# Explain the concept of sampling.

Published:

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

INTERNAL RESEARCH ASSIGNMENT

Batch: 2013-15

Semester:2nd (2nd Shift) Section B

Subject code:MS-108

Topic of assignment: SAMPLING(QUES-3)

Date of submission: 27th November 2014

………………………………………………………………………………………………

Date of submission of assignment: 27th nov’ 2014

## Question 2 Explain the concept of sampling. Differentiate between cluster and stratified sampling.

Ans.

Sampling

Sampling is the process of selecting a subset of the target population that will allow reliable and valid inferences about the target population. The primary goal of sampling is to create a small group from the population that is as similar to the larger population as possible. A sample is a subset of the target population who will participate in the study.

Samplingis concerned with the selection of a subset of individuals from within a statistical populationto estimate characteristics of the whole population.Acceptance samplingis used to determine if a production lot of material meets the governingspecifications. Two advantages of

sampling are that the cost is lower and data collection is faster than measuring the entire population.

1. Sampling is cheaper than a census survey. It is obviously more economical, for instance, to cover a sample of households than all households in a territory although the cost per unit of study may be higher in a sample survey than in a census.

2. Since magnitude of operations involved in a sample survey is small, both the execution of the fieldwork and the analysis of the results can be carried out speedily.

3. Sampling results in greater economy of effort as relatively small staffs is required to carry out the survey and to tabulate and process the survey data.

4. A sample survey enables the researcher to collect more detailed information than would otherwise be possible in a census survey. Also, information of a more specialised type can be collected, which would not be possible in a census survey on account of availability of a small number of specialists.

5. Since the scale of operations involved in a sample survey is small, the quality of interviewing, supervision and other related activities can be better than the quality in a census survey.

1. Risk of rejecting a “good” lot (producer’s risk)

2. Risk of accepting a “bad” lot (consumer’s risk)

4. Requires additional planning and documentation

l5.Yields less actual information about the product

6. Will not detect all defective product in a lot

7. Designed to maintain a given level of quality; will not drive improvement

Stratified and Cluster Sampling

Stratified Sampling

Given the same number of sampling units, stratified sampling often provides a more representative sample than does simple random sampling. Under this design the list of sampling units is first grouped (or stratified) based on certain characteristics. A simple random sample is then taken for each group (or stratum). For example, all Texas students can be grouped by region, then students are sampled randomly from each region. This way, a known percentage of sampling units with characteristics based on the grouping variables such as geographical region, gender, or ethnicity, are always in the sample. Consequently, stratified sampling typically produces a more representative sample and leads to more accurate estimation of the parameters of interest.

Stratification increases precision without increasing sample size. Stratification does not imply any departure from the principles of randomness it merely denotes that before any selection takes place, the population is divided into a number of strata, then random samples taken within each stratum. It is only possible to do this if the distribution of the population with respect to a particular factor is known, and if it is also known to which stratum each member of the population belongs. Examples of characteristics which could be used in marketing to stratify a population include: income, age, sex, race, geographical region, possession of a particular commodity.

Stratification can occur after selection of individuals, e.g. if one wanted to stratify a sample of individuals in a town by age, one could easily get figures of the age distribution, but if there is no general population list showing the age distribution, prior stratification would not be possible. What might have to be done in this case at the analysis stage is to correct proportional representation. Weighting can easily destroy the assumptions one is able to make when interpreting data gathered from a random sample and so stratification prior to selection is advisable. Random stratified sampling is more precise and more convenient than simple random sampling.

When stratified sampling designs are to be employed, there are 3 key questions which have to be immediately addressed:

1 The bases of stratification, i.e. what characteristics should be used to subdivide the universe/population into strata?

2 The number of strata, i.e. how many strata should be constructed and what stratum boundaries should be used?

3 Sample sizes within strata, i.e. how many observations should be taken in each stratum.

Cluster Sampling

Another common probability sampling design is cluster sampling. With cluster sampling, the

list of all sampling units is first grouped into clusters based on certain characteristics or

variables of interest. Then, unlike stratified sampling, a predetermined number of clusters are

selected and all sampling units within the chosen clusters are observed. For example, all Texas

campuses can be grouped into regions. Then, a predetermined number of regions can be

selected and all campuses within the chosen regions would be selected.

The process of sampling complete groups or units is called cluster sampling, situations where there is any sub-sampling within the clusters chosen at the first stage are covered by the term multistage sampling. For example, suppose that a survey is to be done in a large town and that the unit of inquiry (i.e. the unit from which data are to be gathered) is the individual household. Suppose further that the town contains 20,000 households, all of them listed on convenient records, and that a sample of 200 households is to be selected. One approach would be to pick the 200 by some random method. However, this would spread the sample over the whole town, with consequent high fieldwork costs and much inconvenience. (All the more so if the survey were to be conducted in rural areas, especially in developing countries where rural areas are sparsely populated and access difficult). One might decide therefore to concentrate the sample in a few parts of the town and it may be assumed for simplicity that the town is divided into 400 areas with 50 households in each. A simple course would be to select say 4 areas at random (i.e. 1 in 100) and include all the households within these areas in our sample. The overall probability of selection is unchanged, but by selecting clusters of households, one has materially simplified and made cheaper the fieldwork.

A large number of small clusters is better, all other things being equal, than a small number of large clusters. Whether single stage cluster sampling proves to be as statistically efficient as a simple random sampling depends upon the degree of homogeneity within clusters. If respondents within clusters are homogeneous with respect to such things as income, socio-economic class etc., they do not fully represent the population and will, therefore, provide larger standard errors. On the other hand, the lower cost of cluster sampling often outweighs the disadvantages of statistical inefficiency. In short, cluster sampling tends to offer greater reliability for a given cost rather than greater reliability for a given sample size.

b) What sample design would you select in each of the following?

i) A study to determine consumer reactions to a new brand of tea.

Ans.

Simple Random Sampling (SRS)

Asimple random sampleis hi selected so that all samples of the same size have an equal chance of being selected from the population.

In simple random sampling (SRS), sampling units are randomly selected from the list of all sampling units. Random selection means that all sampling units in the target population have the same probability of being selected. For example, an SRS of 3rd grade students is constructed by randomly selecting from the complete list of all 3rd grade students in Texas with each student having the same chance of being in the sample. Simplicity in making inferences is one of the main advantages in SRS. Another advantage is that every sampling unit (e.g., student or campus) has an equal chance of participation. However, SRS can result in a non-representative sample of certain characteristics such as ethnicity, gender, social economic status, or geographical location. For example, since all students in the state have an equal chance of being selected in an SRS, it is possible (though unlikely) to have a disproportionately high percentage of students from North Texas.

1. Representativeness and Freedom from Bias

Freedom from human bias and classification error remains one of the biggest advantages simple random sampling offers, as it gives each member of a population a fair chance of being selected. If done right, simple random sampling results in a sample highly representative of the population of interest. In theory, if a researcher has access to all the necessary data about a given population, only bad luck can compromise his sample's representativeness.

## 2. Ease of Sampling and Analysis

• Other sampling methods require much in-depth research and advance knowledge of a population prior to the selection of subjects. In simple random sampling, only the complete listing of the elements in a population (known as the sampling frame) is needed. A simple random sample, being highly representative of a population, also simplifies data interpretation and analysis of results. Trends within the sample act as excellent indicators of trends in the overall population. Many consider generalizations derived from a well-assembled simple random sample to have sufficient external validity.

## 1. Errors in Sampling

• While the randomness of the selection process ensures the unbiased choice of subjects, it could also, by chance, lead to the assembly of a sample which does not represent the population well. This random variation, independent of all human bias and in many cases difficult to pinpoint, is known as "sampling error." The probability of incurring errors in sampling increases with decreased sample size. Researchers therefore set a sample size big enough to minimize the likelihood of freak results.

## 2. Time and Labor Requirement

• As a complete and up-to-date frame is the minimum requirement for a good simple random sample, data gathering often entails a lot of time and labor, especially in cases involving large target populations. The trouble with obtaining a complete sampling frame stems from the inaccessibility of existing data or from the difficulty of constructing the frame on one's own. Comprehensive lists, if they do exist, are often not in the public domain. To gain access, the researcher must either pay for the data or apply for permissions -- a possibly lengthy and cumbersome procedure. These considerations greatly limit simple random sampling's applicability to most population studies.

ii) A study to measure the audience watching a sponsored television programs.

Ans.

Purposive or Judgmental Sample

A purposive, or judgmental, sample is one that is selected based on the knowledge of a population and the purpose of the study. For example, if a researcher is studying the nature of school spirit as exhibited at a school pep rally, he or she might interview people who did not appear to be caught up in the emotions of the crowd or students who did not attend the rally at all. In this case, the researcher is using a purposive sample because those being interviewed fit a specific purpose or description.

Apurposive sampleis a non-representative subset of some larger population, and is constructed to serve a very specific need or purpose. A researcher may have a specific group in mind, such as high level business executives. It may not be possible to specify the population -- they would not all be known, and access will be difficult. The researcher will attempt to zero in on the target group, interviewing whoever is available.

A purposive sample, also commonly called a judgmental sample, is one that is selected based on the knowledge of a population and the purpose of the study. The subjects are selected because of some characteristic.

Field researchers are often interested in studying extreme or deviant cases – that is, cases that don’t fit into regular patterns of attitudes and behaviors. By studying the deviant cases, researchers can often gain a better understanding of the more regular patterns of behavior. This is where purposive sampling often takes place. For instance, if a researcher is interested in learning more about students at the top of their class, he or she is going to sample those students who fall into the "top of the class" category. They will be purposively selected because they meet a certain characteristic.

Purposive sampling can be very useful for situations where you need to reach a targeted sample quickly and where sampling for proportionality is not the main concern. Researchers (typicallymarket researchers) who you might often see at a mall carrying a clipboard and stopping various people to interview are often conducting research using purposive sampling. They may be looking for and stopping only those people who meet certain characteristics.