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In this paper, we shall study an alternative method of deriving Neyman's Optimum allocation of sample size to strata for simple random sampling which is intuitive and simple. In order to obtain this allocation, the within stratum standard deviations of the study variate are required which are unknown and hence are substituted by known quantities. We shall discuss the effects of deviations from the optimum allocation and other related problems.

In this paper we shall consider the problem of judging how good an actual compromise allocation is compared to Neyman's optimum allocation for the case of stratified random sampling by obtaining a bound to the ratio of the corresponding variances. A solution to a more general version of the problem considered by COCHRAN (1977) and RAO (1983) has been obtained and the results have been empirically demonstrated.