You have been told that one purpose of research is to discover new
knowledge that can be generalised to a defined group.
According to Ali (1996), a central and sustainable premise upon which
scientific research is based is the investigation of a problem using a
small representational and proportionate group that is observed and from
whom findings made are generalised to all others who were not
Generalisability of research findings is dependent, as much as possible,
on the extent to which the population of the study is defined and on the adequacy of the sampling procedure used in the in the study. Since
these concepts – population and sample are of fundamental importance
to research, we shall discuss them in this unit in relation to education so that you will understand what they mean and also appreciate their
This concept population, most of the times, is used to describe the total
number of people living in a defined geographical entity or area. This is
as it relates to the common usage of the term population. But in
research, population is not limited to human beings alone, it includes
objects, events, people that have at least a common characteristic which
is common to all of them.
According to Nkpa (1997), a population refers to all the elements in a
well-defined collection or set of values. Kerlinger (1981) defined
population as all members of any well-defined class of people, events or
objects. It means therefore that any entity, group or set which
constitutes a population must have at least one attribute or characteristic
which is common to all of them.
The population of a study therefore represents the target of the study as
defined by the aims and objectives of the study. When you conduct a
research study, you have a particular population in mind. For instance,
chemistry teachers in the unity school, technical drawing teachers in Imo
State Senior Secondary Three students offering physics in the 2007
school certificate examination from Lagos State, women farmers in Etiti
agricultural zone, Professors in Nigerian Universities etc.
A research is expected to yield findings which can be applicable to the
entire universe, a section of the universe, or certain elements in the
universe. For instance, a research which aims at using an instructional
strategy to teach Igbo Language (L2) to non-Igbo speakers of Junior
Secondary Two at Federal Government College, Okigwe, may have the findings applying only to a target population which comprise the non-
Igbo speakers in F.G.C. Okigwe. In other words, the findings are
expected to be generalised only to non-Igbo speakers in JS II of F.G.C.
It means therefore that the population to which a researcher intends to
generalise his or her findings is known as the target population. If the
generalization is to the non-Igbo speakers in JS II of all the unity schools in Nigeria, then non-Igbo speakers in JS II from the unity schools in
Nigeria form the target population.
The term population often implies a huge number of people. But in research, the term represents numbers which may range from very few to very many people, things, objects, events etc. depending on the nature of investigation to be carried out. You have also noticed that in most studies, samples are drawn and studied with a view to generalizing the
findings to the entire population. However, some of the times, it is
necessary to study the entire population. This is possible under the
(i) When the research involves a population of very few subjects. If
the study involves a population of relatively few people,
institutions, objects, events or things. It is better to study the
entire population. Again, if members of the population are few
and hold views or characteristics that should not be neglected, or when sampling cannot be representative of the population, then
the entire population is studied.
(ii) When enough time and resources are available the entire
population can be studied. When there is enough time and fund
the entire population can be studied.
(iii) When the research specifically seeks to determine the population – in some situations there is a need to determine the precise
number of subjects belonging to categorized set of characteristics.
(iv) When the topic demands the study of a specific group,-
sometimes such group can be distinguished from any other group
or persons e.g. the classification of prisoners at the Okigwe
Prisons by gender and geopolitical zones.
From Section 3.1.1, you learnt that certain kinds of research can be
carried out using the entire population. When you study an entire
population, you are more able to generalise your findings to that
population. Most of the times, the target population is too large for a
researcher to study. The number of subjects may be too many for the
researcher to handle with limited resources available. The geographical
spread or area may be two wide to cover with the limited time for the
research. As a result of cost, time and other constraints, it may be very
difficult to study the entire population.
It becomes necessary, reasonable and only feasible to study a portion of
the population which is described as sample. It means therefore that the
portions of populations that are studied on the bases of which
conclusions are made on the entire populations are called samples.
These samples represent populations, so we can have samples of people,
objects, institutions and things. For instance, a researcher who wants to
study local government administration of primary education in Nigeria
may decide to take 100 out of 774 local government areas in Nigeria for
the study. If your study is on mathematics teachers in Imo State, you
can only sample a number of them. It is not possible for you to study all
education students from federal universities in Nigeria. You can only
For the purpose of your research projects, you are constrained to limit
your investigations to smaller controllable samples. To this effect, you
may be faced with a very crucial decision to make. That is, how to
select samples that will truly represent the population to which the
findings would be generalised.
If the sample does not truly represent the population, inferences drawn
or decisions taken about the population characteristics from such sample
cannot be valid, no matter how powerful the statistical techniques used.
Therefore, no new knowledge would be generated and efforts and
resources would have been wasted.
Once you have identified your target population and its characteristics,
two major issues may be required to be taken care of. These are how to
compose the samples and the sample size. The composition of the
samples will be treated in the next section.
On the issue of determining a sample size, which would adequately and
appropriately represent the population it would be drawn from, you will
note that a large sample size increases the likelihood of accurately
estimating the population characteristics from the sample. You should,
therefore, select a sample which is large enough to improve the
possibility of getting results which may be similar to what you would
have obtained if you had used the entire population. There is no single
number which has been fixed as an ideal sample size.
The sample size is dependent on a number of factors. According to Ali
(1996), such factors include:
(a) expense in terms of time and money;
(b) subjects availability to participate in the study;
(c) size of the population of the study;
(d) management and control abilities of the researcher;
(e) complexity of the research conditions and that of the data to be
collected and analysed;
(f) efficiency in drawing the sample itself;
(g) level of cooperation expected of and available from the proposed
However, a large sample is much more likely to be representative of the
Sampling techniques are simply defined as methods of drawing samples
from total populations. These methods are classified into probability
sampling and non-probability sampling;
A probability sampling is one in which chance factors determine which
elements from the population will be included in the sample. It is
therefore theoretically possible to calculate the probability that any
specific element in the population would be included in the sample. In
practice, probability sampling techniques are known to generate valid
samples that are truly representative of their large populations. This is
because of the principle that gives all the individual subjects of the
larger population equal opportunities of being selected and included as
members of the drawn samples. The probability sampling techniques
include: simple random sampling, systematic sampling, stratified
sampling, cluster sampling, etc.
3.4.2 Non-Probability Sampling
These are samples for which the probability of a member of the
population being selected cannot be calculated. According to Nkpa
(1997), statistical inferences cannot be used to legitimately to generalise
statistically from a non-probability sample to the target population.
Generalisation from non-probability sample can only be made by
satisfactorily replicating the investigation in several contents. The non-
probability sampling techniques are known to generate biased samples
which are not truly representative of the total population. The
techniques include: purposive sampling, volunteer sampling, quota
sampling, captive sampling, accidental sampling, availability sampling
3.5 Probability Sampling Techniques
This section will describe the different types of probability sampling
3.5.1 Simple Random Sampling
A critical feature of this sampling technique is that each member or
element of the defined or target population has an equal probability or
chance or opportunity of being selected, and that the selection of each
case, member or element from the population is independent of the
selection of another. By independence, in this case, we mean that the
selection of one member or element or case does not in any way affect
the selection of any other member of the population.
The main purpose of using random sampling techniques is to select a
sample which is representative of the population and which can yield
data that can be used for generalisation to a larger population.
The simple random sampling requirements of independence and equal
probability are met by the use of a variety of methods. These are;-
(a) Balloting or Hat and Draw method
This is otherwise called the lottery method in which all the subjects in
the population are listed or numbered in cards or papers. These papers
are shuffled and re-shuffled. These cards are then drawn from the
container one by one, with or without replacement. Any number picked
up forms part of the sample.
(b) Table of Random Numbers
This is a more systematic, refined and scientifically generated random
numbers. It is a continuous sequence of numbers which do not appear in
any particular order and which is generated by computers. In recent
times, many tables of random numbers have been generated by
computers. These include Snedecor and Cochran’s (1969), Ten
Thousand Random Numbers; The Million Random Digits with 100,000
Normal Deviates by Rand Corporation (1965), Table of 105,000
Random Decimal Digits by the Interstate Commerce Commission
(1979) etc. Some statistical textbooks contain table of random numbers
in their appendices.
To use the table of random numbers, you have to number the population
serially from one to the last person, event, object, case of element. You
can then, at random, select a number from any page or point, row or
column and draw your sample using the first two, three or four digits or
you can use the last two, three or four digits. During the process of
drawing your samples, if a number appears twice, or a number is larger
than the population size, you have to ignore such numbers and continue
until your sample size is composed.
The limitation in the use of simple random sampling is that, it can only
be used with small population, since you have to enumerate or number
all the subjects in the population.
3.5.2 Systematic Sampling
This involves, first listing in a serial order, all the events, persons,
objects or things in the whole population. After this, the population (N)
is divided by the sample size (n) to get the Kth interval. Once the Kth
case is decided, all others are automatically selected. For instance,
assuming you have a population of 1,000 people and your sample size is
100. Then Kth position will be given by N/n = 1000/100 = 10. It means
that every 10th position or interval is automatically selected as part of the
Thus, numbers 10, 20, 30, 40, etc. are already selected. You can even
select any number: 1, 2, 3, …. 10 as the Kth number. For example, if
the Kth case is 5, then 5, 15, 25, 35, 35 etc. become members of the
You would have noticed that independence is not ensured in systematic
sampling. This is because, once the first member – Kth is selected,
every other member of the sample is automatically determined. This is a
limitation in the use of this method.
3.5.3 Cluster Sampling
When the population of the study is very large and widely dispersed or
spreads out, it poses administrative problems to use simple random
sampling. For instance, in a population comprising of all junior
secondary school students in the South East zone you will note that it
will not be easy to enumerate all the members of the population. Again,
it will be impractical to sample from every school. You have noted that
a researcher is always interested in composing a sample which must
represent the characteristics of the target population. But the
characteristics of any given population can be quite enormous.
Therefore, in cluster sampling, the researcher identifies his research
interest characteristics and where or in what areas these characteristics
exist. If the population is large or the area is widespread, he may decide
to zone the area reflecting these characteristics and then random samples
from each of the identified zones.
The emphasis here is on the characteristics of the sub-group and not on
individual. For example, in using the population of all junior secondary
school students, one may decide to sample schools. It means therefore
that any school selected forms a unit of the study. All the students in
that school will be used. Another example is that of a researcher who
wants to use three Nigerian languages – Igbo, Hausa and Yoruba for his
research study. Definitely, he will select the Igbos from the South East,
Hausa from the North and Yorubas from the West. This is because, if
he wants to get his sample from Nigerians, he may end up getting
respondents who are not Igbo, Hausa or Yoruba.
Cluster sampling saves time and resources. It is mostly used in research
where there is an urge or desire to study the characteristics of
respondents in their natural settings or to ensure geographic
representation of noted groups whose special characteristics are of
interest to the researcher.
3.5.4 Stratified Sampling
In a given population, there exists abundance of population
characteristics. A whole range of differences can exist even within a
particular characteristic. For instance, in using weight of individuals,
you have heavyweights, lighter weights, cruiser weights, feather weights
etc. In many educational studies, you will notice that the population is
by nature stratified. You have differences in gender, occupation,
income, socio-economic status, geographical location, qualifications,
age, height, colour, dialects etc.
Stratified sampling is appropriate when the population consists of a
number of sub-groups which are homogeneous or contain members that
share common characteristics, which need to be represented in the
sample. Randomisation is then used to select members from the sub-
groups in such a way that the proportion of each sub-group in the
population is reflected in the sample.
Stratified sampling is appropriate when the study is required to compare
sub-groups or when the sub-groups are likely to influence the level of
the dependent variable.
SELF-ASSESSMENT EXERCISE 3
1. What are the major features of probability sampling?
2. What are the probability sampling techniques?
3.6 Non-Probability Sampling
This can be called biased sampling or non-random sampling technique.
This is because the chances of an element, person, object, event, thing
etc. being included in the sample are not the same. Some may have
more advantages than the others. It does not involve randomisation and
therefore may have high sampling error and generalisation is limited.
The non-probability sampling techniques are further subdivided into:
3.6.1 Purposive Sampling
This is necessitated when the researcher is interested in certain specified
characteristics. It ensures that only those that meet such required
purpose, attributes or characteristics are selected. For instance, a study
of the Vice Chancellors of Federal Universities in Nigeria, or a study
comprising Local Government Chairmen in Imo State.
In these cases, you will notice that you can only use those who are Vice
Chancellors in Federal Universities or the Local Government Chairmen
in Imo State. They are few and are known.
3.6.2 Volunteer Sampling
This is used when every member of the population cannot comply with
the demands of the investigation. Therefore, these individuals who are
willing to comply with the demands of the investigations are used.
These are the volunteers who are willing and ready to cooperate with the
But this is a biased sample because those volunteers differ from the
entire population and from the non-volunteers in many of the
3.6.3 Captive Audience
This is just like an intact class used by the teacher for a research
purpose. The generalisation should not go beyond the class.
3.6.4 Quota Sampling
In this method, the researcher selects a certain number of respondents in
proportion to their number in the population, but without randomisation.
A good example is where all the states in Nigeria are given quota
admissions in federal universities or unity schools.
3.6.5 Accidental Sampling
This can be called availability sampling. This is because it makes use of
the respondents available at the time. Participation is based on
availability. This is very common with pressmen or journalists. They
interview or use anybody available at the time.
From this unit, you have seen that, as a researcher in education, you
must randomly compose the sample you intend to use for any
investigation. When you use non-random and biased samples, the laws
of probability no longer hold. The samples are not truly representative
of the target population and so have large number and variety of
The results of such investigations are unsustainable and applicable to the
samples alone. Sample sizes that are large and composed using