Assessment of Robustness of some Measures of Variation with Normal and Non-Normal Data Sets

Abstract

In any investigation where numerical values are obtained, it is always desirable to have a typical value for all the observations, and the mean as a measure of central tendency is commonly used. Reliability of the value of the mean is strengthened when a corresponding measure of variation (also known as dispersion) for the data is obtained. This paper therefore, presents a study of robustness of some measures of dispersion namely, the variance, standard deviation, absolute mean deviation with divisor ‘n’ (AMD(n)), and absolute mean deviation with divisor ‘n-1’ (AMD(n-1)). The level of robustness of the measures of dispersion in this paper was facilitated by the adoption of simulation technique that utilized the following: small sample sizes; and large sample sizes, for both normal and non-normal data sets of different specifications. Overall, the results obtained showed that AMD (n-1) gave values that were closest in magnitude to standard deviation. The implication of the findings herein is that all the three measures of spread proved to be robust, however AMD (n-1) is a better substitute for the standard deviation.