A Note on the Stability of the Estimates of Standard Errors of the Ordinary Mean Estimate and the Ratio Estimate

Abstract

Summary

The stabilities of the estimates of standard errors of the ordinary mean estimate and the ratio estimate are compared for bivariate normal and log normal distributions. Two numerical examples are also given. It is found that an estimate of the standard error of the ordinary mean estimate is always more stable than an estimate of the standard error of the ratio estimate in the case of simple random sampling from a bivariate normal population. For samples from a bivariate log normal population also this property holds for certain ranges of k and C² , as seen from Table 1. The numerical examples also support this result. Hence there is need for caution in the indiscriminate use of ratio method of estimation. Only sampling with replacement is considered here, but it is likely that the conclusions drawn in this paper hold approximately well in the case of simple random sampling without replacement also.