# Research methodology

21 min readINTRODUCTION

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

investigated.

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

importance.

Population:

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.

Okigwe.

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

following conditions:

(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.

Sample:

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

take samples.

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

sample/

However, a large sample is much more likely to be representative of the

population.

Sampling Techniques:

Sampling techniques are simply defined as methods of drawing samples

from total populations. These methods are classified into probability

sampling and non-probability sampling;

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

etc.

3.5 Probability Sampling Techniques

This section will describe the different types of probability sampling

techniques.

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

sample.

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

sample.

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

researcher.

But this is a biased sample because those volunteers differ from the

entire population and from the non-volunteers in many of the

characteristics.

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.

4.0 CONCLUSION

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

sampling errors.

The results of such investigations are unsustainable and applicable to the

samples alone. Sample sizes that are large and composed using

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