4.3 THE SURVEY QUESTIONNAIRE
4.3.4 SAMPLING FRAMEWORK
Often it is not practical or even possible to acquire information from all the people about whom we want to make inferences. The solution to this problem of not being able to study all the people is to select a number of people who have the characteristics in which the researcher is interested. This process of selecting part of a group under study is known as sampling.
4.3.4.1 DEFINING THE POPULATION
According to Anderson (1990:156) the first task is to define the group of interest or target population since the interest in sampling is to generalize to this target population and one cannot pick a suitable sample unless the target population is fully described. Most often, there are restrictions on membership in the target population and it is important to understand who belongs so that the researcher knows to whom the results can be generalized. Uys and Puttergill (2003:109) contend that a population is theoretically conceptualized and is a collection of cases that the researcher wants to study. They add that the boundaries of this population must be clearly marked off.
The target population for the purposes of this study is ordinary public secondary school principals in the province of KwaZulu-Natal. A public school as defined in the South African Schools Act, 84 of 1996 is a school established by the Member of the Executive Council (MEC) from funds appropriated for this purpose by the provincial legislature. An ordinary public school is distinguished from a public school for learners with special education needs (LSEN). The justification for focusing on ordinary public schools in this study is that the staffing of these schools is the competence of the MEC for Education in that particular province.
The population is also limited to principals of secondary schools in the province of KwaZulu-Natal. A secondary school is defined as a school offering grades eight to twelve. Secondary schools were chosen for two reasons:
Firstly, because the diversity of courses offered in the Further Education and Training (FET) Band makes specific demands on human resource needs and;
Secondly, the subjects/learning areas offered make specific demands on class size.
The KwaZulu-Natal Education Management and Information Systems Directorate (KZN- EMIS) was contacted in order to establish the number of ordinary public secondary schools in the province. According to Patrick Buthelezi, a Senior Manager in this Directorate, 1 453 schools fall into this category. Thus, the population size for the purposes of this study amounts to 1 453 principals.
4.3.4.2 DRAWING THE SAMPLE
According to Uys and Puttergill (2003:109), when developing a sample, a distinction needs to be made between probability and non-probability sampling. In probability sampling the aim is to select cases of the population which will provide representative information about the population. Anderson (1990:198) states that a probability sample is a miniature version of the population to which the survey findings are going to be applied. In non-probability sampling one attempts to define the sample in ways which over-represent groups with certain characteristics. Accurate representation of the population is not always possible, or lists of the population being studied are not available. Since the researcher was able to obtain a list of all 1 453 ordinary public schools in the province, the probability sampling technique was employed.
More specifically, the researcher adopted the stratified systematic sampling technique.
According to Babbie (2001:201), stratified sampling is a method of obtaining a greater degree of representativeness by decreasing the degree of sampling error. In terms of sampling theory, sampling error is reduced by two factors in the sample design:
Firstly, a large sample produces a smaller sampling error than does a small sample and;
Secondly, a homogenous population produces samples with smaller sampling errors than does a heterogeneous population.
Stratified sampling is based on the second factor in sampling theory. Rather than selecting a sample from the total population at large, the researcher ensures that appropriate numbers of elements are drawn from homogeneous subsets of the population.
According to Babbie (2001:201) the ultimate function of stratification is to organize the population into homogenous subsets (with sufficient heterogeneity between the subsets) and to select the appropriate number of elements from each. The choice of stratification variables should be primarily related to variables the researcher wants to represent accurately. In selecting the elements from the population a systematic sampling strategy was used. In a systematic sampling strategy the cases are chosen in an ordered manner by, for example, selecting each third or fifth case in the population. This, according to Uys & Puttergill (2003:111), is called the nth case.
In terms of this study, the researcher considered the geographical location of secondary schools an important stratification variable. In KwaZulu-Natal public schools are grouped into regions and districts. In order to ensure representivity, the two stratification variables of regions and districts were chosen. In KwaZulu-Natal there are four regions, namely, eThekwini, Umgungundlovu, Ukhahlamba, and Zululand. Each region is further sub- divided into three districts each (see table 4.2, page 121).
4.3.4.3 SAMPLE SIZE
According to Anderson (1990:199), the most perplexing question to a researcher is the question of sample size. From the literature reviewed by the researcher on sample size, the researcher noted that there was no fixed measure or guideline in determining sample size. The sample size suggested by scholars ranges from 10% to about 22%. The researcher, therefore, decided to note the comments made by Anderson (1990:199) with regard to sample size. He identifies four major principles governing sample size:
Variability of characteristics being estimated – the greater the variability in the characteristics being estimated among the units, the greater the number required to obtain a precise estimate of this characteristic.
Level of confidence – the laws of statistics deal in probabilities which means that although a sample will 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 could be drawn.
Tolerance for sampling error – How precise do we want the sample to be? The more precision we want the greater will be the sample size requirements.
Sample size versus proportion – a statistical fact is that the size of a sample and not the proportion of the population is the major determinant of precision. Thus, one can have a small sample with an infinitely large population and still get acceptable results. In general, the major gains in precision are made steadily as sample sizes increase to 150 or 200 after which gains in precision are much more modest.
Sekaran (1992:253) developed a table for determining the sample size from a given population (see table 4.1 below).
Table 4.1: Table for determining sample size from a given population POPULATION
SIZE
SAMPLE SIZE
POPULATION SIZE
SAMPLE SIZE
10 10 1 100 285
20 19 1 200 291
50 44 1 300 297
100 80 1 400 302
150 108 1 500 306
200 132 1 600 310
250 152 2 000 322
300 169 5 000 357
500 217 10 000 370
1 000 278 100 000 384
Adapted from: Sekaran (1992:253)
Taking into account the guiding principles advocated by Anderson, and noting the comments by Gilham (2000:14) that a typical response rate to a questionnaire is between
30% to 50%, the researcher opted for a larger sample size as possible. Therefore, the researcher chose to go with the guidelines developed by Sekaran. The researcher, based on a population size of 1 463 (rounded off to 1 500) arrived at a sample size of 306. The researcher thus chose to sample the principals of 306 ordinary public secondary schools in KwaZulu-Natal.
Owing to the fact that the researcher was able to obtain the number of ordinary public secondary schools in each region and district from the KZN EMIS database, a proportional selection of schools from the various regions and districts as suggested by Uys and Puttergill (2003:112) was done. In order to determine the number of ordinary public secondary schools to be sampled in each region, the proportion of schools in the region relative to the number of ordinary public secondary schools in the province was determined using the following formula:
The proportion obtained was then multiplied by the sample size to yield the number of schools to be sampled in each region.
Similarly, in order to determine the number of schools to be sampled in each district, the proportion of ordinary public secondary schools in each district relative to the number of ordinary public secondary schools in the region in which they are located was determined using the formula:
Proportion of schools in Region = No. of schools in Region
No. of schools in Province
Proportion of schools in District= No. of schools in District