# Methods of Sampling

Methods of Sampling: There are two types of sampling such as probability sampling and non-probability sampling (Fig). Probability sampling is one in which every unit of the population has an equal probability of being selected for the sample. Non-probability sampling does not claim representativeness, as every unit does not get the chance of being selected. Probability sampling is based on the concept of random selection, whereas non-probability sampling is ‘non-random sampling.

## Probability or Random Sampling

Probability sampling methods are those in which every item in the population has a known chance or probability of being chosen for the sample. This method is a primary method for selecting large, representative samples for social science and business researchers. In this sampling design, the population must be clearly defined and a list of target populations must be available. It is a lottery method in which individual units are picked up from the whole group by some mechanical process. Probability sampling is also known as chance sampling or random sampling. This sampling technique provides estimates which can be measured precisely and are inherently unbiased. It is possible to evaluate the relative efficiency of various sample designs in probability sampling. It requires a high degree of skill level, expertise, and a lot of time to plan and determine a probability sample. The cost involved in probability sampling is higher as compared to non-probability sampling. There are several methods used for probability sampling such as simple random sampling. systematic sampling, stratified sampling, multiple sampling, multi-stage sampling, cluster sampling, etc.

### Simple Random Sampling:

This method is the most common technique for selecting a probability sample. The random sampling method of selection assures each element of the population has an equal and independent chance of being included in the sample. Items in the sample are selected completely independently of each other. The selection of one unit does not influence the selection of other units. There is no chance of bias of any kind in the selection of sample units. In a simple random sampling method, the investigator can keep himself away from prejudices, bias, and other elements of subjectivity.

• This method is free from bias, prejudices, and free from personal error.
• It is a quite simple method, follows mathematical procedures and there is no need for advanced knowledge of the population.
• It is a less expensive and easily practicable procedure if the population is not large.
• It is representative of the universe, each unit has an equal chance of being selected.
• Assessment of the accuracy of the results is possible by simple error estimation.

The disadvantages of this method are:

• The representativeness of the sample cannot be ensured by this method.
• Random sampling method is not useful for heterogeneous units.
• It requires the study of a whole population and individual characteristics of each item are difficult to study.

A random sample can be selected by the lottery method, Tippet’s number method, grid system, and selection from a sequential method.

(a) Lottery Method: In this method, a lottery is drawn by writing the numbers or the name of various units and putting them in a box. Instead of pieces of paper, plastic discs or Coins can also be used. They are thoroughly mixed and certain numbers are picked up from the box as a sample. This method is suitable for drawing a small number of samples from a small universe.

(b) Tippet’s Number Method: Tippet has constructed a four digits random list of 10,400 institutions. These numbers are the results of combining 41,600 population statistics reports. The random numbers are quite suitable if the size of the population is large. A researcher wants to select 500 supervisors from a sugar cane industry out of a total of 10,000. A supervisor from the list should be numbered and then random numbers should be used to make the selection. For framing the random numbers from 1 to 10,000, open a page of Tippett’s, and then the first 500 numbers are selected. The selection of 500 supervisors will be included in the sample.

(c) Grid System: The map of the entire area is prepared and then a screen with a square is placed upon the map. The squares are selected by a random process. The areas falling within the selected squares are taken as samples.

(d) Selection from Sequential Method: In this method, units are arranged serially according to some particular orders such as alphabetical, numerical, or geographical sequence. Then out of the list, every 5th, 10th, or any other number may be taken up. For example, if we want to select 15 persons, then start from 15th and select 15th, 30th, 45th, 60th, 75th, and so on.

### Stratified Sampling:

This method of selecting samples is a mixture of deliberate and random sampling techniques. In this method, the units of data in a domain are split into various classes or groups (strata) based on their characteristics, and then certain items are selected from these classes by the random sampling technique. This method is also called a mixed technique of sampling.

According to this method, first, the population is divided into homogeneous groups or strata and a sample is taken from each stratum. The basis of classification may be sex, age, class, religion, income, education, landholding, etc. which is known as the stratification factor. The stratification factor is selected in correlation with the problem under study, which becomes a logical basis of stratification.

Each stratum in the universe should be large enough so that the selection of items may be done on a random basis.

The advantages of this method are:

• It is a good representative of the population and it has greater accuracy.
• It is more precise and to a great extent avoids bias.
• Sample size may be small in this method that saves time and cost of data collection.
• This method is mostly used for geographical purposes.

The disadvantages of the stratified sampling method are:

• It requires the knowledge of the traits of the population.
• Stratification or classification sometimes becomes difficult and assignment of each unit of the population to a particular stratum can be even more difficult.
• Attainment of proportion becomes particularly difficult when there is a wide variance in the size of different strata.
• The result sometimes has to be weighted according to the size of strata, which is a difficult task.

There are two types of stratified sampling methods:

(a) Proportionate Stratified Sampling: In this method, a selection from each sampling unit of a sample that is proportionate to the size of the unit or stratum. It gives more representativeness concerning variables used as the basis of classifying categories and increased the chances of being able to make comparisons between strata.

(b) Disproportionate Stratified Sampling: In this method, an equal number of cases are taken from each stratum without any consideration to the size of strata in proportion to the universe. This method of sampling is more effective for comparing strata that have different error possibilities.

(c) Systematic Sampling: In this systematic sampling, only the first unit is selected randomly and the remaining units of the sample are selected at fixed intervals. This method is popularly used in those cases where a complete list of the population from which a sample is to be drawn is available. A voter list, a telephone directory, or a card index system mainly satisfy the conditions of systematic sampling. The researcher first has to arrange the units of the universe on the same basics such as alphabetical, chronological, geographical, numerical, ascending order of capital employed or labor employed, etc.

The first item is selected at random by the lottery method. Subsequent items are selected by: taking every Kth item from the list.

K= N/n

where K is the sampling interval, N is universe size and n is a sample size. For example, let the size of the population be 500 and the sample size 50 that indicates 50 samples are to be drawn from the population of 500.

The sample interval is 500/50 =10.

Suppose, the first sample selected at random from the first interval is 7, then subsequent samples are 17, 27, 37, 47, 57, 67, and so on.

The advantages of systematic sampling are:

• This is a simple method of selecting a sample and is convenient to adopt.
• The time and work involved in sampling by this method are relatively less.
• Samples may be comprehensive and representative of the population.

The disadvantages of systematic sampling are:

• This method is not suitable for a heterogeneous population.
• It is not probability random sampling, since each element has no chance of being selected.
• Any hidden periodicity in the list will adversely affect the representativeness of the sample.
• Knowledge of the population and information of each individual is essential.

### Multi-stage Sampling:

In this method, the selection of the sample is made in different stages. The original units into which the universe is divided are primary units. Each primary unit that falls into the sample is subdivided into secondary units in preparation for the second stage sampling. In three-stage sampling, there may be primary, secondary, and tertiary units. For example, for studying the panchayat system in villages, our country is divided into zones (North, South, East, and West). One state is selected from each zone and then one district is selected from each state. For each district, one block is selected and then three villages are selected from each block. This sampling system helps in comparing the functioning of panchayats in different parts of India. Sampling in each stage may be random but it can also be deliberate or purposive. The individuals are selected from different stages for constituting the multi-stage sampling. The variability of estimates yielded by multi-stage sampling may be greater than that of estimates yielded by simple random sampling for equal size. The variability of estimates is depended on the composition of primary units.

The advantages of multi-stage sampling are:

• A complete listing of the population or universe is not required. Sampling lists, identification, and numbering are required only for sampling units that are selected as samples.
• It is a good representative of the population and easy to administer.
• A large number of units can be sampled for a given cost under multistage sampling because of sequential clustering.

The disadvantages of multi-stage sampling are:

• It is a more difficult and complex method of sampling compared to other methods.
• It involves more errors compared to simple random sampling or systematic sampling for a similar sample size.

### Multi-phase Sampling:

Multi-phase sampling is in which some information is collected from the whole sample and additional information is collected either at the same time or later from a sub-sample of the full sample. It increases the precision of sub-sample results. The cost of the first phase sample is cheaper than the second phase. The first phase information is collected from some records or by mail while the second phase information is obtained by personal interviews. In the leprosy survey, a test like Lepromin is performed for all samples in the first phase. Those who are tested positive in the Lepromin test are screened in the second phase of the culture of the organism. In this method, the information collected at each phase helps the researcher to select a more relevant sample.

### Cluster Sampling:

In cluster sampling, the population may be divided into groups called clusters and drawing a sample of clusters to represent the population. A cluster consists of either the primary sample units or elementary secondary sample units. In a selected cluster either all the sample units are selected or a few of them are chosen by other sampling methods.

Many national surveys are based on cluster sampling where villages, schools, colonies, and corporation areas are considered as a cluster. A plan to make a selection of clusters within clusters is called multi-stage cluster sampling. From each of the selected clusters, select the sample of elements instead of including the entire cluster. This procedure of sampling is called two-stage sampling or sub-sampling. If clusters are geographic units then, it is known as area sampling. In area sampling, the basis of selection is the map rather than a list of the population. Maximum accuracy in cluster sampling is obtained if differences or variability within a cluster is large (heterogeneity) or variability among or between clusters is small (homogeneity).

The advantages of cluster sampling are:

• Cluster sampling is simple, economical, and a good representative of the population.
• It is a commonly used method when no other satisfactory sampling frame for the whole population exists.
• It is much easier to apply this sampling method when large populations or geographical area is studied.
• It is a flexible method and characteristics of clusters can be estimated.

The disadvantages of cluster sampling are:

• Each cluster is not of equal size in a selection of one district from one state or one village from one block. The district or the village can be small, intermediate, or large-sized.
• It may be homogeneity in one cluster but heterogeneity in another.
• Cluster sampling is not free from error and it is not comprehensive.

## Non-probability or Non-random Sampling

Non-probability sampling or non-parametric sampling methods are those which do not provide every component in the population or universe with an equal chance of being included in the sample. It is the process of sampling without the use of randomization. This sampling technique does not follow the rules of probability theory as well as does not claim representativeness. In this sampling, a personal element has a great chance of entering into the selection of the sample. The researcher may select a sample that may get results favorable to him. There is always bias entering into the sampling methods and hence no assurance that every element has a specifiable chance of being selected. Sampling error in non-probability sampling cannot be estimated. There are four non-random designs, which are commonly used in qualitative and quantitative research such as purposive sampling convenience sampling, quota sampling, and snowball sampling.

### Purposive or Judgmental Sampling:

This sampling method is also known as deliberate sampling. In this sampling, the choice of sample items depends primarily on the judgment of the investigator. The investigator includes those elements in the sample which he or she likes in the universe about the characteristics of a research topic. This technique also depends on the sampling design and the purpose of representativeness. Hence, it is also called purposive sampling.

In this method, the researcher has complete freedom to choose his sample according to this wishes and desires. The researcher selects some elements from the whole data as a sample. This is a simple method for selecting the samples and is useful in cases where the entire data is homogeneous and the researcher has knowledge of the various aspects.

The advantages of purposive sampling are:

• This technique of sampling is simple and economical.
• It is a practical method when randomization is not possible. It is commonly used in solving many types of economic and business problems.
• Knowledge of the researcher can be best used in this method of sampling.

The disadvantages of purposive sampling are:

• This sampling is not free from error and it includes uncontrolled variation.
• Researcher can select a sample as per his wish and desire. Hence, a sample may be biased.
• The investigator is unable to understand the whole group and knowledge of the whole group or population is necessary.

### Convenience or Accidental Sampling:

This sampling is also known as haphazard sampling or incidental sampling. In this sampling, the investigator studies all those persons who are most conveniently available or who accidentally come in his contact during an investigation. This method of sampling is most common among market research and newspaper reporters. For example, the investigator engaged in the study of college or university students might visit the canteen, library, playgrounds, departments and interview a certain number of students. During an election period, media personnel often present man-on-the-street interviews that are presumed to reflect public opinion. Convenience sampling is commonly used when the universe is not well defined or sampling unit is not a clear or complete list of the source is not available.

The advantages of convenience sampling are:

• This sampling is a quick, easy and economical method.
• This sampling is frequently used in behavioral sciences and exploratory research.

The disadvantages of convenience sampling are:

• This sampling is not free from error and parametric statistics cannot be used.
• It is not representative of the population and it may be a very biased sample.

### Quota Sampling:

This sampling method is a non-random form of the stratified sampling method. The universe is divided into strata based on certain characteristics and then the quota is fixed for each stratum in proportion to its size. It is the most commonly used method of sampling in market surveys, opinion polls, and municipal surveys.

Quota can be fixed according to their proportion in the entire population. For studying the attitudes of persons towards the use of loudspeakers in religious places with 1000 males and 500 females belonging to different religions, the quota can be fixed in the ratio of one female for every two males. Quota may be fixed based on the number of persons in each of the three religious groups such as Hindu, Muslim, or others.

The advantages of quota sampling are:

• This is a simple method of sampling and is most frequently used in social surveys.
• It is a less costly method than other techniques. There is no need for any information of sampling frame, a total number of elements, their location, or other information about the sampling population.
• It is a practical method as well as completed in a very short period.

The disadvantages of quota sampling are:

• It is not a true representative of the total sampling population.
• It is not possible to estimate the sampling error and it has the interviewer’s bias in the selection.
• It influences regional geographical and social factors.

### Snowball Sampling:

This sampling is the process of selecting a sample using networks. In snowball sampling, the investigator starts the research with the few respondents who are known to him. These respondents give other names who meet the criteria of research, who in turn give more new names. This process of sample selection is continued until an adequate number of persons is interviewed. In this manner, the investigator accumulates more and more respondents. For example, if the investigator can find a few bonded advertisers willing to talk he might ask them for details of other advertisers who might also be willing to interact.

The Snowball sampling method is useful if you are unknown about the group or organization under study. This sampling is useful for studying communication patterns or diffusion of knowledge within a group. The main advantages of this sampling method are less cost and less sample size.

The disadvantages of snowball sampling are:

• It is difficult to use this method when the sample becomes fairly large.
• The choice of the entire sample depends upon the choice of individuals at the first stage. If they belong to a particular faction, the study may be biased.
• Snowball sampling may have serious problems if there are major differences between those who are widely known by others and those who are not.
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