Major types of probability sampling are: simple random

sampling, stratified random sampling and cluster

sampling.

### Simple Random Sampling

A process that gives each element in the populationan equal chance of being included in the sample

is termed as simple random sampling. The elements

are selected, using a list of random numbers appended

with most textbooks of research and statistics. Before

using the table of random numbers, it is first necessary

to number all the elements in the population to be

studied. Then the table is marked at some point

and the cases whose numbers come up as one from

this point down the column of numbers are taken

into the sample until the desired number of elements

is obtained. The selection of any given element places

no limits on other element being selected, thus

making equally possible the selection of any one

of the many possible combinations of elements.

Proportionate Stratified Random Sampling

In stratified random sampling, the population is first

divided into strata. The strata may be based on a

single criterion or on a combination of two or more

criteria. After, stratification a simple random sample

is taken from each stratum, and the sub samples

are then joined to form the total sample.

In case the researcher is interested in the study

of some characteristics of a phenomenon he uses

a proportionate stratified random sampling plan. Of

course, this sampling design presupposes that the

investigator has some knowledge concerning the

population characteristics such as age, sex, marital

status etc.

In the sampling plan the sample will have specified

characteristics in exact proportion to those same

characteristics which are distributed in the population.

To understand this sampling plan we will consider

the following example.

Let us consider the students of a College of Social

Work. The researcher wishes to have proportionate

stratified random sample of them taking year of

study in the college as basis of stratification. Let

us suppose that the students at this college are

distributed as is shown in Table below:

Table : Distribution of Students According to

Year in College

Year Population Proportion of each class

BSW I 50 .25

BSW II 40 .20

BSW III 30 .15

MSW I 40 .20

MSW II 40 .20

Total 200 1.00

Further, we suppose that the researcher decides

to have a sample of 60 students. First, he determines

the proportion of students in each class (as shown

in the second column). Then he calculates the

composition of the sample taking each proportion

of the stratifying characteristics in the population and multiplying it by the desired size of the sample.

Thus, he multiplies 60, the desired sample size by

.25, the proportion of BSW first year students in

the population or

(60) (.25) = 15

As such, he has to include 15 students from the

BSW first year in his sample. This precedence is

repeated for each year as described below:

(60) (.25) = 15

(60) (.20) = 12

(60) (.15) = 9

(60) (.20) = 12

(60) (.20) = 12

Sample Size (N) = 60

Table : Distribution of Students by Proportion

Year Sample Break-up Proportion

BSW I 15 .25

BSW II 12 .20

BSW III 9 .15

MSW I 12 .20

MSW II 12 .20

Total Sample (n) 60 1.00

After having determined the sample size from each

subcategory, the researcher uses simple random

sampling for drawing the desired number of elements

from each category.

### Disproportionate Stratified Random Sampling

This sampling plan is almost similar to proportionatestratified random sampling except that the sub samples

are not necessarily distributed according to their

proportionate weight in the population from which

they were drawn. It is possible that some sub samples

are over represented while other sub groups are

under represented.

Let us suppose that the researcher stratifies the

population into two sub strata using sex as the criteria.

He would get the following break-up of the population:

Table : Distribution of Students by Sex

Sex No. of Students Percentage

Male 160 80

Female 40 20

Total 200 100

If the researcher wants to draw a disproportionate

stratified random sample of 60 from this population,

stratified by sex, then he has to draw 30 from each

substrata, this means male students (30) will be

under represented and female students (30) will be

over represented in the sample. In other words

disproportionate sampling gives equal weights to each

substrata.

There is a clear improvement over simple random

sampling when the sampling is based on a stratification

of population by sex. With this kind of stratification

we get a marked increase in the size of samples

that yields statistics very close to the population

parameters. On the contrary, a reduction in the

size of sample may yield statistics that might deviate

widely from the population parameters.Cluster Sampling

In case the area of study is wide spread, a large

expenses are involved if simple and stratified random

sampling are used. For example, in the preparation

of sampling frame from the population and in covering

the widespread areas by interviewers, a large amount

of expenditure is required. The more widely spread

the area of study, the greater are the travel expenses,

the greater is the time spent in travelling, and

hence expensive — and the tasks of administering,

monitoring and supervision of the research project

and in particular supervising the field staff become

more complicated. For the reasons mentioned above

and few other reasons, large-scale research studies

make use of the methods of cluster sampling.

In cluster sampling, first the whole research area

is divided into sub area, more commonly known as

“clusters”. The simple random or stratified method

is used to select clusters. Finally, researcher arrives

at the ultimate sample size to be studied by selecting

sample from within the clusters, which is carried

out on a simple or stratified random sampling basis.

Let us suppose, for example, that we want to do

a survey of beggars in urban areas of a state. We

may proceed as follows: prepare a list of districts

and group them into clusters, and select a simple

or stratified random sample from each clusters. For

each of the districts included in the sample, list

the cities/towns and take a simple or stratified

random sample of them. If some or all of the towns/

cities thus selected for the sample have more numbers

of beggars that can be studied, we may take a sample

of these towns/cities in each district. The beggars

in these towns/cities will be the sample of the beggars.

Characteristically, the procedure moves through a

series of stages—hence the common term, “multistage”

sampling—from more inclusive to less inclusive sampling

units until we finally arrive at the population

elements that constitute the desired sample.

The four important types of non-probability sampling

are accidental sampling, quota sampling, snowball

sampling and purposive sampling.

### Accidental Sampling

Accidental sampling refers to a method of selectingrespondents who happen to meet the researcher

and are willing to be interviewed. Thus, a researcher

may take the first hundred people he meets who

are willing to be interviewed.

For example, let us consider the situations where

a programme director, wishes to make some

generalisation about the programme in progress, selects

beneficiaries who have come to the agency for a

service or a community organiser, trying to know

how “the people” feel about health status in that

community, interviews available community dwellers

like shop-keepers, daily wage earners, barbers and

others who are presumed to reflect public opinion.

In both the situations those who are available for

study are included in the samples. This is exactly

what we call accidental sampling. It is very obvious

that the sample so collected are biased and there

is no known way (other than by doing a parallel

study with a probability sample) of evaluating the

biases introduced in such samples. However, in the

situation illustrated above, most probably, accidental

sampling is the only way out because of the reason

that the population parameters of the beneficiaries

or the community people are not available with the

researcher.

### Quota Sampling

Quota sampling insures inclusion of diverse elementsof the population in the sample and make sure that these

diverse elements take account of the proportions

in which they occur in the population. For example,

we take a sample from a population with equal number

of boys and girls, and that there is a difference

between the two groups in the characteristic we

wish to study and we fail to interview any girl, the

results of the study would almost certainly be

extremely misleading generalisations about the

population. In practice, elements in small numbers

are frequently under represented in accidental

samples. In anticipation of such possible exclusion

of small groups, quota sampling ensures inclusion

of enough cases from each stratum in the sample.

It should be noted here that the major goal of quota

sampling is the selection of a sample that is a replica

of the population to which one wants to generalise.

Hence it should be clear that the critical requirement

in quota sampling is not that the various population

strata be sampled in their correct proportions, but

rather than there be enough cases from each stratum

to make possible an estimate of the population stratum

value (Kidder, 1981, p. 426). Quota-sampling, however,

is more or less similar to the earlier described

accidental sampling procedure except that it insures

the inclusion of diverse elements of the population.

### Purposive Sampling

Purposive sampling is based on the presumption thatwith good judgment one can select the sample units

that are satisfactory in relation to one’s requirements.

A common strategy of this sampling technique is

to select cases that are judged to be typical of the

population in which one is interested, assuming

that errors of judgment in the selection will tend

to counterbalance each other. For example, if a

researcher is conducting a study of patients who

are not regular in attending out patient department

it might be desirable to choose patients for the sample

from among those who are frequently irregular.

The causes of irregularity can be described by irregular

patients only. If he selects a random sample he

would have got patients who are regular and that

might influence the findings of the study. It is also

possible that in a truly random sample, the regular

patients would nullify the effects of irregular patients.

### Snowball Sampling

Snowball sampling is externally helpful in studyingsome special sampling situation like getting a sample

of drug abusers, or alcoholics or pickpockets. In

snowball sampling we start with a few respondents

of the type we wish to include in our study and

who in turn are expected to guide us to get more

respondents and so on. Like the rotating snowball,

sample increases in its size as we continue to get

more units of study. The technique is especially

useful in the investigation of sensitive topics mentioned

above because this sampling technique depends on

sampled cases having knowledge of other similar

cases. Another argument in favour of using this

sampling technique is that, the victims might be

hesitant to identify themselves if approached by a

stranger but might be friendly to someone who they

know and share their experiences or deviant status

(Gelles, 1978).