A simple model using urns and marbles facilitates derivation of an apparently novel expression for the nongeometric components of variance of samples selected with equal or unequal probabilities. Further analysis of the expression permits broad conclusions as to the relative merits of equal-probability techniques compared to such unequal-probability techniques as geometric cluster-sampling with probability proportional to size, nongeometric sampling with probability proportional to prediction, and list-sampling. Probability sampling in these three major forms is not being fully exploited in forestry. It is hoped that a simplified picture of potential benefits may dispel latent misgivings.
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L. R. Grosenbaugh (1967) studied this question.
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