*3.2. Sampling Procedure and Sample Size Determination*

A multiple-stage sampling procedure was employed. Firstly, Northern Cape Province was chosen from the nine provinces of South Africa, because most households were involved in livestock production, and the province was declared a disaster zone by the South African Government due to agricultural drought. Secondly, four district municipalities in the province were randomly selected using balloting and included Dikgatlong, Magareng, Sol Plaatje, and Phokwane.

**Figure 2.** Maps of South Africa highlighting Northern Cape Province, district municipalities of the Northern Cape, and the four local municipalities of Frances Baard District Municipality. Source: FBDM [38].

Appropriate sample sizes were calculated using the simple random sampling formulae of Cochran [39] and Bartlett et al. [40]. Subsequently, 217 smallholder livestock farmers were selected from 878 farmers registered for government and local government assistance during the 2015/2016 production season (Table 1); this season was the worst drought season in South African history [41]. The assistance from the government included feed and medication for livestock, strengthening access to agricultural credit and farm input, and enhancing smallholder farmers' involvement in agricultural drought resilience activities by giving training and disseminating information.


**Table 1.** Number of farmers who received assistance from the government and sampling procedure.

Note: The "×" represents multiplication. Sources: Northern Cape Department of Agriculture, Forestry and Fisheries (NDAFF) [41], beneficiaries of drought relief program.

A sample of 217 smallholder livestock farmers were interviewed. Cochran's [40] sample size formula was applied to determine the correct sample size (Equation (1)):

$$\text{Sample size } = \frac{\text{(y)}^2 \* \text{(f)}\text{(g)}}{\text{(z)}^2} \tag{1}$$

where y is the level of confidence/alpha level, f and g are the estimates of the variance of the population, and z is the margin of error (5% (0.05)). Therefore (Equation (2)):

$$\text{Sample size} = \frac{\left(1.65\right)^2 \* \left(0.515\right)\left(0.515\right)}{\left(0.05\right)^2} \\ \text{Sample size} = 288.3\tag{2}$$

Resulting in a sample size of 288.3. Note that, if the sample size exceeds 5% of the population, the Cochran's correctional formula should be applied (Equations (3) and (4)):

$$\text{N1} = \frac{\text{Sample size}}{1 + (\text{N0}/\text{population})} \tag{3}$$

$$\text{N1} = \frac{288.83}{1 + (288.83/878)}\\\text{N1} = 217 \tag{4}$$
