Mean Absolute Deviation: Analysis and Applications

Abstract

One way analysis of mean absolute deviation (ANOMAD) about mean and median is derived where the total sum of absolute deviation is partition into exact between sum of absolute deviation and within sum of absolute deviation. Because of the presence of absolute function in mean absolute deviation, the middle term does not exist where it is included in each term. Therefore, the exact partitions are derived using the idea of creating error terms from the same type and take it away from each term to obtain the exact partitions. ANOMAD has advantages: does not square data and offers meaningful measure of dispersion. However, the variance-gamma distribution is used to fit the sampling distributions of between sum of absolute and within sum of absolute. Consequently, two tests of equal medians and means are introduced under the assumption of Laplace distribution. Moreover, two measures of effect sizes are re-defined and studied in terms of ANOMAD.