Vinay

* Introduction:
Sampling is a familiar part of daily life. A customer in a bookstore picks up a book, looks at the cover, and skims a few pages to get a sense of the writing style and content before deciding whether to buy. A high school student visits a college classroom to listen to a professor’s lecture. Selecting a university on the basis of one classroom visit may not be scientific sampling, but in a personal situation, it may be a practical sampling experience. When measuring every item in a population is impossible, inconvenient, or too expensive, we intuitively take a sample. Although sampling is commonplace in daily activities, these familiar samples are seldom scientific. For researchers, the process of sampling can be quite complex. Sampling is a central aspect of business research, requiring in-depth examination. This chapter explains the nature of sampling and ways to determine the appropriate sample design.

* Sampling Terminologies:
1. Sample: A sample is a subset, or some part, of a larger population

2. A population (universe): is any complete group—for example, of people, sales territories, stores, or college students—that shares some common set of characteristics.

3. The term population element refers to an individual member of the population.

4. A census is an investigation of all the individual elements that make up the population—a total enumeration rather than a sample.

* Why sampling:

1. Pragmatic Reasons:

Applied business research projects usually have budget and time constraints. If Ford Motor Corporation wished to take a census of past purchasers’ reactions to the company’s recalls of defective models, the researchers would have to contact millions of automobile buyers. Some of them would be inaccessible (for example, out of the country), and it would be impossible to contact all these people within a short time period. A researcher who wants to investigate a population with an extremely small number of population elements may elect to conduct a census rather than a sample because the cost, labor, and time drawbacks would be relatively insignificant. For a company that wants to assess salespersons’ satisfaction with its computer networking system, circulating a questionnaire to all 25 of its employees is practical. In most situations, however, many practical reasons favor sampling. Sampling cuts costs, reduces labor requirements, and gathers vital information quickly. These advantages may be sufficient in themselves for using a sample rather than a census, but there are other reasons.

2. Accurate and Reliable results

A sample may on occasion be more accurate than a census. Interviewer mistakes, tabulation errors, and other nonsampling errors may increase during a census because of the increased volume of work. In a sample, increased accuracy may sometimes be possible because the fieldwork and tabulation of data can be more closely supervised. In a field survey, a small, well-trained, closely supervised group may do a more careful and accurate job of collecting information than a large group of nonprofessional interviewers who try to contact everyone. An interesting case in point is the use of samples by the Bureau of the Census to check the accuracy of the U.S. Census. If the sample indicates a possible source of error, the census is redone.

3. Destruction of Unit test

Many research projects, especially those in quality-control testing, require the destruction of the items being tested. If a manufacturer of firecrackers wished to find out whether each unit met a specific production standard, no product would be left after the testing. This is the exact situation in many research strategy experiments. For example, if an experimental sales presentation were presented to every potential customer, no prospects would remain to be contacted after the experiment. In other words, if there is a finite population and everyone in the population participates in the research and cannot be replaced, no population elements remain to be selected as sampling units.

* Practical Sampling Concepts

Defining the target population: Once the decision to sample has been made, the first question concerns identifying the target population. What is the relevant population? In many cases this question is easy to answer. Registered voters may be clearly identifiable. Likewise, if a company’s 106-person sales force is the population of concern, there are few definitional problems. In other cases the decision may be difficult. One survey concerning organizational buyer behavior incorrectly defined the population as purchasing agents whom sales representatives regularly contacted. After the survey, investigators discovered that industrial engineers within the customer companies rarely talked with the salespeople but substantially affected buying decisions. For consumer-related research, the appropriate population element frequently is the household rather than an individual member of the household. This presents some problems if household lists are not available. To implement the sample in the field, tangible characteristics should be used to define the population. A baby food manufacturer might define the population as all women still capable of bearing children. However, a more specific operational definition would be women between the ages of 12 and 50. While this definition by age may exclude a few women who are capable of childbearing and include some who are not, it is still more explicit and provides a manageable basis for the sample design.

* Errors in Sampling:

Two basic types of errors that may occur during sampling are 1. Random Sampling Error 2. Systematic or Non Sampling Error

1. Radom Sampling error: you get a few cases with unusual properties accidentally in the sample, which in turn will infect the summarized data (e.g. averages) from the sample. If a random sample is large enough, the divergences to opposite directions mostly cancel each other. 2. Systematic or Non Sampling Error: occurs often in non-random sampling. It is caused by the method of selection, which often inadvertently favors some types of items before others. This nuisance can often cause many times greater a decline in the representativeness of a sample than random divergence could create

* METHODS OF SAMPLING:

1. Probability verses Non Probability Sampling

In probability sampling, every element in the population has a known, nonzero probability of selection. The simple random sample, in which each member of the population has an equal probability of being selected, is the best-known probability sample. In non-probability sampling, the probability of any particular member of the population being chosen is unknown. The selection of sampling units in non-probability sampling is quite arbitrary, as researchers rely heavily on personal judgment

Non Probability Sampling

1. Convienience Sampling:

Rule : As the name suggests, convenience sampling refers to sampling by obtaining people or units that are conveniently available. A research team may determine that the most convenient and economical method is to set up an interviewing booth from which to intercept consumers at a shopping center.

Situation in which method is used along with advantage and disadvantage:
Researchers generally use convenience samples to obtain a large number of completed questionnaires quickly and economically, or when obtaining a sample through other means is impractical. Researchers generally use convenience samples to obtain a large number of completed questionnaires quickly and economically, or when obtaining a sample through other means is impractical.
Similarly, research looking for cross-cultural differences in organizational or consumer behavior typically uses convenience samples. Rather than selecting cultures with characteristics relevant to the hypothesis being tested, the researchers conducting these studies often choose cultures to which they have access (for example, because they speak the language or have contacts in that culture’s organizations). Further adding to the convenience, cross-cultural research often defines “culture” in terms of nations, which are easier to identify and obtain statistics for, even though many nations include several cultures and some people in a given nation may be more involved with the international business or academic community than with a particular ethnic culture. Here again, the use of convenience sampling limits how well the research represents the intended population.

2. Judgement Sampling:

Rule: Judgment (purposive) sampling is a non-probability sampling technique in which an experienced individual selects the sample based on his or her judgment about some appropriate characteristics required of the sample member. Researchers select samples that satisfy their specific purposes, even if they are not fully representative.

Situation in which method is used along with advantage and disadvantage: A fashion manufacturer regularly selects a sample of key accounts that it believes are capable of providing information needed to predict what may sell in the fall. Thus, the sample is selected to achieve this specific objective. Judgment sampling often is used in attempts to forecast election results. People frequently wonder how a television network can predict the results of an election with only 2 percent of the votes reported. Political and sampling experts judge which small voting districts approximate overall state returns from previous election years; then these bellwether precincts are selected as the sampling units. Of course, the assumption is that the past voting records of these districts are still representative of the political behavior of the state’s population.

3. Quota Sampling:

Rule: The purpose of quota sampling is to ensure that the various subgroups in a population are represented on pertinent sample characteristics to the exact extent that the investigators desire. Stratified sampling, a probability sampling procedure described in the next section, also has this objective, but it should not be confused with quota sampling. In quota sampling, the interviewer has a quota to achieve.

Situation in which method is used along with advantage and disadvantage: An interviewer in a particular city may be assigned 100 interviews, 35 with owners of Sony TVs, 30 with owners of Samsung TVs, 18 with owners of Panasonic TVs, and the rest with owners of other brands. The interviewer is responsible for finding enough people to meet the quota. Aggregating the various interview quotas yields a sample that represents the desired proportion of each subgroup.

Disadvantage: Quota samples tend to include people who are easily found, willing to be interviewed, and middle class. Fieldworkers are given considerable leeway to exercise their judgment concerning selection of actual respondents. Interviewers often concentrate their interviewing in areas with heavy pedestrian traffic such as downtowns, shopping malls, and college campuses. Those who interview door-to-door learn quickly that quota requirements are difficult to meet by interviewing whoever happens to appear at the door. People who are more likely to stay at home generally share a less active lifestyle and are less likely to be meaningfully employed.

Advantage: Quota samples tend to include people who are easily found, willing to be interviewed, and middle class. Fieldworkers are given considerable leeway to exercise their judgment concerning selection of actual respondents. Interviewers often concentrate their interviewing in areas with heavy pedestrian traffic such as downtowns, shopping malls, and college campuses. Those who interview door-to-door learn quickly that quota requirements are difficult to meet by interviewing whoever happens to appear at the door. People who are more likely to stay at home generally share a less active lifestyle and are less likely to be meaningfully employed.

4. Snowball Sampling:

Rule: When interviewing members of a population, you can ask the interviewed persons to nominate other individuals who could be asked to give information or opinion on the topic. You then interview these new individuals and continue in the same way until the material gets saturated, i.e. you get no new viewpoints from the new persons.

Situation in which method is used along with advantage and disadvantage: Snowball sampling is a good method for such populations that are not well delimited nor well enumerated, for example the homeless. The drawback is that you get no exact idea of the factual distribution of the opinions in the target population. Besides, people usually propose people that they know well and who share their own views, which mean that small groups of interest often are passed by unnoticed. One method for compensating this could be asking people to nominate both such persons who share the same views and such persons who are of the opposite opinion. Another method is to start the snowball chain from not one but several different people, perhaps from different social groups.

Probability sampling:

1. Simple random sample. The sample is drawn by lot, for example by picking numbered tags from a hat. If you have a list of the population as a computer file, you can let the computer do the random selection. When the population is very large and it already consists of clusters, the items of which are listed in a file, it can be practical do the sampling in the stages as cluster sampling, i.e. select first a sample of clusters and then, from the items in these clusters, select the final sample. For example, if the population consists of all the people in a country, you can first select randomly a few subdivisions of the country and then select the final sample among the people in these subdivisions. If you intend to interview these people in their homes, you will thus save much time of travelling. 2. Systematic sample. If the intended sampling ratio is 1/n, you can start by choosing the first item at random among the first n objects in the list of the population, and after that you pick each n:th object. The procedure is very easy even without a computer, and the result is just as representative, except in the unusual situation that an important property of the objects should be repeated at every n:th case. 3. Weighted random sample (Stratified). When the population is known to include a very small but essential group, there is the risk that no members of this group will fall into a random sample. Among the users of products such important groups are, among others, people with impaired sight, hearing or motor ability, see a list of such people. Other often significant minorities originate from religions, nationalities and language groups. In order to guarantee that at least some cases from an important minority get into the sample, you can deliberately increase the sampling ratio on this important group. This will of course generate unbalance in the measurements that you get, but it will be easy to restore the original balance later. This is done so that when you combine the results, e.g. by calculating the mean of all measurements, you give the measurements from each group its proper weight corresponding to the genuine percentages in the population.
2 .Proportional and Disproportional Sampling:
In proportionate sampling, the strata sample sizes are made proportional to the strata population sizes. For example if the first strata is made up of males, then as there are around 50% of males in the UK population, the male strata will need to represent around 50% of the total sample.

In disproportionate methods, the strata are not sampled according to the population sizes, but higher proportions are selected from some groups and not others. This technique is typically used in a number of distinct situations:
Advantages of Proportional and Disproportional Sampling: 1. Using a stratified sample will always achieve greater precision than a simple random sample, provided that the strata have been chosen so that members of the same stratum are as similar as possible in terms of the characteristic of interest. The greater the differences between the strata, the greater the gain in precision 2. It guarantees better coverage of the population. The researcher has control over the subgroups that are included in the sample, whereas simple random sampling does not guarantee than any one type of person will be included in the final sample.

Disadvantages of Proportional and Disproportional sampling:
1 One main disadvantage of stratified random sampling is that is can be difficult to identify appropriate strata for a study.
2 A second disadvantage is that it is more complex to organize and analyze the results compared to simple random sampling.

3. Cluster Sampling:
Cluster sampling may be used when it is either impossible or impractical to compile an exhaustive list of the elements that make up the target population. Usually, however, the population elements are already grouped into subpopulations and lists of those subpopulations already exist or can be created. For example, let’s say the target population in a study was church members in the United States. There is no list of all church members in the country. The researcher could, however, create a list of churches in the United States, choose a sample of churches, and then obtain lists of members from those churches.
Advantages:
One advantage of cluster sampling is that it is cheap, quick, and easy. Instead of sampling the entire country when using simple random sampling, the research can instead allocate resources to the few randomly selected clusters when using cluster sampling.
A second advantage to cluster sampling is that the researcher can have a larger sample size than if he or she was using simple random sampling. Because the researcher will only have to take the sample from a number of clusters, he or she can select more subjects since they are more accessible.
Disadvantages:
One main disadvantage of cluster sampling is that is the least representative of the population out of all the types of probability samples. It is common for individuals within a cluster to have similar characteristics, so when a researcher uses cluster sampling, there is a chance that he or she could have an overrepresented or underrepresented cluster in terms of certain characteristics. This can skew the results of the study.
A second disadvantage of cluster sampling is that it can have a high sampling error. This is caused by the limited clusters included in the sample, which leaves a significant proportion of the population unsampled.
Example:
Let’s say that a researcher is studying the academic performance of high school students in the United States and wanted to choose a cluster sample based on geography. First, the researcher would divide the entire population of the United States into clusters, or states. Then, the researcher would select either a simple random sample or a systematic random sample of those clusters/states. Let’s say he or she chose a random sample of 15 states and he or she wanted a final sample of 5,000 students. The researcher would then select those 5,000 high school students from those 15 states either through simple or systematic random sampling. This would be an example of a two-stage cluster sample.

4. Multistage Area Sampling:
Multi-stage sampling is like cluster sampling, but involves selecting a sample within each chosen cluster, rather than including all units in the cluster. Thus, multi-stage sampling involves selecting a sample in at least two stages. In the first stage, large groups or clusters are selected. These clusters are designed to contain more population units than are required for the final sample.

In the second stage, population units are chosen from selected clusters to derive a final sample. If more than two stages are used, the process of choosing population units within clusters continues until the final sample is achieved.
Example:
An example of multi-stage sampling is where, firstly, electoral sub-divisions (clusters) are sampled from a city or state. Secondly, blocks of houses are selected from within the electoral sub-divisions and, thirdly, individual houses are selected from within the selected blocks of houses
Sample location in Jakarta, we wish to get the sample using Multi Stage Random Sample.

First, we determine cluster from Jakarta, such as south, west, north, east, and center.
Second, we determine some samples from each cluster (south, west, north, east, and center) using Simple Random Sample, we call “kelurahan”, or in other word we using Stratified Random Sampling in Jakarta area.
Third, we determine some samples from each “kelurahan” using Simple Random Sample, then we call “RW”,
Fourth, like previous step, we determine some samples from each “RW” using Simple Random Sample, then we call “RT”,
Fifth, we determine some samples from each “RT” using Simple Random Sample, then we call “starting point”
Sixth, we determine sample using Systematic Random Sampling from “starting point”. We move house to house to find chosen respondent based on interval which determined.
Advantages
1. cost and speed that the survey can be done in 2. convenience of finding the survey sample 3. normally more accurate than cluster sampling for the same size sample
Disadvantages
1. Is not as accurate as SRS if the sample is the same size 2. More testing is difficult to do

Sample Size:
Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is determined based on the expense of data collection, and the need to have sufficient statistical power.
Sample Size Calculation:
Step 1: Base Sample-size Calculation
The appropriate sample size for a population-based survey is determined largely by three factors: (i) the estimated prevalence of the variable of interest – chronic malnutrition in this instance, (ii) the desired level of confidence and (iii) the acceptable margin of error.

For a survey design based on a simple random sample, the sample size required can be calculated according to the following formula.
Formula:
n= | t² x p(1-p) | | m² |
Description:
n=required sample size t=confidence interval p=proportion estimate m=margin of error

Example: In the Al Haouz project in Morocco, it has been estimated that roughly 30% (0.3) of the children in the project area suffer from chronic malnutrition. This figure has been taken from national statistics on malnutrition in rural areas. Use of the standard values listed above provides the following calculation
Calculation:
n= | 1.96² x .3(1-.3) | | .05² | n = | 3.8416 x .21 | | .0025 | n = | .8068 | | .0025 | n = | 322.72 ~ 323 |