Statistics Dictionary

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Optimum Allocation

Optimum allocation refers to a method of sample allocation, used with stratified sampling. Optimum allocation is designed to provide the most precision for the least cost. Based on optimal allocation, the best sample size for stratum h is:

nh = n * [ ( Nh * Sh ) / sqrt( ch ) ] / [ Σ ( Ni * Si ) / sqrt( ci ) ]

where nh is the sample size for stratum h, n is total sample size, Nh is the population size for stratum h, Sh is the standard deviation of stratum h, and ch is the direct cost to sample an individual element from stratum h. Note that ch does not include indirect costs, such as overhead costs.

Note the summation term in the denominator. Subscript i identifies the stratum. The value of i ranges from 1 to M, where is M is the number of strata in the population. Thus,

Σ ( Ni * Si / sqrt (ci ) = N1 * S1 / sqrt (c1 ) + N2 * S2 / sqrt (c2 ) + ... + NM * SM / sqrt (cM )