Stratification and sample size of data sources for agricultural mathematical programming models

A comparison is made between the variance of the estimator of the total of a variable obtained from both a simple and a stratified random sampling, in which the sample sizes of some strata are equal to the stratum population size.It is shown that in this case, the advantage of the stratified sample could depend on the sample size. The paper presents inequalities that determine, as a function of the sample size, when the variance of the estimator obtained with simple sampling is lower than the variance obtained with the stratified sampling. The results give insight in order to prevent overstratification.