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Procedures for determining optimal two-stage sampling designs are well documented when a single variable is measured. Many surveys, however, measure several variables simultaneously, in which case the overall optimal sampling plan is traditionally chosen from among the optima for each variable considered individually. We use a graphical approach to illustrate that the traditional method is not always appropriate and that intersections of variance constraints should be considered as candidates for the overall optimum.

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(1919). XXXII.—The status of Parabates, Foerster, and Parabatus, Thomson [Hymenoptera, Ichneumonidae] Annals and Magazine of Natural History: Vol. 3, No. 16, pp. 319-324.

(1886). More Notes on Phœnician Gems and Amulets. Palestine Exploration Quarterly: Vol. 18, No. 1, pp. 43-50.

(1873). Notes on the Coptic Dayrs of the Wady Natrun and on Dayr Antonios in the Eastern Desert. Archaeological Journal: Vol. 30, No. 1, pp. 105-116.

(1931). XIX.—The identity of Campsomeris aureola, Saussure (nec Klug), and of Curvivittata, Cameron (Hymenoptera, Scoliidae) Annals and Magazine of Natural History: Vol. 8, No. 44, pp. 167-173.

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(1889). The Tell es Salahiyeh Monument; The “Via Maris.”; Note on a Coin Engraved on p.77, Quarterly Statement, 1889. Palestine Exploration Quarterly: Vol. 21, No. 3, pp. 152-153.