3.3 Data and sources
3.3.1 Study area
This study was carried out in Rwanda's Southern province,
particularly in Gisagara district. A district is an administrative unit that
comes next to the province (the highest local administrative unit) while a
sector is an administrative unit that comes next to the district. There are 13
sectors (Nyanza, Kigembe, Kansi, Kibirizi, Muganza, Mugombwa, Mukindo, Musha,
Gishubi, Mamba, Gikonko, Ndora, and Save) in Gisagara district. More
information about Gisagara district is provided in appendix 2 and appendix 3.
Gisagara district was purposively chosen because land fragmentation is so
common there (Bizimana et al., 2004 and Musahara, 2006).
3.3.2 Sampling methods
In this study, a two-stage sampling technique was used to
select the sample. Stage one involved a random selection of sectors. Out of the
13 sectors, 7 were randomly selected and these were Save, Kibirizi, Kansi,
Musha, Gikonko, Gishubi and Mamba. Simple random sampling was applied at stage
one.
A sampling frame (a list of households) was obtained for each
sector and at stage two respondents were selected from each sector using
systematic random sampling (whereby the first kth household was
selected randomly) as shown in table 3.4 below. A sample size of 280 households
was selected.
However, after excluding outliers, a sample size of 241
households remained. Primary data for this study were collected using a
structured household questionnaire (see appendix 1). The structured household
questionnaires were administered to respondents by enumerators under
supervision of the researcher. The field survey was conducted from
20th May 2009 to 25th June 2009.
Table 3.3: Systematic random sampling
procedure
|
Sector
|
Total Households ()
|
Desired Sample size (
|
th interval ()
|
|
Kibirizi
|
5530
|
40
|
138
|
|
Kansi
|
4055
|
40
|
101
|
|
Gikonko
|
4420
|
40
|
111
|
|
Gishubi
|
5084
|
40
|
127
|
|
Mamba
|
6677
|
40
|
167
|
|
Musha
|
4853
|
40
|
121
|
|
Save
|
5640
|
40
|
141
|
|
Total
|
36259
|
280
|
|
Source: the sampling frames were obtained
from each sector's official reports
3.3.3 Data analysis
Data collected were coded, entered and cleaned using the
Statistical Package for Social Scientists (SPSS) computer program. The data
were then transferred to Stata in which econometric analyses were carried out.
Diagnostic tests (to check for normality, multicollinearity and outliers) were
then carried out. As a result, 39 outliers were removed leaving a sample size
of 241 households. Descriptive statistics (percentages, means and standard
deviations) were generated.
A Cobb-Douglas stochastic production function was estimated
using the single-step procedure suggested by Kumbhakar et al. (1991) that
produces maximum likelihood estimates of the stochastic production function.
This procedure is superior to the two-stage procedure because it does not
violate the assumption that the inefficiency effects are independently and
identically distributed (Battesse and Coelli, 1995).
| 
