EVALUATION
3. RESEARCH DESIGN AND METHODOLOGY
3.6 SAMPLING FRAMEWORK
3.6.2 DRAWING THE SAMPLE
According to Cohen, Manion and Morrison (2001: 99) one must decide whether to use a probability or a non-probability sample in the development of a sample.
A probability sample is useful if the researcher wishes to be able to make generalizations, because it seeks representativeness of the wider population. This form of sampling is popular in randomized controlled trials. On the other hand the non-probability sampling deliberately avoids representing the wider population but instead selects certain groups, a particular named section of the wider population. A probability sample will have less risk of bias than a non-probability sample which being under-representative of the whole population may demonstrate skewness or bias.
More specifically the researcher adopted the stratified systematic sampling technique.
A stratified random sample is a useful blend of randomization and categorization thus enabling both a quantitative and qualitative piece of research to be undertaken (Babbie:
2001:201). The advantages are twofold:
• A quantitative piece of research will be able to use analytical and inferential statistics.
• A qualitative piece of research will be able to target those groups in institutions or clusters of participants who will be able to be approached to participate in the research (Cohen, Manion and Morrison 2001:101).
Stratified sampling, according to sampling theory is a method of obtaining a greater degree of representativeness by decreasing the degree of sampling error by two factors in the sample design. The other factor with regard to sampling theory is that stratified sampling allows the researcher to’ organize the population into homogenous subsets with
sufficient heterogeneity between the subsets and to select the appropriate number of elements from each’ (Babbie 2001: 201).
The choice of stratification variables should be related to variables the researcher wants to represent in the data. In selecting elements from the population, a systematic sampling strategy was used. This involved selecting schools from a list in a systematic manner rather than in a random manner. The researcher decided how frequently to make
systematic selection by a simple statistic – the total number of the wider population being represented divided by the sample size required:
Frequency interval = the total number of the wider population the required number in the sample
In this study, the researcher considered geographical location of schools an important stratification variable. In KwaZulu-Natal, public schools are grouped into regions and districts.
3.6.2.1 SAMPLE SIZE
A question that plagues researchers is how large their samples for the research should be.
From the literature reviewed by the researcher on sample size, it can be noted that there is no correct clear-cut answer, for the correct sample size depends on the purpose of the study and the nature of the population under scrutiny. Anderson (1990) states that sampling size is a matter of judgment as well as mathematical precision.
Accordingly Cohen et al (2001: 93) give the following advice regarding sample size:
• The researcher must obtain a minimum sample size that will accurately target the population being targeted.
• For populations of equal size, the greater the heterogeneity on a particular variable, the larger the sample that is needed.
• To the extent that a sample fails to represent accurately the population involved, there is sampling error. The more precision required, the greater the sampling size requirement.
• Confidence level – the law of statistics deal in probabilities which means that although a sample can reflect the target population, different samples will vary
from one another. The larger the sample, the more alike on average it will be to other such samples that can be drawn.
Furthermore, Borg and Gall (1979: 194-195) advocate that in survey research there should be no fewer than 100 cases in a major subgroup and twenty to fifty in a minor subgroup. Anderson (1990: 199) states that it is a statistical fact that the size of the sample and not the proportion of the population is the major determinant of precision.
Thus one can have a small sample and an infinitely large population and still get acceptable results. In general, the major gains in precision are made steadily as sample size increase to 150 or 200.
Cohen, Mahon and Morrison (2001: 95) developed a table showing sample size, confidence levels and sampling error.
Table 3.1: Table for determining sample size from a given population.
Size of total population
Sampling error of 5% with a confidence level of 95%
Size of sample population
Sampling error of 1% with a confidence level of 99%
Size of sample population 50 44 50
100 79 99
200 132 196
500 217 476
1000 278 907
2000 322 1,661
5000 357 3,311
10000 370 4,950
20000 377 6,578
50000 381 8,195
100000 383 8,926
(adapted) Taking cognizance of Gilham (2000:14) and the comments made by Borg and Gall (1979), the researcher arrived at the conclusion that a typical response rate to a questionnaire is between 30% to 50% on a sample size of 300 based on a sample of approximately 7000 schools. The researcher was able to obtain the number of public schools and the number of educators from the KZN EMIS database. A proportional selection of schools from the regions was selected.
To determine the number of ordinary public schools to be sampled in the region the following formula was used:
Proportion of schools in Region = No. of schools in Region
The proportion obtained was then multiplied by the number of ordinary public schools sampled in the respective region. To obtain the final sample additional factors were also considered.
The researcher looked at resourced and under-resourced schools as well as the as the size of the school staff. Secondary Schools with less than 30 educators were rejected as were primary schools with less than 20 educators. It was also decided to select schools on a proportional basis giving the researcher 40% primary schools and 60% secondary schools as secondary schools incorporate both the General and Further Education and Training phases. A separate questionnaire was administered to the principals and the staff development team of selected schools to gauge the part played by management in the IQMS.
3.6.2.2 SELECTION OF SCHOOLS
In order to determine the schools that will be selected as part of the sample, the
researcher emailed to the KZN EMIS Directorate and requested copies of lists of ordinary public schools together with their postal addresses arranged according to regions. This constituted the sampling frame. One can decide how frequently to make systematic sample by using a simple formula – the total number of the wider population being
represented divided by the sample size required:
F = N/Sn where:
• F = frequency interval.
• N = the total number of the wider population. (Box 4.1)
• Sn = the required number of the sample.
The researcher was working with 1400 educators. By looking at the table of sample size one can see that 300 educators are required to be in the sample. Hence the frequency interval is:
1400/303 = 4, 62
Hence the researcher picked out every fifth school in the list of alphabetically arranged public schools in each regions. Calder (1979: 90) suggests that in probability sampling every person should have an equal chance of being selected. However, if every fifth name is selected this means that every person does not have an equal chance to be selected. To minimize this problem, the researcher decided that the initial listing will be selected randomly and the starting point for systematic sampling is similarly selected randomly.
3.6.3 ADMINISTERING THE QUESTIONNAIRE AND SECURING