Exploration and description / Formulae

We have suggested two alternative formulae for S_T², namely the variance among the T_i s. We shall demonstrate their use in two different scenarios.

Scenario 1 : dip-tank areas selected at random with equal probabilities.

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

This is an unbiased estimate but is likely to be comparatively large, especially if dip-tank areas vary in size. We shall also assume in this scenario that knowledge of the numbers of homesteads in a dip-tank area prior to the start of a survey is not available.

Scenario 2 : dip-tank areas selected at random but proportional to dip-tank area size.

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

This estimate will tend to be smaller than in Scenario 1, especially if the average number of cattle per homestead are relatively uniform across dip-tank areas. In contrast to Scenario 1 we shall assume that we know the numbers of homesteads in a dip-tank area for all dip-tank areas in a sub-region.