysis is carried out with several well-known hypothesis tests. Some conclusions are drawn and future research is proposed
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