Exploration and description / Formulae

Let us start by showing how to estimate the total number of cattle in a single dip-tank area. We shall base our calculations on formulae given by Rowlands et al. (2003) for a similar survey in Zimbabwe.

Let us consider dip-tank area i, where i represents one of the dip-tank areas sampled. Suppose that m_i homesteads are sampled in this dip-tank area and that there are M_i homesteads in total in this area. Suppose that y_ij animals are recorded per homestead (j = 1 ... m_i), and that _i represents the mean number of cattle per homestead. This can be calculated as: _i =y_ij / m_i

Then the estimate of the total number of cattle in the dip-tank area is T_i = M_ii

and the variance of T_i = M_i (M_i-m_i) s_i ²/m_i , where s_i² is the sample variance equal to

                         (y_ij - _i)² /(m_i - 1)   ( j = 1 ... m_i ).

The standard error of the total in this dip-tank area is thus the square root of the variance

=

Thus, we can write the estimate of the total number of cattle in the dip-tank area as