Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 3, May 2015, Pages: 138-149
Received: Apr. 2, 2015; Accepted: Apr. 11, 2015; Published: Apr. 21, 2015
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Elsayed A. H. Elamir, Department of Statistics and Mathematics, Benha University, Benha, Egypt & Management & Marketing Department, College of Business, University of Bahrain, Manama, Kingdom of Bahrain
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Analysis of mean absolute deviation (ANOMAD) for randomized block design is derived where the total sum of absolute deviation (TSA) is partition into exact block sum of absolute deviation (BLSA), exact treatment sum of absolute deviation (TRSA) and within sum of absolute deviation (WSA). The exact partitions are derived by getting rid of the absolute function from MAD by using the idea of re-expressing the mean absolute deviation as a weighted average of data with sum of weights zero. ANOMAD has advantages: offers meaningful measure of dispersion, does not square data, and can be extended to other location measures such as median. Two ANOMAD graphs are proposed. However, the variance-gamma distribution is used to fit the sampling distributions for the mean of BLSA and the mean of TRSA. Consequently, two tests of equal means and medians are proposed under the assumption of Laplace distribution.
ANOVA, Effect Sizes, Laplace Distribution, MAD, Variance-Gamma Distribution
To cite this article
Elsayed A. H. Elamir, Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 3, 2015, pp. 138-149. doi: 10.11648/j.ajtas.20150403.19
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