Sample Design and Sampling Process

Week 11 (i)

SAMPLE DESIGN AND SAMPLING PROCESS

Introduction

Samples are parts or potions of population. A population is the specified total of study elements. A target population, also known as the universe, includes all the members of a real or hypothetical set of people, event or objects to which we wish to generalize the results of our research. A study population is that aggregation of elements from which the sample is actually selected.

Sampling means selecting a given number of subjects from a defined population. The selected items together are then assumed to be representative of that population. Once the researcher has clearly defined the problem and developed an appropriate research design and data collection instruments, the next step in the research process is to select those elements from which the information will be collected. If it were possible a researcher would collect data from every member of the population of interest. Such a compete study of a population is called a census. However since conducting a census is a very expensive and time consuming exercise, a more efficient way would be to collect information from a potion of the population. Such a potions of the population are known as a samples. A researcher may therefore study a sample and on the basis of the information collected from the sample, make inferences about the population. The ability to make this inference from a sample to a population depends on the method by which the sample is selected.

Unlike sampling, if the researcher were to collect data from each and every element of the population then the procedure would be called a census or 100% investigation.

The study of population behavior or characteristics through samples has various advantage and these include:-

i. Accuracy of results- Due to its smaller size and nature, sampling results have more accurate results as compared to census

ii. Least cost – Studies involving the use of samples take comparatively less costs in terms of resources used.

iii. Greater speed for data collection – Collecting data from samples is faster because the researcher is dealing with smaller subjects.

iv. Appropriate for a quality tests- Where the life span of say electric bulbs manufactured is to be tested by subjecting them to destructive high voltage, it would be appropriate to destroy only a proposition rather than the entire population elements.

Sampling frame

A sampling frame is the actual list of sampling units’ from which the sample is selected. It is a list of elements from which the sample is actually drawn. In a simple sampling design, the sampling frame is a list of the study population.

Sampling procedure

The sampling procedure involves the use of eight steps:-

Determination of relevant population and parameters

The first step is the selection of the population which we are interested in studying. A properly defined population includes the explicit definition of all elements of concerns. This definition usually includes four components. These are elements, Sampling units, place and time.

Selection of sampling frame

The second step involves selecting an appropriate sampling frame. This is intended to represent the elements of the population, and the ideal sampling frame is a complete listing of all elements of the population. However, such a listing is rarely available and the sampling frame actually used is likely to differ somewhat from the theoretical target population.

Choose between random and non random sampling

Random and non –random sampling are also known as probability and non –probability sampling. Random (probability) sampling gives each element in the target population an equal and non-zero probability of being selected. Non – random ( non probability) sampling means that not all elements within a target population have an equal chance of being selected.

Probability sampling offers the researcher the advantage of being able to calculate the sampling error of measure, where the non- probability sample does not offer this possibility.

Selection of the sampling method.

This is the stage where we decide how we are going to choose the actual elements of the study sample. If we choose random or probability sampling methods, the options we have include simple random sampling, systematic random sampling, stratified random sampling, cluster random sampling or multistage cluster sampling methods. It we opt for non – random or non – probability samples the choices we have include quota sampling, convenience sampling, purposive sampling or snow ball sampling.

Determination of the necessary sample size.

Samples should be large enough to be representative of the population or interest for analysis of sub-groups and for statistical analysis. Target sample size also have to allow for non- response and in longitudinal design allow for sample attrition due to deaths or dropouts over time. Samples which are very large, have a risk of rejecting a true null hypothesis that there is no differences between groups which are being compared ( type 1 error) and accepting the hypothesis that there are difference which is actually false. Samples which are too small have a risk of failing to demonstrate a real difference between groups that are being compared resulting in a type II error. A type II error is the failure to reject a null hypothesis when it is actually false ie the acceptance of no differences when they actually exist.

Select sample and collect data.

This is the stage when you select the actual individual elements under investigation following the procedures laid out. You then collect data using an appropriate data gathering techniques such as interviews, questionnaires or observations.

Sample validation

Validation involves determining if the sample we have selected is representative of the target population that we wish to generalize our results. In which case, we may which to compare the characteristics of the sample with those already known to exist within the population from which the sample was drawn.

Sampling methods

Once the population of interest is determined, the researcher has to decide whether data will be collected from all study units or from some of the units in the population.

The nature of sampling

Most people intuitively understand the idea of sampling on the taste from a drink which tells us whether it is sweet or sour. If we select a few employment record out of a complete set, we usually assume our selection reflects the characteristics of the full set. If some of our staff favors a flexible work schedule, we infer that others will also. These examples vary in the representative ness, but each is a sample.

The basic idea of sampling is that by selecting some of the elements in a population, we may draw conclusions about the entire population. A population element is the subject on which the measurement is being taken. It is the unit of study. For example, each office worker questioned about a flexible work schedule is a population element, and each business account analyzed is an element of an account population. A population is the total collection of elements about which we wish to make some inferences. All office workers in the firm compose a population of interest; all 4,000 files define a population of interest. A census is a count of all the elements in a population. If 4,000 files define the populations, a census would obtain information form every one of them.

Why Sample?

The economic advantages of taking a sample rather than a census are massive:

1. Why should we spend thousands of shillings interviewing all 4,000 employees in our company if we can find out what we need to know by asking only a few hundreds?

2. Deming argues that the quality of a study is often better with sampling than with a census. He suggests, sampling possesses the possibility of better interviewing (testing), more thorough investigation of missing, wrong or suspicious information. Research findings substantiate this opinion.

3. Sampling also provides much quicker results than does a census. The speed of execution reduces the time between the recognition of a need for information and the availability of that information.

4. Some situations require sampling. When we test the breaking strength of materials, we must destroy them; a census would mean complete destruction of all materials.

5. Sampling is also the only process possible if the population is infinite.

6. In few cases, it would be impossible or dangerous to use whole population.i.e testing of vaccine for AIDS- could result in death.

The advantages of sampling over census studies are less compelling when the population is small and the variability is high. Two conditions are appropriate for a census study: a census is

1. feasible when the population is small and 2. Necessary when the elements are quite different form each other.

When the population is small and variable, any sample we draw may not be representative of the population from which it is drawn. The resulting values we calculate from the sample are incorrect as estimates of the population values. When the sample is drawn properly, however, some simple elements underestimate the parameters and others over estimate them. Variations in these values counteract each other, this counteraction results in a sample value that is generally close to the population value. For these offsetting effects to occur, however, there must be enough members in the sample, and they must be drawn in a way to favor neither overestimation nor underestimation.

Key steps in the sampling procedures

Figure below outlines the step-by –step procedures that researcher can follow when drawing a sample from a population.

The sampling procedure

The definition of the population in any study is determined by the purpose of the study. But, the population should be defined very carefully, and in such a manner the another researcher would be able to identify it sufficiently well to reproduce it. The researcher, for example, must specify whether the population consists of individuals such as housewives, college students or lawyers etc.

Secondly, researcher must determine the sampling frame. A sampling frame is the list of study objects from which the sample will be drawn. An ideal sample frame should contain every population object only. Sampling frames can be obtained from research agencies, government departments or organization

The researcher must next determine the sampling procedure ie. Either probability or non – probability techniques.

The researcher must then determine the appropriate sample size. A rule of thumb is that the larger the samples, the more accurate the conclusions draw are likely to be.

Finally, the researcher must them determine the appropriate sample size.

Types of sampling designs

The members of a sample are selected either on a probability basis or by another means. Probability sampling is based on the concept of random selection, a controlled procedure that assures that each population element is given a known nonzero chance of selection.

It contrast, non probability sampling is non random and subjective. Each member does not have a known, nonzero chance of being included. Allowing interviewers to choose sample member ‘at random’ (meaning ‘ as they wish ‘ or ‘wherever they find them’) is not random sampling. Only probability samples provides estimates of precision.

Types of sampling designs

| | |Presentation Basis |
|Element selection |Probability |Non probability |
|Unrestricted |Simple random |Convenience |
|Restricted |Complex random |Purposive |
| |Systematic |Judgment |
| |Cluster |Quota |
| |Stratified |Snowball |
| |Multi-stage cluster | |

1 Probability Sampling

The unrestricted, simple random sample is the simplest form of probability sampling. Since all probability samples must provide a known nonzero chance of selection for each population element, the simple random sample is considered a special case in which each population element has a known and equal chance of selection. In this section, we use the simple random sample to build a foundation for understanding sampling procedures and choosing probability samples.

2. Simple Random Sampling

In simple random sampling, all study objects have an equal chance of being included in the sample. Researchers begin with a complete list of all members of a population and then choose sample items at random. It should be noted that in simple random sampling, each study object is selected completely independently of other objects.

The sampling process involves assigning a unique identification number to each study object in the sampling frame. After this, the researcher must design a method of selecting study objects in a manner that allows all equal chance of being selected. One way of doing this is writing these identification numbers on smallpieces of paper, mixing them thoroughly in a box, and then picking the papers without looking. The numbers on the pieces of paper picked identify the study objects to be included in the sample. In some cases, however, this procedure (lottery method) may be impractical or tedious.

Another procedure used in selecting study objects in simple random sampling involves the use of tables of random numbers. The researcher begins picking randomly objects from any preselected place in the table of random numbers. Then s/he systematically chooses numbers by either moving vertically or horizontally. The sample will therefore consist of the study objects whose numbers are chosen.

Complex probability Sampling

Simple random sampling is often impractical. It requires a population list that is often not available. The design may also be wasteful because it fails to use all the information about a population. In addition, the carrying out of a simple random design may be expensive in time and money. These problems have led to the development of alternative designs that are superior to the simple random design in statistical and/or economic efficiency.

A more efficient sample in a statistical sense is one that provides a given precision (standard error of the mean) with a smaller sample size. A sample that is economically more efficient is one that provides a desired precision at a lower dollar cost. We achieve this with designs that enable us to lower the costs of data collecting, usually through reduced travel expense and interviewer time.

In the discussion that follows, four alternative probability sampling approaches are considered: systematic, stratified, cluster and multi-stage.

4. Systematic Sampling

This method is frequently used in production and quality control sampling. In this approach, every n'th element in the population is sampled, beginning with a random start of an element in the range of 1 to n. After a randomly selected start point a sample item would be selected every n'th item. Assume that in an assembly line it was decided to sample every 10th item and a start point of 67 was chosen randomly, the sample would be the following items:
67th, 77th, 87th 97thand so on.

The gap between selections is known as the sampling interval and is itself often randomly selected. A concern with this technique is the possible periodicity in the population that may coincide with the sampling interval and cause bias.

5. Stratified Sampling

Most populations can be segregated into several mutually exclusive sub-populations, or strata. Thus, the process by which the sample is constrained to include elements from each of the segments is called stratified random sampling.

There are three reasons why a researcher chooses a stratified sample:

* To increase a sample's statistical efficiency; * To provide adequate data for analyzing the various subpopulations, and * To enable different research methods and procedures to be used in different strata.

With the ideal stratification, each stratum is homogeneous internally and heterogeneous with other strata. The size of the strata samples is calculated with two pieces of information:
(i) How large the total sample should be and
(ii) How the total sample should be allocated among strata.

5. Cluster Sampling

In a simple random sample, each population element is selected individually. The population can also be divided into groups of elements with some groups randomly selected for study. This is cluster sampling. Animmediate question might be: How does this differ from stratified sampling? They may be compared as follows:

|Stratified sampling |Cluster sampling |
|We divide the population into a few subgroups each with many |We divide the population into many subgroups, each with a few |
|elements in it. The subgroups are selected according to some |elements in it. The subgroups are selected according to some |
|criterion that is related to the variables under study. |criterion of ease or availability in data collection. |
|We try to secure homogeneity within subgroups. |We try to secure heterogeneity within subgroups and homogeneity |
|We randomly choose elements from within each subgroup. |between subgroups, but we usually et reverse. |
| |We randomly choose a number of subgroups, which we then typically |
| |study in total. |

When done properly, cluster sampling also provides an unbiased estimate of population parameters. Two conditions foster the use of cluster sampling:' (l) the need of more economic efficiency than can be provided by simple random sampling and (2) the frequent unavailability of a practical sampling frame for individual elements.

Non-Probability Sampling
Any discussion of the relative merits of probability versus non probability sampling clearly shows the technical superiority of the former. In probability sampling, researchers use a random selection of elements to reduce or eliminate sampling bias. Under such conditions, we can have substantial confidence that the sample is representative of the population from which it is drawn. In addition, sample designs, we can estimate an interval range within which the population parameter is expected to fall. Thus, we not only can reduce the chance for sampling error but also can estimate the range of probable sampling error present.

With a subjective approach like non probability sampling, the probability of selecting population elements is unknown. There are a variety of ways to choose persons or cases to include in the sample. Often we allow the choice of subjects to be made by field workers on the scene. When this occurs, there is greater opportunity for bias to enter the sample selection procedure and to distort the findings of the study. Also, we cannot estimate any range within which to expect the population parameter. Given the technical advantages of probability sampling over non probability sampling, why would anyone choose the latter? There are some practical reasons for using these less precise methods.

Practical Considerations

We may use non probability sampling procedures because they satisfactorily meet the sampling objectives. While a random sample will give us a true cross section of the population, this may not be the objective of the research. If there is no desire or need to generalize to a population parameter, then there is much less concern about whether the sample fully reflects the population. Often researchers have more limited objectives. They may be looking only for the range of conditions or for examples of dramatic variations. This is especially true in exploratory research where one may wish to contact only certain persons or cases that are clearly typical.

Additional reasons for choosing non probability over probability sampling are cost and time. Probability sampling clearly calls for more planning and repeated callbacks to ensure that each selected sample member is contacted. These activities are expensive. Carefully controlled non probability sampling often seems to give acceptable results, so the investigator may not even consider probability sampling.

While probability sampling may be superior in theory, there are breakdowns in its application. Even carefully stated random sampling procedures may be subject to careless application by the people involved. Thus, the ideal probability sampling may be only partially achieved because of the human element.

It is also possible that non probability sampling may be the only feasible alternative. The total population may not be available for study in certain cases. At the scene of a major event, it may be infeasible to even attempt to construct a probability sample. A study of past correspondence between two companies must use an arbitrary sample because the full correspondence is normally not available.

In another sense, those who are included in a sample may select themselves. In mail surveys, those who respond may not represent a true cross section of those who receive the questionnaire. The receivers of the questionnaire decide for themselves whether they will participate. There is some of this self-selection in almost all surveys because every respondent chooses whether to be interviewed.

Methods

1. Convenience. Non probability samples that are unrestricted are called convenience samples. They are the least reliable design but normally the cheapest and easiest to conduct. Researchers or field workers have the freedom to choose whoever they find, thus the name convenience. Examples include informal pools of friends and neighbors or people responding to a newspaper's invitation for readers to state their positions on some public issue.

While a convenience sample has no controls to ensure precision, it may still be a useful procedure. Often you will take such a sample to test ideas or even to gain ideas about a subject of interest. In the early stages of exploratory research, when you are seeking guidance, you might use this approach. The results may present evidence that is so overwhelming that a more sophisticated sampling procedure is unnecessary. In an interview with students concerning some issue of campus concern. you might talk to 25 students selected sequentially. You might discover that the responses are so overwhelmingly one-sided that there is no incentive to interview further.

2. Purposive Sampling. A non probability sample conforms to certain criteria is called purposive sampling. There are two major types -judgment sampling and quota sampling. a) Judgment Sampling occurs when a researcher selects sample members to conform to some criterion. In a study of labor problems, you may want to talk only with those who have experienced on-the-job discrimination. Another example of judgment sampling occurs when election results are predicted from only a few selected precincts that have been chosen because of their predictive record in past elections.

When used in the early stages of an exploratory study, a judgment sample is appropriate. When one wishes to select a biased group for screening purposes, this sampling method is also a good choice.

Companies often try out new product ideas on their employees. The rationale is that one would expect the firm's employees to be more favourably disposed towards a new product idea than the public. If the product does not pass this group, it does not have prospects for success in the general market.

b. Quota Sampling is the second type of purposive sampling. We use it to improve representative ness. The logic behind quota sampling is that certain relevant characteristics describe the dimensions of the population. If a sample has the same distribution on these characteristics, then it is likely representative of the population regarding other variables on which we have no control. Suppose the student body of KEMU is 55 percent female and 45 percent male. The sampling quota would call for sampling students at a 55 to 45 percent ratio. This would eliminate distortions due to a non representative gender ratio.

In most quota samples, researchers specify more than one control dimension. Each should meet two tests:

1. It should have a distribution in the population that we can estimate.

2. It should be pertinent to the topic studied: We may believe that responses to a question should vary, depending on the gender of the respondent. If so, we should seek proportional responses from both men and women. We may also feel that undergraduates differ from graduate students, so this would be a dimension. Other dimensions such as the student's academic discipline, ethnic group, religious affiliation, and social group affiliation may be chosen. Only a few of these controls can be used. To illustrate, suppose we consider the following: Gender - two categories - male, female Class level - two categories - graduate and undergraduate College - six categories - Arts and Science, Agriculture, Architecture, Business, Engineering, other. Religion - four categories - Protestant, Catholic, Jewish, other Fraternal affiliation - two categories - member, nonmember Family social-economic class - three categories - upper, middle, lower.

Quota sampling has several weaknesses. First, the idea that quotas on some variables assume a representative ness on others is argument by analogy. It gives no assurance that the sample is representative on the variables being studied. Often, the data used to provide controls may also be dated or inaccurate. There is also a practical limit on the number of simultaneous controls that can be applied to ensure precision. Finally, the choice of subjects is left to field workers to make on a judgmental basis. They may choose only friendly looking people, people who are convenient to them, and so forth.

Despite the problems with quota sampling, it is widely used by opinion pollsters and marketing and other researchers. Probability sampling is usually much more costly and time-consuming. Advocates of quota sampling argue that while there is some danger of systematic bias, the risks are usually not that great. Where predictive validity has been checked (eg, in election polls), quota sampling has been generally satisfactory.

3. Snowball. This design has found a niche in recent years in applications where respondents are difficult to identify and are best located through referral networks. In the initial stage of snowball sampling, individuals are discovered and mayor may not be selected through probability methods. This group is then used to locate others who possess similar characteristics and who, in turn, identify others. Similar to a reverse search for bibliographic sources, the 'snowball' gathers subjects as it rolls along.

Variations on snowball sampling have been used to study drug cultures, teenage gang activities, power elites, community relations, insider trading and other applications where respondents are difficult to identify and contact.

Dimensional Sampling. The researcher identifies the various characteristics of interest in a population and obtains at least one correspondent for every combination of those factors. It is a further refinement of the quota sampling technique. ( i.e, you have a number of features, Male/female, so you choose one man to represent the men and one woman to represent the women)

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Define the population

Decide on sampling frame

Determine the sampling procedure

Decide on appropriate sample size

Select the sample elements