 # sampling technique in statistics

There are two types sampling technique in statistics or sampling designs, method in research i.e. Probability/random sampling and Non-probability/Non-random sampling which are discuss below:

Probability sampling (Random sampling) technique in statistics

It is the technique of selecting the sample randomly. In this method, a sample is selected in such a way that each and every unit of population has a predetermined probability of being selected into the sample. technique of probability sampling.

1. Simple random sampling.
2. Systematic sampling.
3. Stratified sampling.
4. Cluster sampling.
5. Multi-Stage sampling.

Non-random/Non-probability sampling technique

If a sample is selected according to the investigator’s personal judgment or at not random, then the sampling is known as non-probability or nonrandom sampling. In this sampling, the selection of a sample does not depend upon a chance. Non-random samplings are not preferred more as compared to random sampling. But, they are more useful when the samples are to be drawn from rare events/cases. Types of Non-random Sampling technique in statistics: there are 4 types of non random or non probability sampling i.e. Judgment sampling, Convenience sampling, Quota sampling, Snowball sampling which are discuss below:

#### What is Simple Random Sampling technique? and its types

Simple random sampling in statistics is a technique of selecting/drawing small unit of population such that each and every unit has equal chance of being selected into the sample. Each and every units of population are equally likely. It is an elementary/basic sampling technique. It is used in most of the cases. If size of the population is, N then each unit of the population has equal probability, 1/N of being selected into the sample.

Types of Simple random sampling :-There are two technique of simple random sampling/sampling techniques/sampling designs in statistics i.e. Simple Random Sampling Without Replacement(SRSWOR) and Simple Random Sampling With Replacement(SRSWOR) which are discuss below:

##### Simple Random Sampling Without Replacement(SRSWOR)

If an item selected from population in any draw is not replaced before the next draw then the sampling is known as SRSWOR. If the second draw is made without the replacement of first draw then it is called SRSWOR. Let N be the total unit of population and n be the size of the sample. Then, out of N unit of population, n size of the sample can be drawn without replacement in NCn ways and each unit has the same probability 1/NCn.

##### Simple Random Sampling With Replacement(SRSWR)

If an item selected from population in any draw is replaced before the next draw then the sampling is called SRSWR. If the second draw is made with the replacement of first draw then it is called SRSWR. Let N be the total unit of population and n be the sizes of the sample. Then, out of N unit of population, n sizes of the sample with replacement can be drawn in Nnways and each unit has same probability, 1/Nn of being selected into the sample.

How we Selection of a simple random sample:

Lottery Method

Using Random Number Table.
(Tippet’s random number table (1927), Fisher and
Yates’s table (1938), Kendal and Smith’s table
(1939) are some commonly used random number
tables)

Lottery method is the simplest method of selecting a random sample. In this method, all the units of the population of size N are numbered from 1 to N on N homogenous slips. These slips are put on a box or bag and mixed thoroughly. Then the slips are selected one by one until a sample of required size n is obtained. This method is applicable on both the SRSWOR and SRSWR sampling technique.
Using Random Number Table:
When the population size N is sufficiently large, then the lottery method becomes quite tedious and time consuming in practice. In that case, a simple random sample can be selected by using table of random numbers. These random numbers are generally generated by computers or by a table of random numbers. The tables are made by some mechanism such that one digit numbers 0 to 9 are independently and approximately equally distributed throughout the table. This can be made also for 2 digits (00, 01, 02, ……. , 99), three digits and so on.
Tippet’s random number table (1927), Fisher and Yates’s table (1938), Kendal and Smith’s table (1939) are some commonly used random number tables. This method is considered as better than the lottery method since the lottery method is time consuming. Example:

Merits and demerits simple random sample:

Merits of SRS:
1.It represents the universe in better way.
2.There is no possibility of personal biased.
3.It is more economic method.
4.It is more efficient of estimates as the sample is increased.
Demerits of SRS:
1. It is expensive and time consuming, especially when the population is very large.
2.Omission of any units may fail whole method.
3.It requires the completely up to-date list of population from which the samples to be drawn.
4. If the population is heterogeneous in character, it may not give accurate result.

#### Systematic sampling technique

Systematic method of sampling is preferred when the population is finite, sampling frame is available and units of the population are more or less homogenous. In this sampling, the first unit is selected by using simple random sampling and the remaining units are selected automatically (systematically) with some predetermined pattern. For this, first of all, the units are serially listed and arranged in alphabetical or
numerical order. Then the sampling interval is found by using the relation,
K = N/n ; where,
K = Sampling interval
N = Population size
n = Sample size
The first sample is selected from the first interval and other samples are selected at equal sampling intervals.

For example; suppose, there are 100 items and if 10 items are to be selected. Therefore, we have, in the usual notation, N = 100, n = 10 then the sampling interval (K) is given by,
K = N/n = 100/10 = 10 ie. Available data are arranged into 10 equal interval groups (0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70,70-80,80-90, 90-100). Now, we select the first unit from first interval 0-10, by using simple random sampling technique in statistics. Suppose, the number 5 is selected at first then the other samples; 15, 25, 35, 45, 55, 65, 75, 85, 95 are selected automatically. It is mostly used in different surveys.

Merits and demerits of Systematic Sampling

Merits:
1.It is simple, cheap and convenient to apply.
2. Less time consuming, less manpower are required.
3.It is operationally more convenient than SRS and give more satisfactory results.
Demerits:
1.It cannot be used if the population size is infinite or unknown.
2. The individuals of population must be arranged in some order and sampling interval should be equal.

#### Stratified sampling technique

When the characteristics of individuals of population are heterogeneous, population size is known then stratified sampling is preferred to use than simple random sampling and systematic sampling technique. The population is divided, at first, into different groups or classes on the basis of certain characteristics, called ‘strata’, in such a way that the characteristics of the units are homogeneous within strata and heterogeneous between strata. Then the required samples are drawn from each stratum by using SRS technique.
For example; if we want to study about the production of crops in Nepal. First of all, we divide the whole Nepal into three regions as Mountain, Hill and Terai. Then the samples are drawn from each region, statistically called the stratum, by using the SRS method. The stratified sampling is more convenient from the organizational point of view.

Merits and demerits of Systematic Sampling

Merits:
1.It is the best method for heterogeneous population.
2.Samples are more representatives.
3.The estimation of population parameters is more efficient.
Demerits:
1.This method requires more time and cost.
2.Experienced and expert persons are required for the stratification of the unit into different strata.

#### Cluster Sampling methods of Probability sampling

Cluster sampling is more appropriate to use when the population characteristics are not homogeneous, details sampling frame are not available, but some information may be available for small segments of the population. In this sampling, first of all, the population is divided into different groups, called ‘clusters’ in such a way that the characteristics of the units within the clusters are heterogeneous and between the clusters are homogeneous. Then one or few clusters are selected by using SRS and each and every unit of selected clusters is studied.
For example, suppose we want to study about the condition of disable people of Nepal. Firstly, we divide the whole Nepal into different zones, statistically called, clusters. Then a zone is selected randomly by using SRS method and study detail of all individuals of that zone.

Merits and demerits Cluster Sampling
Merits:

1.It is an appropriate method of collecting the samples from population, even when the sampling frame is not available.
2.It is more preferable when the samples are to be selected on the basis of regional or aerial way.
3.It is also less expensive.
Demerits:
1.The efficiency decreases with increase in cluster size.
2.The samples may not be more representative in case of rare characteristics group of people.

#### Technique of Multi-Stage Sampling

Multi-stage sampling is the combination of different stages of sampling in which an ultimate sample is determined in different stages. In this sampling, initially, the population is divided into large groups; called primary stage units (PSU). These PSUs are then divided into smaller groups; called secondary stage units (SSU). Again, these SSUs are divided into smaller groups, called third stage units (TSU) and so on, until we come to the ultimate units of sample size. Here, if the ultimate sample is selected from PSU by using SRS, then it is called first stage sampling. Similarly, if the sample is selected from SSU then it is called second stage sampling and so on.
Example Multi-Stage Sampling technique in statistics; in crop surveys, for estimating total crop yield in a district, VDC, can be considered as primary stage unit (PSU), the villages as secondary stage unit (SSU), crop field as third stage unit (TSU) and a plot of fixed size as the ultimate unit of sampling.

Merits and demerits Multi-Stage Sampling

Merits:
1.It is flexible method.
2.It enables the use of existing division and subdivision of country which saves time, labors and then money.
3.It is more convenient when area of investigation is large.
Demerits:
1.This method is less accurate than that of single stage sampling.
2.If the samples are not carefully taken from different stages, it may give faulty results.

#### Judgment sampling method in statistics

In this sampling methods, the choice of the sample items depends upon the judgment or view or choice of the sampler or investigator. The investigator includes those items in the sample, which he/she thinks are most important with regard to the characteristics under investigation.

Merits and demerits judgment sampling

Merits:
1.It is a simple method of sampling for a quick decision.
2.It may give better results when sample size is small.
3.If the sampler is trained and experienced then the results obtained by this method is reliable.
Demerits:
1.It gives an unreliable conclusion if the investigator is personally biased.
2.This method does not possess probabilistic technique.

#### Convenience Sampling method in statistics

In convenience sampling, an investigator selects the sample on the basis of the convenience of the investigator. This method is also called ‘chunk sampling’. A chunk refers that the fraction of the population being investigated which is selected neither by probability nor by judgment but by convenience. Samples are selected where the units are available or available sources.
For example; if anyone wants to collect the opinion of the people about the new fiscal policy of Nepal, he/she can take interview of different economists by telephone or cell phone which is convenient to him/her.

Merits and demerits Convenience Sampling

Merits:
1.It is a simple method of sampling for a quick decision.
2.It may give better results when sample size is small.
3. If the sampler is trained and experienced then the results obtained by this method is reliable.
Demerits:
1.It gives an unreliable conclusion if the investigator is personally biased.
2.This method does not possess probabilistic technique.
3.Sampling error cannot be estimated because it is not based on random sampling.

#### Quota Sampling technique

Quota sampling is similar to the stratified sampling, but no any probability is associated for selecting the sample. In this sampling technique statistics, some quotas or groups of population are set up according to some specified characteristics or criteria and the selection of quota is made according to the personal judgment of the investigator.
For example; In a radio listening survey, the interviewers may be told to interview 500 people living in a certain area and that out of every 100 persons interviewed, 60% are housewife,25% are students and 15% are professionals but here interviewer is free to select the people to be interviewed.

Merits and demerits Quota Sampling:

Merits:
1.It is a simple method of sampling for a quick decision.
2.It may give better results when sample size is small.
Demerits:
1.It gives an unreliable conclusion, if the investigator is personally biased.
2.This method does not possess probabilistic technique.

#### Snowball Sampling technique

The snowball sampling methods is extensively used in the situations when the population is unknown and rare, and it is hard to select the subjects there from. In this method, survey subjects are selected on referral from other survey respondents. A respondent is identified according to the objective of the study and other respondents are identified according to the referral from the respondent. This technique is generally used in hidden population, which are difficult for researchers to access. Thus, this method is also called as the referral sampling
method or chain sampling method
. It’s called snowball sampling because (in theory) once you have the ball rolling, it picks up more “snow” along the way and becomes larger and larger.