Exploration and description / Formulae

However, if the numbers of homesteads in non-sampled dip-tank areas are not known, then the best unbiased estimate of the total is: T = (M₁+...+M_n) x N/n

The among dip-tank area within sub-region component of the variance of T is calculated as U = N(N-n) S_T² where S_T² is the variance among T₁ ... T_n.

S_T² can be calculated in one of two ways:

(i) S_T² = [(T₁ - T)² + ... + (T_n - T)²] / (n-1) where T = (T_i)/n

(ii) S_T² = [(T₁ -M₁)² + ...+ (T_n -M_n)²] / (n-1)

The choice of methods is described in the next page.

We also need to include the within dip-tank area variance components S₁²... S_n² that have already been calculated.

Thus, the complete formula for the variance of T, the estimated total number of animals in the dip-tank area, is given by Var(T) = U + N (S₁²+...+ S_n²) / n.

The standard error is the square root of this expression.