International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2020, Vol. 5, Issue 5, Part B

Use of the theory of Euclidean distance in testing for multivariate normality with application to breast cancer diagnostic data


Author(s): Mbanefo Solomon Madukaife

Abstract: This paper presents an adaptive technique for assessing multivariate normality (MVN). It is shown that the squared L2¬ norm otherwise known as the squared Euclidean distance of a standard d-variate normal distribution is chi-squared distributed with d degrees of freedom. Based on this, an adaptive test for MVN was proposed as the sum of squared differences between the ordered set of the squared normalized L2 norms of the observation vectors and the set of the population pth quantiles from the chi-squared distribution with d degrees of freedom. The critical values of the test were evaluated for different sample sizes and different number of random variables contained in the multivariate data through extensive simulations. For some selected sample sizes and number of random variables, the empirical power of the proposed test was compared with those of some other widely used techniques for assessing multivariate normality. The results showed that the test can be recommended as a good tool for testing MVN of a dataset especially for large sample cases. The test was applied to a data set extracted from the Wisconsin breast cancer diagnostic data and the result showed that the data set was not multivariate normal.

Pages: 128-134 | Views: 19 | Downloads: 3

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How to cite this article:
Mbanefo Solomon Madukaife. Use of the theory of Euclidean distance in testing for multivariate normality with application to breast cancer diagnostic data. Int J Stat Appl Math 2020;5(5):128-134.
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