Sample designs may be classified into different categories based on two factors, namely, the representation basis and the element selection technique. Under the representation basis, the sample may be classified as

- Non-probability sampling
- Probability sampling

While probability sampling is based on random selection, the non-probability sampling is based on ‘non-random’ selection of samples.

### Non-Probability Sampling

Non-probability sampling is the sampling procedure that does not afford any basis for estimating the probability that each item in the population would have an equal chance of being included in the sample. Non-probability sampling is also known as deliberate sampling, judgment sampling and purposive sampling. Under this type of sampling, the items for the sample are deliberately chosen by the researcher; and his/her choice concerning the choice of items remains supreme. In other words, under non-probability sampling, the researchers select a particular unit of the universe for forming a sample on the basis that the small number that is thus selected out of a huge one would be typical or representative of the whole population. For example, to study the economic conditions of

people living in a state, a few towns or village may be purposively selected for an intensive study based on the principle that they are representative of the entire state. In such a case, the judgment of the researcher of the study assumes prime importance in this sampling design.

#### Quota Sampling

Quota sampling is also an example of non-probability sampling. Under this sampling, the researchers simply assume quotas to be filled from different strata, with certain restrictions imposed on how they should be selected. This type of sampling is very convenient and is relatively less expensive. However, the samples selected using this method certainly do not satisfy the characteristics of random samples. They are essentially

judgment samples and inferences drawn based on that, would not be amenable to statistical treatment in a formal way.

#### Probability sampling

Probability sampling is also known as ‘choice sampling’ or ‘random sampling’. Under this sampling design, every item of the universe has an equal chance of being included in the sample. In a way, it is a lottery method under which individual units are selected from the whole group, not deliberately, but by using some mechanical process. Therefore, only chance would determine whether an item or the other would be included in the sample or not. The results obtained from probability or random sampling would be assured in terms of probability. That is, the researcher can measure the errors of estimation or the significance of results obtained from the random sample. This is the superiority of random sampling design over the deliberate sampling design. Random sampling satisfies the law of

statistical regularity, according to which if on an average the sample chosen is random, then it would have the same composition and characteristics of the universe. This is the reason why the random sampling method is considered the best technique of choosing a representative sample.

The following are the implications of the random sampling

- it provides each element in the population an equal probable chance of being chosen in the sample, with all choices being independent of one another and
- it offers each possible sample combination an equal probable opportunity of being selected.

### 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 a 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. A sampling of this kind is called 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 the 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, the 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, the stratified sampling method yields more reliable and detailed information.

#### Cluster Sampling

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.

#### Area Sampling

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 39banks 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 a 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 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 the simple random sample. The method is also less cumbersome and is also relatively less expensive.

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