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Sampling

Meaning

Population- Empirical field studies require collection of f irst-hand information or data pertaining to

the units of study from the field. The units of study may include geographical areas like districts,

talukas, cities or villages which are covered by the study, or institutions or households about which

information is required, or persons from whom information is required, or persons from whom

information is available.

The aggregate of all the units pertaining to a study is called the population or the universe.

Population is the target group to be studied. All the items under consideration in any field of inquiry

constitute Universe or Population. The population or universe may be finite or infinite.

Sampleis subset of a larger population. It is the aggregate of elements about which we wish to

make inferences. A member of the population is an element. It is the subject on which measurement

is taken. It is the unit of study.

Samplingis the process of selecting a small number of elements from a larger defined target group

of elements such that the information gathered from the small group will allow judgments to be

made about the larger groups. In the other words, it is the process of drawing a sample from a

larger population is called sampling.

Sampling frame -The list of sampling units from which a sample is taken is called sampling frame,

e.g., a map, a telephone directory, a list of industrial undertakings, a list of car licensees etc.

Example:A researcher wants to survey the brand preferences of households regarding toilet soaps

in Jayanagar area of the city of Bangalore. A household is the sampling unit. The total of all

households in Jayanagar area is the population. Suppose in a detailed map of Jayanagar, but list of

households is not available, each block may be considered a sampling unit. A list of such blocks willbe used as the frame.

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Need to sample

Lower costneed for sample arises due to budget constraints, where it is not feasible to study

population.

Greater speed of data collection

Due to time constraints in data collection, we can employsampling.

When greater accuracy of results is needed- Sampling will lead to greater accuracy of

results

Impracticable to survey the entire population

Census Vs. Sampling

Data originally collected for an investigation are known as primary data. Such data are collected

original in character. The primary data may be collected by following either census method or the

sampling method.

Census -A count of all the elements in populationis census. When all the units are studied, such a

complete coverage is census survey. A complete detail of all the items in the population is known

as a census inquiry. Besides this type of inquiry involves a great deal of time, money and energy.

Example- According to the Census 2001, in India out of total population of 1028 million about 285

millions live in urban areas and 742 millions live in rural areas.

Sample survey- When only a sample of universe is studied, the study is called a sample survey.

The process of designing a field study, among other things, involves a decision to use sampling or

not. The researcher must decide whether he should cover all the units or a sample of units.

In making this decision' of census or sampling, the following factors are considered:

1. The size of the population: If the population to be studied is relatively small, say 50 institutions or

200 employees or 150 households, the investigator may decide to study the entire population. The

task is easily manageable and the sampling may not be required. But if the population to be studied

is quite large, sampling is warranted. However, the size is a relative matter. Whether a population is

large or small depends upon the nature of the study, the purpose for which it is undertaken, and the

time and other resources available for it.

2. Amount of funds budgeted for the study: The decision regarding census or sampling depends

upon the budget of the study. Sampling is opted when the amount of money budgeted is smaller

than the anticipated cost of census survey.

3. Facilities:The extent of facilities available- staff, access to computer facility and accessibility to

population elements- is another factor to be considered in deciding to sample or not. When the

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availability of these facilities is extensive, census survey may be manageable. Otherwise, sampling

is preferable.

4. Time:The time limit within which the study should be completed is another important factor to be

considered in deciding the question of census or sample survey. This, in fact, is a primary reason for

using sampling by academic and marketing researchers.

Advantages of sampling over census

Sampling reduces the time and cost of research studies.With the use of sampling, it has

become possible to undertake even national or global studies at a reasonable cost and time.

Such economy in time and cost improves the viability of several field studies like credit surveys,

poverty surveys and marketing surveys.

Sampling saves labour.A smaller staff is required both for fieldwork and for processing and

analyzing the data.

The quality of a study is often better with sampling than with a complete coverage. The

possibility of better interviewing, more thorough investigation of missing, wrong or suspicious

information, better supervision, and better processing is greater in sampling than in complete

coverage.

Sampling provides much quicker results than does a census. The speed of execution

minimizes the time between the recognition of a need for information and the availability of that

information. The speed of execution is vital in feasibility studies, evaluation studies and business

research. Timely execution of a study is essential for making use of its findings.

Sampling is the only procedure possible, if the population is infinite, e.g. consumer

behaviour surveys etc.

Statistical sampling yields a crucial advantage over any other way of choosing a part of

the population for a study.

Limitations of Sampling

1.Sampling demands a thorough knowledge of sampling methods and procedures and an exerciseof greater care; otherwise the results obtained may be incorrect or misleading.

2.When the characteristic to be measured occurs only rarely in the population, a very large sample

is required to secure units that will give, reliable information about it. A large sample has all the

drawbacks of a census survey.

3.A complicated sampling plan may require more labour than a complete coverage.

4.It may not be possible to ensure the representativeness of the sample, even by the most perfect

sampling procedures. Therefore sampling results in a certain degree of sampling errors, i.e., there

will be some difference between the sample value and the population value.

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Characteristics of Good Sample

Whether the result obtained from a sample survey would be accurate or not depends upon the

quality of the sample.

1. Representativeness:A sample must be representative of the population. Probability sampling

technique yield representative sample.

2. Accuracy: Accuracy is defined as the degree to which bias is absent from the sample. An

accurate (unbiased) sample is one which exactly represents the population. It is free from any

influence that causes any difference between sample value and population value (say, average).

3. Precision:The sample must yield precise estimate. Precision is measured by the standard error

or standard deviation of the, sample estimate. The smaller the standard error or estimate, the

higher is the precision of the sample.

4. Size:A good sample must be adequate in size in order to be reliable. The sample should be of

such size that the inferences drawn from the sample are accurate to the given level of

confidence.

Steps in sampling

There are five steps which precede collection of the data by means of sample.

1. Defining the population or universe.The population or universe is the specific group of items

which the researchers wish to study and about which they plan to generalize. If a theatre owner is

investigating the movie going habits of local college students, the population will be the students

enrolled on a particular date. The definition of the universe, in any particular case is determined

solely by the research objectives of the particular study.

2. Development of a frame.A frame is a list of the population. It consists of names and addresses

of the individuals and institutions. It can also specify a definite location, boundary, an address or a

set of rules by which sampling unit can be identified. For example, a researcher has undertaken a

study for finding the proportion of the grocery stores in the Chennai metropolitan area, which stock

cardamom. Here grocery stores would be observed. For the purpose of identifying the stores, a list

of all Chennai metropolitan area grocery stores must be obtained. From the list it will be easy to

choose. If no such list is available one may choose a sample of areas.

3. Selection of sample design.The researcher can go for probability or non-probability design. If

the researcher wants to estimate the sampling error of the results, a probability sample should be

used. If it is very difficult to develop a frame, a non-probability sample should be used. The

researcher should feel confident that the sample used provides a legitimate and accurate picture of

the universe.

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4. Selecting the sample size. The sample size should never be less than thirty. But the final

decision on proper sample size really depends on whether the researcher feels reasonably

confident that his sample is large enough to accurately depict the population.

5. Selecting the representative sample. The selected sample should have all the characteristics

of the population and it must provide the whole information about the population from which it is

drawn.

Types of Sampling Methods or techniques

Sampling methods or techniques may be classified into two generic types:

(a) Probability or Random Sampling

(b) Non-probability or Non-random Sampling

Probability Sampling Methods

1. Simple random sampling

2. Stratified random sampling

3. Systematic random sampling

4. Cluster sampling

5. Area sampling

6. Multi-stage

7. Double sampling

8. Sequential methods

Non probability Sampling Methods

1. Convenience or accidental sampling

2. Purposive or Judgmental sampling

3. Quota sampling

4. Snow-ball sampling

Probability Sampling Methods

A probability sampling scheme is one in which every unit in the population has a chance (greater

than zero) of being selected in the sample, and this probability can be accurately determined.

Simple Random Sampling

Random sampling refers to the sampling technique in which each and every item of the population

is given an equal chance of being included in the sample. The selection is thus free from personal

bias because the investigator does not exercise his discretion or preference in the choice of items.

Since selection of items in the sample depends entirely on chance this method is also known as the

method of chance selection.

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Random sampling is sometimes referred to as 'representative sampling'. If the sample is chosen at

random and if the size of the sample is sufficiently large, it will represent groups in the universe. A

random sample is also known as 'probability sample, because every item of the universe has an

equal opportunity of being selected in the sample.

Methods of obtaining a random sample

To ensure randomness of selection one may adopt any of the following methods:

1. Lottery Method.This is a very popular method of taking a random sample. Under this method,

all the items of the universe are numbered on separate slips of paper of identical -size and shape.

These slips are then folded and mixed up in a container or drum, a blindfold selection is then made

of the number of slips required to constitute the desired sample size. The selection of items thus

depends entirely on chance.

Example:If we want to take a sample of 10 persons out of a population of 100, the procedure is to

write the name of all the 100 persons on separate slips of paper, fold these slips, mix them

thoroughly and then make a blindfold selection of 10 slips

2. Table of Random Numbers:The lottery method discussed above becomes quite cumbersome

to use as the size of population increases. An alternative method of random selection is that of

using the table of random numbers.

Three such tables are available, namely

(i) Tippett's table of random numbers,

(ii) Fisher and Yate's numbers, and

(iii) Kendall and Babington Smith numbers.

Tippett's numbers are most popular. They consist of 41,600 digits taken from census reports and

combined by fours to give 1400 four-figure numbers. We give here the first forty sets as an

illustration of their general appearance. .

2952 6641 3992 9792 7969 5911 3170 5624

4167 9524 1545 1396 7203. 5366 1300 2693

2370 7483 3408 2762 3563 1089 6913 7691

0560 5246 1112 6107 6008 8126 4233 8776

2754 9143 1405 9025 7002 6111 8816 6446

One may question, and quite rightly, as to how it was ensured that these digits are random. It may

be pointed out that the digits in the table were chosen haphazardly but the real guarantee of their

randomness lies in practical tests. Tippett's numbers have been subjected to numerous tests and

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used in many investigations and their randomness has been well established for all practical

purposes.

An example to illustrate how Tippett's table of random numbers may be used is given below.

Suppose we have to select 20 items out of 6,000. The procedure is to number all the 6,000 items

from 1 to 6000. A page from Tippett's table may then be consulted and the first twenty numbers up

to 6000 noted down. Items bearing those numbers will be included in the sample. Making use of the

portion of table given above, the required numbers are:

2952 3992 5911 3170 5624 4167

1545 1396 5366 1300 2693 2370

3408 2762 3563 1089 0560 5246

1112 4233

The items which bear the above numbers constitute the sample.

Fisher and Yate's tableconsist of 15,000 numbers. These have been arranged in two digits in 300

blocks, each block consisting of 5 rows, and 5 columns.

Kendall and Smith tablealso constructed random numbers (10,000 in, all) by using a randomizing

machine. However, this method of random selection cannot be followed in case of articles like ghee,

oil petrol, wheat, etc.

3. Use of computer

If the population is very large and if computer facilities are available, a computer may be used for

drawing a random sample. The computer can be programmed to print out a series of random

numbers as the researcher desires.

Advantages of random sampling

All the elements in the population have an equal chance of being selected.

Since the selection of items in the sample depends entirely on chance there is no possibility of

personal bias affecting the results.

A random sample represents the universe in a better way. As the size of the sample increases,

it becomes increasingly representative of the population.

The analyst can easily assess the accuracy of his estimate because sampling errors follow the

principles of chance. The theory of random sampling is developed much more than any other

type of sampling and provides the most reliable information at the least cost.

Disadvantages of random sampling

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It is often impractical, because of non-availability of population list, or of difficulty in listing the

population.

Sometimes it is difficult for the investigator to have up-to date lists of all the items of the

population to be sampled. This restricts the use of random sampling method.

The task of preparing slips is time-consuming and expensive.

The size of the sample required to ensure statistical reliability is usually large under random

sampling than in stratified sampling.

From the point of view of field survey it has been claimed that cases selected by random

sampling tend to be too widely dispersed geographically and that the time and cost of collecting

data become too large.

Stratified random sampling

Stratified random sampling is a method of probability sampling in which the population is divided

into different homogeneous subgroups or strata or classes and a sample is drawn from each

subgroup or stratum at random. Each stratum is then sampled as an independent sub-population,

out of which individual elements can be randomly selected. A stratified sample is obtained by

independently selecting a separate simple random sample from each population stratum.

Example,if we are interested in studying the consumption pattern of the people of Delhi, the city of

Delhi may be divided into various parts (such as zones or wards) and from each part a sample may

be taken at random. However, the selection of cases from each stratum must be done with great

care and in accordance with a carefully designed plan as otherwise random selection from the

various strata may not be accomplished.

Stratified sampling may be either proportional or disproportional.

In proportional samplingthe cases are drawn from each stratum in the same proportion as they

occur in the universe. For example, if we divide the city of Delhi into four zones A, B, C and D with

40%, 30%, 20% and 10% of the total population respectively and if the sample size is one thousand

then we should draw 400, 300, 200 and 100 cases respectively from zones A, B, C and D, i.e.,

sample is proportional to the size in the universe. .

In disproportional stratified sampling an equal number of cases is taken from each stratum,

regardless of how the stratum is represented in the universe. Thus, in the above example, an equal

number of items from each zone may by drawn, that is, 250. This approach is obviously inferior to

the proportional stratified sampling.

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Advantages of stratified sampling

1. More representatives. Since the population is first divided into various strata and then a sample

is drawn from each stratum there is little possibility of any essential group of the population being

completely excluded. A more representative sample is thus secured. Stratified sampling is

frequently regarded as the most efficient system of sampling.

2. Greater accuracy. Stratified sampling ensures greater accuracy. The accuracy is maximum if

each stratum is so formed that it consists of uniform or homogeneous items.

Disadvantages of stratified sampling

1.Each stratum must contain, as far as possible, homogeneous items as otherwise the results may

not be reliable. However, this is a very difficult task and may involve considerable time & expense.

Utmost care must be exercised in dividing the population into various strata.

2.This method requires a prior knowledge of the composition of the population, which is not always

possible.

3.This method is also subject to classification errors. It is possible that researcher may misclassify

certain elements.

4.The items from each stratum should be selected at random. But this may be difficult to achieve in

the absence of skilled sampling supervisors and a random selection within each stratum may not be

ensured.

Systematic Sampling or Fixed Interval Method

This method is popularly used in those cases where a complete list of the population from which

sample is to be drawn is available. The method is to select every kth item from the list where 'k'

refers to the sampling interval. The first item between the first and the kth is selected at random.

Sampling Interval or k = (size of the universe / size of the sample)

Example, if a complete list of 1,000 students of a college is available and if we want to draw a

sample of 200 this means we must take every fifth item (i.e., k=5). The first item between one and

five shall be selected at random. Suppose it comes out to be three. Now we shall go on adding five

and obtain numbers of the desired sample. Thus, the second item would be the 8th student, thethird 13th student; the fourth, 18th student and so on.

Advantages of Systematic Sampling

1.It is much simpler than random sampling. It is easy to use.

2. The time and work involved in sampling by this method are relatively smaller. The results

obtained are also found to be generally satisfactory provided care is taken to see that there are no

periodic features associated with the sampling interval.

3.This method is cheaper than simple random sampling.

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4.Sample is spread evenly over the population.

5. It is statistically more efficient than a simple random sample when population elements are

ordered chronologically, by size, class etc.

Disadvantages of Systematic Sampling

1. This method ignores all the elements between two kth elementselected. Further, except the first

element, other selected elements are not chosen random.

Hence, this sampling cannot be considered to a probability sampling in the strict sense of the term.

2.As each element does not have an equal chance of being selected, the resulting sample is not a

random one. For studies aiming at estimations or generalization, this disadvantage would be a

serious one.

3. If the population is ordered in a systematic way with respect to the characteristic the investigator

is interested in, then it is possible that only certain types of items will be included in the population,

or at least more of certain types than others.

For instance, in a study of salaries of workers the list may be such that every tenth worker of the list

gets wages above Rs. 5000 per month.

Cluster sampling

Where the population elements are scattered over a wider area and a list of population elements is

not readily available, the use of simple or stratified random sampling method would be too

expensive and time-consuming. In such cases cluster sampling is usually adopted.

Cluster sampling means random selection of sampling units consisting of population elements.

Each such sampling unit is a cluster of population elements. Then from each selected sampling unit,

a sample of population elements is drawn by either simple random selection or stratified random

selection.

Example: Suppose a researcher wants to select a random sample of 1,000 households out of

40,000 estimated households in a city for a survey. A direct sample of individual households would

be difficult to select, because a list of households does not exist and would be too costly to prepare.

Instead, he can select a random sample of a few blocks/wards. The number of blocks to be selected

depends upon the average number of estimated households per block. Suppose the average

number of households per block is 200, then 5 blocks comprise the sample. Since the number of

households per block varies, the actual sample size depends on the block which happen to be

selected. Alternatively, he can draw a sample of more blocks and from each sample blocks a certain

number of households may be selected by systematic sampling.

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Advantages of Cluster sampling

1. This method is much easier and more convenient to apply when large populations are studied or

large geographical areas are covered.

2.The cost of this method is much less when compared with other sampling method.

3.Units of study can be easily substituted for other units within the same random section.

Disadvantages of Cluster sampling

1. The cluster sizes may vary and this variation could increase the bias of the resulting sample. For

example, if the researcher were to interview all adults in households in each selected street the

number of adults would vary from house to house. There would be certain bias resulting from the

large coverage of big families.

2.The sampling error in this method of sampling is greater. Thus, this method is statistically less

efficient than other probability sampling methods.

Area Sampling

This is an important form of cluster sampling. In larger field surveys, clusters consisting of specific

geographical areas like districts, talukas, villages or blocks in a city are randomly drawn. As the

geographical areas are selected as sampling units in such cases, their sampling is called area

sampling. It is not a separate method of sampling, but forms part of cluster sampling.

Multi-stage sampling

In this method, sampling is carried out in two or more stages. The material is regarded as made up

of a number of first stage sampling units, each of which is made of a number of second stage units,

etc. At first, the first stage units are sampled by some suitable method, as such random sampling.

Then, a sample of second stage units is selected from each of the selected first stage units again by

some suitable method which may be the same as, or different from the method employed for the'

first stage units. Further stages may be added as required. Example:Suppose, it is decided to take

a sample of 5,000 households from the State of U.P.

At the first stage, the State may be divided into a number of districts and a few districts

selected at random.

At the second stage, each district may be sub-divided into a number of villages and sample of

villages may be taken at random.

At the third stage, a number of households may be selected from each of the villages selected

at the second stage. In this way, at each stage the sample size becomes smaller and smaller.

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Merits of multistage sampling

1. Multistage sampling introduced flexibility in the sampling method which is lacking in other

methods. It enables existing divisions and sub-divisions of the population to be used as units at

various stages, and permits the field work to be concentrated and yet large area to be covered.

2. Another advantage of the method is that sub-division into second stage unit, (i.e., the

construction of the second stage frame) need be carried out for only those first stage units which

are included in the sample.

3. It is, therefore, particularly valuable in surveys of underdeveloped areas where no frame is

generally sufficiently detailed and accurate for, sub-division of the material into reasonable small

sampling units.

Limitations of multistage sampling

However, a multi-stage sample is in general less accurate than a sample containing the same

number of final stage units which have been selected by some suitable single stage process.

Other probability sampling techniques

In addition to the four basic probability-sampling techniques, there are a variety of other sampling

techniques. Most of these may be viewed as extensions of the basic techniques and were

developed to address complex sampling problems. Two techniques with some relevance to

marketing research aredouble sampling & sequential sampling.

Double ( or Two-Phase) Sampling and Multi-Phase Sampling

Double sampling also called two-phase sampling, certain population elements are sampled twice. In

the first phase, a sample is selected and some information is collected from all the elements in the

sample. In the second phase, a sub sample is drawn from the original sample and additional

information is obtained from the elements in the sub-sample. The process may be extended to three

or more phases, and the different phases may take place simultaneously or at different times.'

Double sampling can be useful when no sampling frame is readily available for selecting finalsampling units but when the elements of the frame are known to be contained within a broader

sampling frame.

For example, a researcher wants to select households in a given city that consume apple juice.

The households of interest are contained within the set of all households, but the researcher does

not know which they are.

In applying double sampling, the researcher would obtain a sampling frame of all households in

the first phase. This would be constructed from the city directory or purchased. Then a sample

of households would be drawn, using systematic random sampling to determine the amount of

apple juice consumed.

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In the second phase, households that consume apple juice would be selected and stratified

according to the amount of apple juice consumed. Then a stratified random sample would be

drawn and detailed questions regarding apple juice consumption asked.

Sequential methods

In sequential sampling, the population elements are sampled sequentially, data collection and

analysis are done at each stage, and a decision is made as to whether additional population

elements should be sampled. The sample size is not known in advance, but a decision rule is stated

before sampling begins. At each stage, this rule indicates whether sampling should be continued or

whether enough information has been obtained. Sequential sampling has been used to determine

preferences for two competing alternatives. In one study, respondents were asked which of two

alternatives they preferred, and sampling was terminated when sufficient evidence was

accumulated to validate a preference. It has also been used to establish the price differential

between a standard model and a deluxe model of a consumer durable.

Non-probability Sampling Methods

Non-probability sampling the selection of elements based on assumptions regarding the population

of interest, which forms the criteria for selection. Hence, because the selection of elements is non-

random, non-probability sampling does not allow the estimation of sampling errors. The primarymethods of non-probability sampling are:

Convenience sampling or Accidental sampling

Convenience sampling is a type of non-probability sampling which involves the sample being drawn

from that part of the population which is close to hand. It means selecting sample units in a just 'hit

and miss' fashion, e.g., interviewing people whom we happen to meet. This sampling also means

selecting whatever sampling units are conveniently available, e.g.,a teacher may select students in

his class. This method is also known as accidental sampling because the respondents whom theresearcher meets accidently are included in the sample.

Usefulness:Though convenience sampling has no status, it may be used for simple purpose such

as testing ideas or gaining ideas or rough impression about a subject of interest. It lays groundwork

for a subsequent probability sampling. Sometimes it may have to be necessarily used.

Advantages:

1.Convenience sampling is the cheapest and simplest.

2.It does not require a list of population.

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3.It does not require any statistical expertise.

Disadvantages:

1.Convenience sampling is highly biased, because of the researcher's subjectivity, and so it does

not yield a representative sample.2.It is the least reliable sampling method. There is no way of estimating the representativeness of

the sample.

3.The findings cannot be generalized.

Purposive (or Judgement) sampling

Judgment sampling relies upon belief that participants fit characteristics. A judgement sample is

obtained according to the discretion of someone who is familiar with the relevant characteristics of

the population. This method means deliberate selection of sample units that conform to some pre-

determined criteria. This is also known as Judgement sampling. This involves selection of cases

which we judge as the most appropriate ones for the given study. It is based on the judgement of

the researcher or some expert. It does not aim at securing a cross section of a population.

The chance that a particular case be selected for the sample depends on the subjective judgement

of the researcher. For example, a researcher may deliberately choose industrial undertakings in

which quality circles are believed to be functioning successfully and undertakings in which quality

circles are believed to be a total failure.

Advantages:

1. It is less costly and more convenient.

2. It guarantees inclusion of relevant elements in the sample. Probability sampling plans cannot give

such guarantee.

Disadvantages:

1.This does not ensure the representativeness of the sample.

2.This is less efficient for generalizing when compared with random sampling.

3.This method requires more prior extensive information about the population one studies. Without

such information, it is not possible to adjudge the suitability of the sample items to be selected.

4.This method does not lend itself for using inferential statistics, because, this sampling does not

satisfy the underlying assumption of randomness.

Quota sampling

This is a form of convenient sampling involving selection of quota groups of accessible sampling

units by traits such as sex, age, social class, etc. when the population is known to Consist of various

categories by sex, age, religion, social class etc., in specific proportions, each investigator may be

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given an assignment of quota groups specified by the pre-determined traits in specific proportions.

He can then select accessible persons, belonging to those quota groups in the area assigned to

him. "Quota Sampling is therefore a method of stratified sampling in which selection within strata is

non-random. It is this non-random element that constitutes its greatest weakness. "

Quotas are stratified by such variables as sex, age, social class and religion. It is easy to classify

the accessible respondents under sex, age and religion, but it is very difficult to classify them into

social categories, since social class usually involves a combination of factors such as occupation,

income and caste and the interviewer's subjective judgement and bias play some role in the social

class classification of respondents.

Snow-ball sampling

Snowball sampling relies upon respondent referrals of others with like characteristics. This is the

colourful name for a technique of building up a list or a sample of a special population by using an

initial set of its members as informants. For example, if a researcher wants to study the problem

faced by Indians through some source like Indian Embassy. Then he can ask each one of them to

supply names of other Indians known to them, and continue this procedure until he gets an

exhaustive list from which he can draw a sample or make a census survey. This sampling technique

may also be used in socio-metric studies. For example, the members of a social group may be

asked to name the persons with whom they have social contacts, each one of the persons so

named may also be asked to do so, and so on. The researcher may thus get a constellation of

associates and analyse it.

For example, if the investigator was able to find a few bonded labourers willing to talk to him he

might ask them for the names and locations of others; who might also be willing to be interviewed.

Sampling of this type has often been done in studies for elite groups, either those in power in a

community or members of upper classes. In community studies there is often the feeling that only

those in power really know who else has power.

Sampling and non-sampling error

To appreciate the need for sampling surveys, it is necessary to understand clearly the role of

sampling and non-sampling errors incomplete enumeration and sample surveys. The errors arising

due to drawing inference about the population on the basis of a few observations (sample) is termed

sample errors. Clearly the sampling error in this sense is nonexistent in a complete enumeration

survey, since the whole population is surveyed. However, the errors mainly arising at the stages of

ascertainment and processing of data which are termed non-sampling errors are common both in

complete enumeration and sample surveys.

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1. Sampling errors

Even if utmost care has been taken in selecting a sample, the results derived from the sample may

not be representative of the population from which it is drawn, because samples are seldom, if ever,

perfect miniatures of the population. This gives rise to sampling errors. Sampling errors are thus due

to the fact that samples are used and to the particular method used in selecting the items from the

population.

Sampling errors are of two types-biased and unbiased.

(1) Biased errors.These' errors arise from any bias in selection, estimation, etc For example, if in

place of simple random sampling, deliberate sampling has been used in a particular case some bias

is introduced ,in the result and hence such errors are called biased sampling errors.

(2) Unbiased errors. These errors arise due to chance differences between the members of

population included in the sample and those not included.

Thus the total sampling error is made up of error due to bias, if any, and the random sampling error.

The essence of bias is that it forms a constant component of error that does not decrease in a large

population as the number in the sample increases. Such error is, therefore, also known as

cumulative or non-compensating error. The random sampling error, on the other hand, decreases

on an average as the size of the sample increases. Such error is, therefore, also known as non-

cumulative or compensating error.

Causes of bias

Faulty process of selection.

Faulty work during the collection of information.

Faulty methods of analysis.

2. Non-sampling errors

When a complete enumeration of units in the universe is made one would expect that it would give

rise to data free from errors. However, in practice, it is not so. For example, it is difficult to

completely avoid errors of observation or ascertainment. So also in the processing theory to theavailable facilities and resources. That is, it represents a compromise between idealism and

feasibility. One should use simple workable methods instead of unduly elaborate and complicated

techniques.

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Criteria for Selecting Sampling Techniques

1.Purpose of the survey

What does the researcher aim at? If he intends to generalize the findings based on the sample

survey to the population, then an appropriate probability sampling method must be selected. The

choice of a particular type of probability sampling depends on the geographical area of the survey

and the size and nature of the population under study. On the other hand, if he is interested in just

understanding the nature of the phenomenon under study, and does not aim at generalizing his

finding, some non-probability sampling method will suffice.

2.Measurability

The application of statistical inference theory requires computation of the sampling error from the

sample itself. Probability samples only allow such computation. Hence, where the research

objective requires statistical inference, the sample should be drawn by applying simple random

sampling method or stratified random sampling method, depending on whether the population is

homogeneous or heterogeneous. All probability samples are non-measurable, e.g., selecting a

single cluster, a systematic sampling from a population with periodic variation, and cluster sampling

in which the primary clusters are not identified.

3. Degree of precision

Should the results of the survey be very precise, or even rough results could serve the purpose?

The desired level of precision is one of the criteria of sampling method selection. Where a high

degree of precision of results would serve the purpose (e.g., marketing surveys) any convenient

non-random sampling like quota sampling would be enough.

4. lnformation about population:

How much information is available about the population to be studied? Where no lists of population

and no information about its nature are available, it is difficult to apply a probability sampling

method. Then exploratory study with non-probability sampling may be made to gain a better idea of

the population. After gaining sufficient knowledge about the populations through the exploratory

study, appropriate probability sampling design may be adopted.

5. The Nature of the population:

In terms of the variables to be studied, is the population homogeneous or heterogeneous? In the

case of a homogeneous population, even a simple random sampling will give a representative

sample. If the population is heterogeneous, stratified random sampling is appropriate. "Systematic

sampling would, however, be preferred in those cases where the list of units of population is

available or easily obtainable and where there is no periodic variation or trend present in thepopulation.

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6. Geographical area of the study and the size of the population:

If the area covered by a survey is very large (e.g., a country or a state) and the size of the

population is quite large, multi-stage cluster sampling would be appropriate. But if the area and the

size of the population are small, single stage probability sampling methods could be used.

7. Financial resources:

Is the available finance a limiting factor or not? If the available finance is limited, it may become

necessary to choose a less costly sampling plan like multistage cluster sampling or even quota

sampling as a compromise. However, if the objectives of the study and the desired, level of

precision cannot be attained within the stipulated budget, there is no alternative than to give up the

proposed survey. Where finance is not a constraint, a researcher can choose the most appropriate

method of sampling that fits the research objective and the nature of population.

8. Time limitation:

The time limit within which the research project should be completed restricts the choice of a

sampling method. Then, as a compromise, it may become necessary to choose less time

consuming methods like simple random sampling instead of stratified sampling/sampling with

probability proportional to size; multi-stage cluster sampling instead of single-stage sampling of

elements. Of course, the precision has to be sacrificed to some extent.

9. Economy should be another criterion in choosing the sampling method.

It means achieving the desired level of precision at minimum cost. "A sample is economical if the

precision per unit cost is high or the cost per unit of variance is low." The precisions and costs of

various measurable probability sampling methods can be compared and the method which achieves

the optimal balance between reliability of results and costs may be selected. This calls for much

thought and ingenuity.

The above criteria frequently conflict and the researcher must balance and bend them to obtain a

good sampling plan. The chosen plan thus represents an adaptation of the sampling theory to the

available facilities and resources. That is, it represents a compromise between idealism andfeasibility. One should use simple workable methods instead of unduly elaborate and complicated

techniques.

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PRINCIPLE STEPS OF SAMPLING

Objectives of the survey

The first step when assessing a sample survey is to well identify the general objectives of the survey.

Without a lucid statement of the objectives, it is easy in a complex survey to forget the objectives

when engrossed in the details of planning, and to make decisions that are at variance with the

objectives.

One of the principal choice is between average values (mean of the population) or total values. In

fact, depending on this choice, techniques for the optimal sample size and estimators factors are

different.

A number of measures exist that have been used by various agencies to measure the economic

significance of fisheries to the regional economy. In addition, a number of performance indicators

also exist that can be used to assess the performance of fisheries management in achieving its

economic objectives (see chapter 1 and related annexes).

2 Population to be sampled

The word population is used to denote the aggregate from which the sample is chosen. The definition

of the population may present some problems in the fishing sector, as it should consider the complete

list of vessels and their physical and technical characteristics.

The population to be sampled (the sampled population) should coincide with the population aboutwhich information is wanted (the target population). Some-times, for reasons of practicability or

convenience, the sampled population is more restricted than the target population. If so, it should be

remembered that conclusions drawn from the sample apply to the sampled population. Judgement

about the extent to which these conclusions will also apply to the target population must depend on

other sources of information. Any supplementary information that can be gathered about the nature

of the differences between sampled and target population may be helpful.

For example, let us consider the Italian statistical sampling design for the estimation of "quantity and

average price of fishery products landed each calendar month in Italy by Community and EFTA

vessels" (Reg. CE n. 1382/91 modified by Reg. CE n. 2104/93). Aim of the survey is to estimate

total catches and average prices for individual species. Therefore, the sampling basis consists of the

more than 800 landing points spread over the 8 000 km of Italian coasts. It is not however feasible to

consider the list of the landing points as the list of elementary units. To overcome these difficulties, a

sampled population, distinct from the target population but including units in which the considered

phenomenon takes place, has been considered. In synthesis, the elementary units considered are the

landings of the vessels belonging to the sampled fleet. Thus, the list from which the sampling units

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are extracted is constituted by all the vessels belonging to the Italian fishery fleet.

3 Data to be collected

It is well to verify that all the data are relevant to the purposes of the survey and that no essential data

are omitted There is frequently a tendency to ask too many questions, some of which are never

subsequently analysed. An overlong questionnaire lowers the quality of the answers to important as

well as unimportant questions.

4 Degree of precision desired

The results of sample surveys are always subject to some uncertainty because only part of the

population has been measured and because of errors of measurement. This uncertainty can be

reduced by taking larger samples and by using superior instruments of measurement. But this usually

costs time and money. Consequently, the specification of the degree of precision wanted in the

results is an important step. This step is the responsibility of the person who is going to use the data.

It may present difficulties, since many administrators are unaccustomed to thinking in terms of the

amount of error that can be tolerated in estimates, consistent with making good decisions. The

statistician can often help at this stage.

5 The questionnaire and the choice of the data collectors

There may be a choice of measuring instrument and of method of approach to the population. The

survey may employ a self-administered questionnaire, an interviewer who reads a standard set of

questions with no discretion, or an interviewing process that allows much latitude in the form and

ordering of the questions. The approach may be by mail, by telephone, by personal visit, or by a

combination of the three. Much study has been made of interviewing methods and problems.

A major part of the preliminary work is the construction of record forms on which the questions and

answers are to be entered. With simple questionnaires, the answers can sometimes be pre-coded, that

is, entered in a manner in which they can be routinely transferred to mechanical equipment. In fact,

for the construction of good record forms, it is necessary to visualise the structure of the final

summary tables that will be used for drawing conclusions.

Information may be collected using a number of different survey methods. These include personal

interview, telephone interview or postal survey. The questionnaire design needs to vary based on the

approach taken.

Personal interviews involves visiting the individual from which data are to be collected. The

interviewer controls the questionnaire, and fills in the required data. The questionnaire can be less

detailed in terms of explanatory information as the interviewer can be trained on its completion

before starting the interview process. This type of survey is best for long, complex surveys and it

allows the interviewer and fisher to agree a time convenient for both parties. It is particularly useful

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when the respondent may have to go and find information such as accounts, log book records etc.

The personal interview approach also allows the interviewer to probe more fully if he/she feels that

the fisher has misunderstood a question, or information provided conflicts with other earlier

statements.

Data collectors are usually external to the phenomenon that is being examined and, moreover, they

are often part of some public structure, in order to avoid possible influences due to personal interests.

However, on the basis of the experience acquired in this field by Irepa, it has been demonstrated

(Istat, Irepa 2000) that it is essential to have data collectors belonging to the fishery productive chain

in order to obtain correct and timely data. Therefore, data collectors should belong to the productive

or management fishery sectors.

During meetings on socio-economic indicators partners involved presented several questionnaires.

These questionnaires are aimed to collect the information required to calculate the socio-economic

indicators and some of them are reported in appendix C.

6 Selection of the sample design

There is a variety of plans by which the sample may be selected (simple random sample, stratified

random sample, two-stage sampling, etc.). For each plan that is considered, rough estimates of the

size of sample can be made from a knowledge of the degree of precision desired. The relative costs

and time involved for each plan are also compared before making a decision.

7 Sampling units

Sample units have to be drawn according to the sample design.

To draw sample units from the population, several methods can be used, depending on the type of

the chosen sample strategy:

sample with equal probabilities

sample with probabilities proportional to the size (PPS).

In the first case, each unit of the population has the same probability to take part of the sample, while

in the case of a PPS sample each unit has a different probability to be sampled and this probability is

proportional to the following measure: Pi = Xi/Xh, where, i = a generic vessel, h = stratum, X= a size

parameter, for example the overall length of a vessel.

8 The pre-test

It has been found useful to try out the questionnaire and the field methods on a small scale. This

nearly always results in improvements in the questionnaire and may reveal other troubles that will be

serious on a large scale, for example, that the cost will be much greater than expected.

9 Organization of the field work

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In a survey, many problems of business administration are met. The personnel must receive training

in the purpose of the survey and in the methods of measurement to be employed and must be

adequately supervised in their work.

A procedure for early checking of the quality of the returns is invaluable.

Plans must be made for handling non-response, that is, the failure of the enumerator to obtain

information from certain of the units in the sample.

10 Summary and analysis of the data

The first step is to edit the completed questionnaires, in the hope of amending recording errors, or at

least of deleting data that are obviously erroneous. The check on the elementary data to eliminate

non-sampling errors can be achieved by means of computer programmes implemented to correct the

erroneous values and to permit statistical data analysis. These programmes are mainly based on

graphical analysis of elementary data.

Thereafter, the computations that lead to the estimates are performed. Different methods of

estimation may be available for the same data.

In the presentation of results it is good practice to report the amount of error to be expected in the

most important estimates One of the advantages of probability sampling is that such statements can

be made, although they have to be severely qualified if the amount of non-response is substantial

11 Information gained for future surveys

The more information we have initially about a population, the easier it is to devise a sample that

will give accurate estimates. Any completed sample is potentially a guide to improved future

sampling, in the data that it supplies about the means, standard deviations, and nature of the

variability of the principal measurements and about the costs involved in getting the data. Sampling

practice advances more rapidly when provisions are made to assemble and record information of this

type.

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FACTORS HELP TO DECIDE SAMPLING METHOD AND DESIGN:

Determining an appropriate sampling design is a challenging issue and has greater implications on

the application of the research findings. The following are the factors to be considered on choosing u

on random sampling techniques.

1. Research objectives

A clear understanding of the statement of the problem and the objectives will provide the initial

guidelines for determining the appropriate sampling design. If the research objectives include the

need to generalize the findings of the research study, then a probability sampling method should be

opted rather than a non probability sampling method. In addition the type of research viz.,

exploratory or descriptive will also influence the type of the sampling design.

2. Scope of the research

The scope of the research project is local, regional, national or international has an implication on the

choice of the sampling method. The geographical proximity of the defined target population

elements will influence not only the researchers ability to compile needed list of sampling units, but

also the selection design. When the target population is equally distributed geographically a cluster

sampling method may become more attractive than other available methods. If the geographical area

to be covered is more extensive then complex sampling method should be adopted to ensure proper

representation of the target population.

3. Availability of resources

The researchers command over the financial and human resources should be considered in deciding

the sampling method. If the financial and human resource availability are limited, some of the more

time-consuming, complex probability sampling methods cannot be selected for the study.

4. Time frame

The researcher who has to meet a short deadline will be more likely to select a simple, less time

consuming sampling method rather than a more complex and accurate method.

5. Advanced knowledge of the target population

If the complete lists of the entire population elements are not available to the researcher, the

possibility of the probability sampling method is ruled out. It may dictate that a preliminary study be

conducted to generate information to build a sampling frame for the study. The researcher must gain

a strong understanding of the key descriptor factors that make up the true members of any target

population.

6. Degree of accuracy

The degree of accuracy required or the level of tolerance for error may vary from one study to

another. If the researcher wants to make predictions or inferences about the true position of all

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members of the defined target population, then some type of probability sampling method should be

selected. If the researcher aims to solely identify and obtain preliminary insights into the defined

target population, non probability methods might prove to be more appropriate.

6. Perceived statistical analysis needs

The need for statistical projections or estimates based on the sample results is to be considered. Only

probability sampling techniques allow the researcher to adequately use statistical analysis for

estimates beyond the sample respondents. Though the statistical method can be applied on the non

probability samples of people and objects, the researchers ability to accurately generalize the results

and findings to the larger defined target population is technically inappropriate and questionable. The

researcher should also decide on the appropriateness of sample size as it has a direct impact on the

data quality, statistical precision and generalizability of findings

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Marketing sampling plan

A marketing sampling plan maps out how your company intends on gathering data to fulfill its short-

and long-term marketing objectives. Methods for collecting market data include polling, surveys and

focus groups. Because of its significance, the creation of a marketing sampling plan should be

consistent with your company's overall business strategy.

Understanding the Market

It is important to identify your target market, or the type of consumers that your company wants to

attract. Key items to focus on include demographic and socioeconomic trends. Take time to

understand the size of the target market and whether it is a truly representative sample. This is

paramount to formulating a relevant sampling plan. The information you obtain forms the basis forthe company's overall marketing strategy for such expenses as advertising and promotion, branding

and product positioning.

Data Collection

Decide how, where and when you intend to collect information about your target consumers.

Secondary data uses already existing information, such as government census reports or trade

publications. Secondary data may also include internal company information like sales invoices.

Primary data supplements secondary data and focuses on obtaining first-hand information. Decide on

a combination of secondary and primary data collection that satisfies your company's overall

marketing research objective.

Research Methodology

Choose which market research methodologies you want to include in the marketing sampling plan.

Quantitative market research methods rely on numerical measurement, such as the use of surveys

and statistics. Qualitative market research uses in-person interviews, focus groups and similar

methods to gather information. Focus on assessment of findings and how the company intends on

using the information it gathers. It is important to define the market research within the framework of

the company's marketing objectives.

Consideration

Your marketing sampling plan will evolve. You may find that you have to update it, particularly if

the company changes strategies or enters new markets. Secondary data, while useful, has its limits

but is a good building block because it is inexpensive. Primary data is expensive but often necessary.Therefore, craft a marketing sampling plan with your company's budget in mind.

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After deciding on the research approach and instruments, the marketing researcher must design a

sampling plan. This calls for three decisions:

1. Sampling unit:

Who is to be surveyed? The marketing researcher must define the target population that will

be sampled. In the American Airlines survey providing an internet facility in their First class

with a nominal fee, should the sampling unit be only firstclass or business travelers,

firstclass vacation travelers or both? Should travelers under age 18 be interviewed?

Should both husbands and wives be interviewed? Once the sampling unit is determined, a

sampling frame must be developed so that everyone in the target population has an equal or

known chance of being sampled.

2. Sample size:

How many people should be surveyed? Large samples give more reliable results than small

samples. However, it is not necessary to sample the entire target population or even a

substantial portion to achieve reliable results. Samples of less than 1% of a population can

often provide good reliability, with a credible sampling procedure.

3. Samplingprocedure:

How should the respondents be chosen? To obtain a representative sample, a probability

sample of the population should be drawn. Probability sampling allows the calculation of

confidence limits for sampling error. Thus, one could conclude after the sample is taken that

the interval 5 to 7 trips per year has 95 chances in 100 of containing the true number of

trips taken annually by first class passengers flying between Chicago and Tokyo.?

Three types of probability sampling are described below part A. When the cost or time

involved in probability sampling is too high, marketing researchers will take non-probability

samples. Part B describes three types.

A. Probability Sample

Simple random sample: every member of the population has an equal chance of selection.

Stratified random sample: The population is divided into mutually exclusive groups (such as

age groups), and random samples are drawn from each group.

Cluster (area) sample: The population is divided into mutually exclusive groups (such as city

blocks) and the researcher draws a sample of the groups to interview.

B. Non-probability Sample

Convenience sample: The researchers select the most accessible population members.

Judgment sample: The researcher selects population members who are good prospects for

accurate information.

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Quota sample: The researcher finds and interviews a prescribed number of people in each of

several categories.

Some marketing researchers feel that non-probability samples are very useful in many

circumstances, even though they do not allow sampling error to be measured.

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SAMPLING FRAME IN MARLETING:

Instatistics,a sampling frameis the source material or device from which asample is drawn. It is a

list of all those within apopulation who can be sampled, and may include individuals, households or

institutions.

Importance of the sampling frame is stressed by Jessen:

In many practical situations the frame is a matter of choice to the survey planner, and sometimes a

critical one. [...] Some very worthwhile investigations are not undertaken at all because of the lack of

an apparent frame; others, because of faulty frames, have ended in a disaster or in cloud of doubt.

Raymond James Jessen

Sampling frame types and qualities

In the most straight, such as when dealing with a batch of material from a production run, or using

acensus,it is possible to identify and measure every single item in the population and to include any

one of them in our sample; this is known as direct element sampling.[1]However, in many other

cases this is not possible; either because it is cost-prohibitive (reaching every citizen of a country) or

impossible (reaching all humans alive).

Having established the frame, there are a number of ways for organizing it to improve efficiency and

effectiveness. It's at this stage that the researcher should decide whether the sample is in fact to be

the whole population and would therefore be acensus.

This list should also facilitate access to the selected samplingunits.A frame may also provide

additional 'auxiliary information' about its elements; when this information is related to variables or

groups of interest, it may be used to improve survey design. While not necessary for simple

sampling, a sampling frame used for more advanced sample techniques, such asstratified sampling,

may contain additional information (such asdemographic information). For instance, an electoralregister might include name and sex; this information can be used to ensure that a sample taken from

that frame covers all demographic categories of interest. (Sometimes the auxiliary information is less

explicit; for instance, a telephone number may provide some information about location.)

An ideal sampling frame will have the following qualities:

all units have a logical, numerical identifier

all units can be foundtheir contact information, map location or other relevant information is

present

http://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Sampling_(statistics)http://en.wikipedia.org/wiki/Statistical_populationhttp://en.wikipedia.org/wiki/Censushttp://en.wikipedia.org/wiki/Sampling_frame#cite_note-S.C3.A4rndalSwensson2003-1http://en.wikipedia.org/wiki/Sampling_frame#cite_note-S.C3.A4rndalSwensson2003-1http://en.wikipedia.org/wiki/Sampling_frame#cite_note-S.C3.A4rndalSwensson2003-1http://en.wikipedia.org/wiki/Censushttp://en.wikipedia.org/wiki/Statistical_unithttp://en.wikipedia.org/wiki/Stratified_samplinghttp://en.wikipedia.org/wiki/Demographic_informationhttp://en.wikipedia.org/wiki/Demographic_informationhttp://en.wikipedia.org/wiki/Stratified_samplinghttp://en.wikipedia.org/wiki/Statistical_unithttp://en.wikipedia.org/wiki/Censushttp://en.wikipedia.org/wiki/Sampling_frame#cite_note-S.C3.A4rndalSwensson2003-1http://en.wikipedia.org/wiki/Censushttp://en.wikipedia.org/wiki/Statistical_populationhttp://en.wikipedia.org/wiki/Sampling_(statistics)http://en.wikipedia.org/wiki/Statistics

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the frame is organized in a logical, systematic fashion

the frame has additional information about the units that allow the use of more advanced

sampling frames

every element of the population of interest is present in the frame every element of the population is present only oncein the frame

no elements from outside the population of interest are present in the frame

the data is 'up-to-date

The most straightforward type of frame is a list of elements of the population (preferably the entire

population) with appropriate contact information. For example, in anopinion poll,possible sampling

frames include anelectoral register or atelephone directory.Other sampling frames can include

employment records, school class lists, patient files in a hospital, organizations listed in a thematic

database, and so on. On a more practical levels, sampling frames have the form ofcomputer files

Not all frames explicitly list population elements; some list only 'clusters'. For example, astreet

map can be used as a frame for a door-to-door survey; although it doesn't show individual houses, we

can select streets from the map and then select houses on those streets. This offers some advantages:

such a frame would include people who have recently moved and are not yet on the list frames

discussed above, and it may be easier to use because it doesn't require storing data for every unit in

the population, only for a smaller number of clusters.

Sampling frames problems

The sampling frame must be representative of the population and this is a question outside the scope

of statistical theory demanding the judgment of experts in the particular subject matter being studied.

All the above frames omit some people who will vote at the next election and contain some people

who will not; some frames will contain multiple records for the same person. People not in the frame

have no prospect of being sampled.

Because a cluster-based frame contains less information about the population, it may place

constraints on the sample design, possibly requiring the use of less efficient sampling methods and/or

making it harder to interpret the resulting data.

Statistical theory tells us about the uncertainties in extrapolating from a sample to the frame. It

should be expected that sample frames, will always contain some mistakes. In some cases, this may

lead tosampling bias.Such bias should be minimized, and identified, although avoiding it

http://en.wikipedia.org/wiki/Opinion_pollhttp://en.wikipedia.org/wiki/Electoral_registerhttp://en.wikipedia.org/wiki/Telephone_directoryhttp://en.wikipedia.org/wiki/Computer_filehttp://en.wikipedia.org/wiki/Street_maphttp://en.wikipedia.org/wiki/Street_maphttp://en.wikipedia.org/wiki/Sampling_biashttp://en.wikipedia.org/wiki/Sampling_biashttp://en.wikipedia.org/wiki/Street_maphttp://en.wikipedia.org/wiki/Street_maphttp://en.wikipedia.org/wiki/Computer_filehttp://en.wikipedia.org/wiki/Telephone_directoryhttp://en.wikipedia.org/wiki/Electoral_registerhttp://en.wikipedia.org/wiki/Opinion_poll

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completely in a real world is nearly impossible. One should also not assume that sources which claim

to be unbiased and representative are such.

In defining the frame, practical, economic, ethical, and technical issues need to be addressed. The

need to obtain timely results may prevent extending the frame far into the future. The difficulties can

be extreme when the population and frame aredisjoint.This is a particular problem

inforecasting where inferences about the future are made from historical data.In fact, in 1703,

whenJacob Bernoulliproposed toGottfried Leibniz the possibility of using historical mortality data

to predict theprobability of early death of a living man,Gottfried Leibniz recognized the problem in

replying

Nature has established patterns originating in the return of events but only for the most part. New

illnesses flood the human race, so that no matter how many experiments you have done on corpses,

you have not thereby imposed a limit on the nature of events so that in the future they could not vary.

Gottfried Leibniz

Kish posited four basic problems of sampling frames

1. Missing elements: Some members of the population are not included in the frame.

2. Foreign elements: The non-members of the population are included in the frame.

3. Duplicate entries: A member of the population is surveyed more than once.

4. Groups or clusters: The frame lists clusters instead of individuals.

http://en.wikipedia.org/wiki/Disjoint_setshttp://en.wikipedia.org/wiki/Forecastinghttp://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Jacob_Bernoullihttp://en.wikipedia.org/wiki/Gottfried_Leibnizhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Gottfried_Leibnizhttp://en.wikipedia.org/wiki/Gottfried_Leibnizhttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Gottfried_Leibnizhttp://en.wikipedia.org/wiki/Jacob_Bernoullihttp://en.wikipedia.org/wiki/Datahttp://en.wikipedia.org/wiki/Forecastinghttp://en.wikipedia.org/wiki/Disjoint_sets

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SAMPLING:JOANNE BIRCHALL FROM RAINBOW RESEARCH

Unless you are in the luxurious position of having access to everyone who forms your population,

you will need to take some form of sample from which to glean information for Market Research

purposes. In addition to accessibility, the method chosen will depend upon a variety of statistical and

practical factors. You will want to ensure your sample size is sufficient for the purpose of the

analysis you intend to perform, ensure your sample is representative of the population you are

attempting to say something about, and of course you will need to take into account your

affordability.

This section covers the following:

- Sampling methods

- Calculating a sample size

- Calculating a sampling error

Sampling Methods

In most surveys, access to the entire population is near on impossible, however, the results from a

survey with a carefully selected sample will reflect extremely closely those that would have been

obtained had the population provided the data.

Sampling therefore is a very important part of the Market Research process. If you have surveyed

using an appropriate sampling technique, you can be confident that your results will be generalised to

the population in question. If the sample were biased in any way, for example, if the selection

technique gave older people more of a chance of selection than younger people, it would be

inadvisable to make generalisations from the findings.

There are essentiality two types of sampling: probability and non-probability sampling.

Probability Sampling Methods

Probability or random sampling gives all members of the population a known chance of being

selected for inclusion in the sample and this does not depend upon previous events in the selection

process. In other words, the selection of individuals does not affect the chance of anyone else in the

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population being selected.

Many statistical techniques assume that a sample was selected on a random basis. There are four

basic types of random sampling techniques:

1) Simple Random Sampling

This is the ideal choice as it is a perfect random method.Using this method, individuals are

randomly selected from a list of the population and every single individual has an equal chance of

selection.

This method is ideal, but if it cannot be adopted, one of the following alternatives may be chosen if

any shortfall in accuracy.

2) Systematic Sampling

Systematic sampling is a frequently used variant of simple random sampling. When performing

systematic sampling, every kth element from the list is selected (this is referred to as the sample

interval) from a randomly selected starting point. For example, if we have a listed population of 6000

members and wish to draw a sample of 2000, we would select every 30th (6000 divided by 200)

person from the list. In practice, we would randomly select a number between 1 and 30 to act as our

starting point.

The one potential problem with this method of sampling concerns the arrangement of elements in the

list.? If the list is arranged in any kind of order e.g. if every 30th house is smaller than the others

from which the sample is being recruited, there is a possibility that the sample produced could be

seriously biased.

3) Stratified Sampling

Stratified sampling is a variant on simple random and systematic methods and is used when there are

a number of distinct subgroups, within each of which it is required that there is full representation. A

stratified sample is constructed by classifying the population in sub-populations (or strata), base on

some well-known characteristics of the population, such as age, gender or socio-economic status.

The selection of elements is then made separately from within each strata, usually by random or

systematic sampling methods.

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Stratified sampling methods also come in two typesproportionate and disproportionate.

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:

The costs of collecting data may differ from subgroup to subgroup.

We might require more cases in some groups if estimations of populations values are likely to be

harder to make i.e. the larger the sample size (up to certain limits), the more accurate any estimations

are likely to be.

We expect different response rates from different groups of people. Therefore, the less co-operative

groups might be over-sampled to compensate.

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CONCLUSION:

Sampling is the process of selecting units (e.g., people, organizations) from a population of interest

so that by studying the sample we may fairly generalize our results back to the population from

which they were chosen. Let's begin by covering some of thekey terms in sampling like

"population" and "sampling frame." Then, because some types of sampling rely upon quantitative

models, we'll talk about some of thestatistical terms used in sampling.Finally, we'll discuss the

major distinction betweenprobability andNonprobability sampling methods and work through the

major types in each.

Researchers usually cannot make direct observations of every individual in the population they are

studying. Instead, they collect data from a subset of individualsasampleand use those observations

to make inferences about the entire population.

Ideally, the sample corresponds to the larger population on the characteristic(s) of interest. In that case,

the researcher's conclusions from the sample are probably applicable to the entire population.

This type of correspondence between the sample and the larger population is most important when a

researcher wants to know what proportion of the population has a certain characteristic like a

particular opinion or a demographic feature. Public opinion polls that try to describe the percentage of

the population that plans to vote for a particular candidate, for example, require a sample that is highly

representative of the population.

http://www.socialresearchmethods.net/kb/sampterm.phphttp://www.socialresearchmethods.net/kb/sampstat.phphttp://www.socialresearchmethods.net/kb/sampprob.phphttp://www.socialresearchmethods.net/kb/sampnon.phphttp://www.socialresearchmethods.net/kb/sampnon.phphttp://www.socialresearchmethods.net/kb/sampprob.phphttp://www.socialresearchmethods.net/kb/sampstat.phphttp://www.socialresearchmethods.net/kb/sampterm.php

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References:

Methodology of research in social science, 2ndEd., OR Krishnaswamy & M. Ranganathan,

Himalaya Publications.

Research Methodology, 2ndEd., CR. Kothari, New Age Int. Publishers.

Business research methods, BBM BU textbook, Appannaiah Reddy & Ramanath, Himalaya

Publications.

BOOKS FOR REFERENCE:

1. OR Krishna Swamy, Research Methodology.

2. Wilkinson & Bhandarkar, Methodology and Techniques of Social Research.

3. V.R Michael, Research Methodology in Management.

4. CR. Kothari, Research Methodology.

Note: Module is just a reference material. Please do refer the books mentioned above.