In 1954, A.M. Mood developed the square rank test for dispersion known as Mood test. It is based on the sum of squared deviations of the ranks of one sample from the mean rank of the combined samples. The null hypothesis is that there is no difference in spread against the alternative hypothesis that there is some difference. The Mood test assumes that location remains the same. It is assumed that differences in scale do not cause a difference in location. The samples are assumed to be drawn from continuous distributions.
In two-sample scale tests, the population distributions are usually assumed to have the same location with different spreads. However, Neave and Worthington (1988) cautioned that tests for difference in scale could be severely impaired if there is a difference in location as well.
In a two-sample problem composed of X = { x 1, x 2, …, x m } with distribution F(X) and Y = { y 1, y 2, …, y n } with distribution G(Y), arrange the combined samples in ascending order of...
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References and Further Reading
Bradley JV (1978) Robustness? Br J Math Stat Psychol 31:144–152
Fahoome G (2002) Twenty nonparametric statistics and their large sample approximations. J Mod Appl Stat Meth 1:248–268
Fisher RA (1935) The design of experiments. Oliver and Boyd, Edinburgh
Mood AM (1954) On the asymptotic efficiency of certain nonparametric two-sample tests. Ann Math Stat 25:514–522
Neave HR, Worthington PL (1988) Distribution-free tests. Unwin Hyman, London
Odiase JI, Ogbonmwan SM (2008) Critical values for the Mood test of equality of dispersion. Missouri J Math Sci 20(1):40–52
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Odiase, J.I., Ogbonmwan, S.M. (2011). Mood Test. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_378
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