**Method
Of Selecting A Random Sample:**

The process of selecting a random
sample involves writing the name of each element of a finite population on a
slip of paper and putting them into a box or a bag. Then they have to be
thoroughly mixed and then the required number of slips for the sample can be
picked one after the other without replacement. While doing this, it has to be
ensured that in successive drawings each of the remaining elements of the
population has an equal chance of being chosen. This method results in the same
probability for each possible sample.

**Complex Random Sampling Designs:**

Under restricted sampling
technique, the probability sampling may result in complex random sampling
designs. Such designs are known as mixed sampling designs. Many of such designs
may represent

combination
of non-probability and probability sampling procedures in choosing a sample.

Some of
the prominent complex random sampling designs are as follows:

**Systematic
Sampling:**

In some cases, the best way of sampling is to select
every first item on a list. Sampling of this kind is called as systematic
sampling. An element of randomness is introduced in this type of sampling by
using random numbers to select the unit with which to start. For example, if a
10 per cent sample is required out of 100 items, the first item would be
selected randomly from the first low of item and thereafter every 10th
item. In this kind of sampling, only the first unit is selected randomly, while
rest of the units of the sample is chosen at fixed intervals.

**Stratified
Sampling:**

When a population from which a
sample is to be selected does not comprise a homogeneous group, stratified
sampling technique is generally employed for obtaining a representative sample.
Under stratified sampling, the population is divided into many sub-populations
in such a manner that they are individually more homogeneous than the rest of
the total population. Then, items are selected from each stratum to form a
sample. As each stratum is more homogeneous than the remaining total
population, the researcher is able to obtain a more precise estimate for each
stratum and by estimating each of the component parts more accurately; he/she
is able to obtain a better estimate of the whole. In sum, stratified sampling
method yields more reliable and detailed information.

When the total area of research
interest is large, a convenient way in which a sample can be selected is to
divide the area into a number of smaller non-overlapping areas and then
randomly selecting a number of such smaller areas. In the process, the ultimate
sample would consist of all the units in these small areas or clusters. Thus in
cluster sampling, the total population is sub-divided into numerous relatively
smaller subdivisions, which in themselves constitute clusters of still smaller
units. And then, some of such clusters are randomly chosen for inclusion in the
overall sample.

When clusters are in the form of some geographic
subdivisions, then cluster sampling is termed as area sampling. That is, when
the primary sampling unit represents a cluster of units based on geographic
area, the cluster designs are distinguished as area sampling. The merits and
demerits of cluster sampling are equally applicable to area sampling.

**Multi-Stage
Sampling:**

A further development of the principle of cluster
sampling is multi-stage sampling. When the researcher desires to investigate
the working
efficiency of nationalized banks in India and a sample of few banks is required for this purpose, the first stage
would be to select large primary sampling unit like the states in the country.
Next, certain districts may be selected and all banks interviewed in the chosen
districts. This represents a two-stage sampling design, with the ultimate
sampling units being clusters of districts.

On the other hand, if instead of
taking census of all banks within the selected districts, the researcher
chooses certain towns and interviews all banks in it, this would represent
three-stage sampling design. Again, if instead of taking a census of all banks
within the selected towns, the researcher randomly selects sample banks from
each selected town, then it represents a case of using a four-stage sampling
plan. Thus, if the researcher selects randomly at all stages, then it is called
as multi-stage random sampling design.

**Sampling
With Probability Proportional To Size:**

When the case of cluster sampling
units does not have exactly or approximately the same number of elements, it is
better for the researcher to adopt a random selection process, where the probability
of inclusion of each cluster in the sample tends to be proportional to the size
of the cluster. For this, the number of elements in each cluster has to be
listed, irrespective of the method used for ordering it. Then the researcher
should systematically pick the required number of elements from the cumulative
totals. The actual numbers thus chosen would not however reflect the individual
elements, but would indicate as to which cluster and how many from them are to
be chosen by using simple random sampling or systematic sampling. The outcome
of such sampling is equivalent to that of simple random sample. The method is
also less cumbersome and is also relatively less expensive. Thus,
a researcher has to pass through various stages of conducting research once the
problem of interest has been selected. Research methodology familiarizes a
researcher with the complex scientific methods of conducting research, which
yield reliable results that are useful to policy-makers, government, industries
etc. in decision-making.