Sample Size Calculation Methodology
The LFS is based on a stratified multi-stage design. Each district was treated as an independent domain, which was then stratified into urban/rural areas. At the first stage, smaller geographic regions or clusters were selected. The indicator used to determine the first stage sample size was the “female labour force participation rate” derived from the September 2017 LFS with a margin of error less than 20 percent for all districts. The sample size was calculated using the following formula:
n^H = ( z^2* r (1-r)*deff*nrr)/[(e r)]^2 pñ)
where n^H is the number of households required. A description of the parameters as well as the values used for the calculation is provided in Table 1.
Table 1
First Stage Sample Size Calculation
| Parameters | Description of Parameters | Output Results |
|---|---|---|
| r | Female Labour Force Participation rate | 0.5072 |
| e | Relative margin of error | 0.0597 |
| Confidence (z): 95% | There is a 95% probability that the confidence interval will contain the true population mean | 1.96 ((1.96)2 is approximated to 4) |
| Design effect (deff) | The ratio of the actual variance to the variance expected with simple random sample | 3 |
| p | Females within the Working Age Population (Sub Population) | 130,475 |
| nrr | A percentage of non-responses is added to the sample. This is derived from the previous LFS round. | 1.06 |
| n ̃ | Average household size (Derived from previous labour force survey) | 3.7 |
| Total | 2,800 |
The first stage determined that 18 clusters would be selected from the following districts: Corozal, Orange Walk, Belize and Cayo and 20 clusters from Stann Creek and Toledo. To allocate the number of clusters for each Urban/Rural area, the square root N proportional method was used. The method consists in first taking the square root of the urban and rural population for each district, summing them up and then assigning a proportion of the 18 or 20 clusters to each stratum (Urban/Rural) according to the importance of the square root of the population in the urban or rural area of the district. Table 2 below shows the distribution of clusters by district and stratum.
Table 2
Sample Size by district
| Corozal | Orange Walk | Belize | Cayo | Stann Creek | Toledo | Total | |
|---|---|---|---|---|---|---|---|
| No. of Clusters | 18 | 18 | 18 | 18 | 20 | 20 | 112 |
| Urban | 7 | 7 | 11 | 9 | 7 | 6 | 47 |
| Rural | 11 | 11 | 7 | 9 | 13 | 14 | 65 |
| Margin of Error | 0.154 | 0.167 | 0.13 | 0.15 | 0.155 | 0.198 | 0.0597 |
At the second stage, households were selected within each of the clusters selected at the first stage. A total of 2,800 households were randomly selected in all six districts with 25 households to be sampled within each cluster.
The sample selection was done in a two-step process. First, to select the clusters, the sample frame was prepared from the updated database of visitation records. The sample was stratified using the 12 stratum (Urban/Rural by district). The sample was then designed to have a greater probability of sampling the larger units; thus, the probability proportional to size (PPS) without replacement method was used. The units were then defined as per the outcome in Table 2. The second step in selecting the households was completed using the simple systematic method with unit counts of 25 for each stratum.
Weighting
To obtain population estimates, weights were attributed to each sampling region. First, the sampling regions were determined taking into consideration the district, urban/rural, sex, and age group where:
s = District * 1000 + U/R * 100 + sex * 10 + age group
District: 1 = Corozal, 2 = Orange Walk, 3 = Belize, 4 = Cayo, 5 = Stann Creek, and 6 = Toledo
U/R: 1 = Urban and 2 = Rural
Sex: 1 = Male and 2 = Female
Age group:
1 = 0 to 13
2 = 14 to 24
3 = 25 to 34
4 = 35 to 44
5 = 45 to 54
6 = 55+
Second, the estimate of the population for each sampling region was determined where:
Ps = population assigned to sampling region s obtained from the current mid-month estimate weighted by totals from the 2010 census.
i.e. Ps = E * Rs / C
where E = total population by district, U/R, Sex from the latest mid-month estimates
Rs = total population of sampling region from 2010 census
C = total population by district, U/R, sex from 2010 census
Finally, the weight for each sampling region was determined where:
Ws = Ps/Ns where Ns = number of sample observations in sample region s.
