Introduction to Types of Sampling Design with Examples
In this article we will go through the topic Types of Sampling Design with Examples. Sampling design refers to the methodical plan or strategy used by researchers to select a subset of individuals or items from a larger population for study. The choice of sampling design significantly impacts the validity, reliability, and generalizability of research findings. Sampling procedures commonly used can be broadly categorized into the following
(i) Probability Sampling
(ii) Non-probability Sampling
(i) Probability Sampling
Probability sampling is a process of sample selection in which members of the sample are chosen by chance methods such as flipping coins, drawing numbered balls from an urn or through tables of random numbers, the selection of the units for the sample is carried out by chance procedures or with known probabilities of selection.
We shall discuss following kinds of probability sampling techniques
1. Unrestricted Random Sampling
(a) Simple Random Sampling
(b) Systematic Sampling
2. Restricted Random Sampling
(a) Stratified sampling
(b) Cluster sampling
(c) Area Sampling
(d) Multistage sampling
(e) Multiphase sampling
1. Unrestricted Random Sampling
(a) Simple Random Sampling
Simple random sampling is the most common and familiar type of probability sampling method. In simple random sampling method, each item of the population has equal chance of being selected in the sample. A random sample may be selected by using any one of the following methods:
(i) Lottery method
(ii) Use of Random number tables
Lottery Method
In this method a ticket, chit or token may be associated to each unit of the population. For example, suppose a population consists of N units then each unit has its own identification mark from 1 to N. Then all the chits, tickets or tokens are placed in a container in which thorough mixing is possible, before each draw.
Draws are continued until a sample of required size is obtained. The drawing may be with replacement or without replacement. If a unit selected in a draw is returned back before the next draw, this is known as Simple random sampling with replacement. If the selection procedure is continued without returning the sample unit once drawn, to the population, it is called simple random sampling without replacement.
Use of Random Number Tables
If the population size is large the process of numbering units on tickets, chits or token becomes cumbersome. In such cases random number tables are more appropriate. A random number table is a collection of random numbers. The random numbers are generated through a probabilistic mechanism.
The numbers have the following properties
(a) The probability of appearing any digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, at any particular place is the same i.e. 1/10.
(b) The occurrence of any two digits in any two places is independent of each other. Some of the random number tables in common use are follows
(a) Fisher and Yates tables
(b) Tippett random number tables
(c) Kendall and Smith tables.
A part of the random number table is given at the end of this book.
Example 1: Suppose a sample of size 20 is to be selected from a population of 100. First number the units from 1 to 100, the order being quite immaterial. While numbering the units ensure that each unit in the population has uniform digits, in this case two (00 to 99). Thus, first unit would have a two-digit number 00, 2nd unit 01, 10th unit 09 and so on. After all the units have been given two-digit numbers the table of random numbers may be used one may start from the left-hand top corner of the table of random numbers and proceed systematically down the sets of two-digit column rejecting a number if it has appeared earlier. Using the table given in the book a sample of 20 out of 100 will be thus chosen.
| 23 11 07 72 05 43 61 89 14 93 31 25 38 49 57 81 97 36 09 75 |
Types of Sampling Design with Examples
Merits of Simple Random Sampling
1. This is a very simple technique and serves well to introduce to basic ideas of sampling.
2. As the method is based on probability theory therefore it is possible to calculate sampling error.
3. Accurate mathematical tests can be applied to judge the randomness of the samples.
Demerits of Simple Random Sampling
1. In many cases either it is not possible or it is very difficult to make a list of all the items of the universe.
2. If the universe is spread to a wider geographical area, it is not possible to give equal opportunity to all the units of universe.
3. If the universe consists of many heterogeneous groups, simple random sampling is unsuitable.
(b) Systematic Sampling
In case of systematic sampling first a sampling fraction is calculated. For example, in the foregoing example, a sample of 20 out of 100 units was chosen. The sampling fraction k is N/n, where N is the total number of units in the population and n is the size of the sample. In above case k= 100/20 = 5. Second a number between 1 to 5 is chosen at random. Suppose the number thus selected happens to be 4. Then the sample will comprise units associated with numbers
4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 89, 94, 99.
As is clear from the above that selection of the sample by this method is extremely convenient. After choosing the initial unit, the process of selecting subsequent units for the sample follows a clear pattern. Systematic random sampling is also known as quasi-random sampling due to its structured approach.
Merits of Systematic Sampling
1. The main merit of systematic sampling lies in its simplicity, operational convenience and even spread sample over the population.
2. The technique is faster and less subject to error than simple random sampling.
3. It is statistically more efficient than simple random sampling.
Demerits of Systematic Sampling
1. In case the order of the items on the list is not random then estimation standard error becomes complex.
2. If the population has unforeseen periodicity, then use of systematic sampling may substantially contribute to the estimate of the population mean.
Types of Sampling Design with Examples
2. Restricted Random Sampling
(a) Stratified Random Sampling
In case of homogenous population, a small sample selected by simple random sampling method from a large population may well, represent the population but if the population is heterogeneous the simple random sampling may not always provide a representative miniature of the population. Therefore, when there is considerable heterogeneity present in the population with regard to a subject matter under study, it is often good to divide the population in segments or Involving different strata and picking a specific number of sampling units from each stratum guarantees a fair representation across all pertinent segments.
For example, for designing a suitable marketing strategy for a consumer durable, the population of customers may be divided into strata on the basis of their income level and then from each strata a certain number of consumers may be selected randomly. If N is taken as size of the population, N1, N2…Nk can be size of its sub-groups or strata, such that
N=N₁+N2+ N3 + …. + Nk
If n is the sample size and n₁, n₂ …. nk are the number of items selected from respective strata then n = n₁ + n₂+…+ nk.
Reasons for stratification
1. To have better understanding about the constituents of the universe.
2. To gain a higher degree of relative precision.
3. To improve sampling design.
4. To ensure adequate representation to various groups of population, which may be of some interest or importance.
Basis of stratification
The stratification should be performed in such a manner that each strata is homogeneous within itself with respect to the characteristic under study (i.e. variance with in strata should be minimum). On the other hand, strata should be heterogeneous between themselves (i.e. variance between strata should be maximum) In case of companies, the nature of business, year of incorporation, location, profits, losses, assets, liabilities, products, processes, technology, collaboration etc., may be useful as good basis. At times, stratification of the population is based on considerations of administrative convenience
Number of Strata
Though there is no restriction over the number of strata. There may be as many strata as possible so that each stratum will be as homogenous as possible. But practical consideration like cost, time and effort limits the number of strata that is feasible.
Allocation of sample size to different strata
There are three criteria for allocating sample size to different strata
(i) Size of the strata (number of units in the stratum)
(ii) Variability within the stratum
(iii) The cost of taking observation per sampling unit from each stratum.
Proportional Allocation
A sample in which each stratum has a uniform sampling fraction is called proportionate stratified sample. This allocation procedure is widely used in practice due to its straightforwardness. The number of units allocated to the ith stratum is proportional to Ni/N where Ni is the size of ith stratum and N is the size of the population. If n is the size of the sample, then ni = n Ni /N (i=1,2, …k)
Example:
| Income per month ₹ | Households | Sample Proportionate |
| 0-1000 | 4,000 | 40 = 100 ×4000/10,000 |
| 1001-2000 | 3,000 | 30 = 100 ×3000/10,000 |
| 2001-3000 | 2,000 | 20 = 100 ×2000/10,000 |
| 3001 and above | 1,000 | 10 = 100 ×1000/10,000 |
| Total | 10,000 |
Types of Sampling Design with Examples
(b) Cluster Sampling
Cluster sampling is a procedure of selection in which the elements of the sample are chosen from the population in groups or clusters rather than singly. The clusters used are often pre-existing natural or administrative grouping of the population, such as villages, schools, colleges, factories, political subdivisions etc.
For example, if in a survey sampling units are households in a rural area, then if simple random sampling is used to select households they will be located over several villages. On the other hand, a village can be regarded as a cluster of households. We select few villages randomly and include every household in the selected villages in our sample.
Optimum Cluster Size
For a given sample size, the variance of an estimator increases (or estimator becomes less precise) with a large size of cluster. On the other hand, the cost decreases with the large size of cluster. Therefore, it is necessary to determine a balancing point by finding the optimum cluster size (i.e. cluster size which minimizes variance of the cluster for a fixed cost or minimize the cost) for a given level of precision.
Merits of Cluster Sampling
(i) Collection of data from neighbouring units is economical, easy and convenient than units spread over a region.
(ii) Since all the units in a cluster are included in the sample, this minimizes transport cost.
(iii) This method also proves powerful when data about population are not readily available.
(iv) As the sample units are located at one place it requires less time.
Demerits of Cluster Sampling
(i) On account of the similarity of the units in the cluster selection of a few clusters may not give a really representative sample. In fact, cluster sampling will be more representative when cluster have a high degree of intra-cluster heterogeneity.
(i) When compared with simple random sampling error may be more in the cluster sampling method.
(c) Area Sampling
Area sampling is special form of cluster sampling. A cluster sampling with cluster based on geographical subdivisions is known as area sampling. With in the selected area, the researcher may select all the numbers of the area or a part of the area may be selected. In the area sampling boundaries of the area must be well defined. For instance, in the case of a village, wards or streets may serve as a good identification.
Merits of Area Sampling
(i) To conduct studies on wider geographic area, area sampling is the best method.
(ii) Area sampling is especially helpful where list of the concerning population is not available.
(iii) Field interview can be made more efficient.
Demerits of Area Sampling
(i) There will be much similarity among sample units located in the same area it will reduce the statistical efficiency.
(ii) When the area is dissimilar, the sampling error may be high.
Types of Sampling Design with Examples
(d) Multi-stage sampling
Multi stage sampling is a process of selecting a sample in two or more successive stages. For example, if a bank wants to gather information regarding quality of customer services in a particular state, then a random sample of districts is selected in first stage from the list of districts. In the second stage from each of the selected districts a number of branches are selected at random, and in the third stage from each of the selected branches a number of depositors (which will be ultimate sampling units) is selected randomly for collecting information.
Merits of Multi-Stage Sampling
(i) Multistage sampling leads to more precision in the study.
(ii) It is more convenient and economic in comparison to simple random sampling.
(iii) This method contributes to better quality in carrying out the final selection.
Demerits of multi-stage sampling
Demerits of the multi-stage sampling are the same as that of cluster sampling.
(e) Multi-phase sampling
The main distinction between a multi-stage sampling and multi-phase sampling is that in the former each successive stage has a different unit of sample where as in the latter while additional information is gathered from a sub-sample, the unit of the sample remains the same and is not altered.
For example, suppose a survey is undertaken to determine the nature and extent of health facilities available in a city and the general opinion of the people. In the first phase, a general questionnaire may be sent out to ascertain who amongst the respondents had at one time or other used hospital services.
Then in the second phase, a comprehensive questionnaire may be sent to only those respondents to ascertain what they feel about the medical facilities in the hospitals. A sample of this type is a two-phase sample.
Merits of Multi-phase Sampling
It is economical and less time consuming and require less efforts.
Demerits of Multiphase Sampling
Demerits of multi-phase sampling are same as that of cluster sampling.
Types of Sampling Design with Examples
Non-Probability Sampling
It is the sampling procedure which does not provide any basis for estimating the probability that each item in the population possesses to be included in the sample. In such cases the sampling error cannot be measured. The error in the estimator tends to increase as there is no guarantee for the representativeness of the sample. In this method selection of sampling units depends entirely on the discretion or judgement of the investigator.
This method provides a lot of freedom to the investigator in the selection of sampling units. In general, there are five types of non-probability sampling methods that may be useful to the investigator under appropriate conditions.
These are Convenience, Purposive, Judgement, Quota Sampling and Snowball Sampling.
(a) Convenience Sampling
As the name implies in this method samples are selected at the convenience of the investigator or researcher. A survey based on such a sample may not be useful if the selected units are not representative. It is not possible in convenience sampling to know the “representativeness” of the selected units as such, it introduces an unknown degree of bias in the estimate.
In view of this limitation convenience sampling should be avoided as far as possible. This method may be quite useful in exploratory research designs as a basis for generating hypothesis. The method is also useful in testing questionnaire etc. at the pretest phase of the study. Convenience sampling is extensively used in marketing studies and otherwise, where focus is on getting new ideas and insights into a given problem.
(b) Purposive Sampling
In this method of sampling the sample units are chosen in order to meet some predetermined criteria though they may not be representative. For example, a candidate formulating his strategies for an upcoming campaign, might like to obtain the viewpoints of persons who are known to be opposing his candidature. This would obviously help in designing his strategy for winning election.
(c) Judgement Sampling
In this process, sampling is done on the judgement of the researcher. The sample may or may not accurately represent the population. But in the opinion of the researcher, it is representative. The inclusion and exclusion of units in the sample is based on the judgement of the researcher.
Many times, it may be desirable to use judgement sampling. For example, an expert may be asked to select a sample of representative business firms. The sample could be representative or non-representative. The judgement sampling may be more suitable when a small sample of a few units is to be selected. However, when a large sample is to be selected, the element of bias in the selection could be quite large in case of judgement sampling.
Types of Sampling Design with Examples
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