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A Numerical Study of the Small Sample Properties of the Coefficient of Variation
Thesis Abstract:
The study attempted to determine the nature of bias and distribution of the coefficient of variation from small samples. The study involved machine generation of 1,000 samples. The study involved machine generation of 1,000 samples of size 4 from each of normal and gamma populations with different parameters. Using the actual 1970 population counts of the 14 towns of Zambales, 18 towns of Nueva Vizcaya and 29 towns of Rizal, all simple ramdom samples of sizes 3 and 5 were drawn, and the magnitudes of the bias and distribution of the sample coefficient of variation were observed.
The coefficient of variation from finite populations of Zambales, Nueva Vizcaya and Rizal shows that the sample CV consistently underestimates the true CV, sometimes to a seriuos magnitude. The values of relative bias for the three provinces for sample size 3 are -.56, -.05, and -.41, respectively. Hence, gross underestimation occurs when the population CV is very large(say greater than 1) and the sample size is small, and when the population is highly skewed or bimodal as in Rizal and Zambales, respectively.
The distribution of the coefficients of variation is much affected by the form of parent population. The distribution of sample coefficients of variation form gamma population is markedly skewed to the right. In the case of Zambales, the distribution is bimodal, the parent population distribution being also bimodal. For Nueva Vizcaya and Rizal, the distributin of the sample coefficient of variation is nearly symmetric.
The study implies that for sample surveys involving the province as a separate area of invistigation (stratum) and the town as a primary sampling unit, it may be possible to tell in advance whether the sample CV should not be used just by looking at the bimodality and/or extreme skewness and large variabilty(CV is greater than 1)