TOPIC: report on sampling techniques

PREPARED BY

RAJESH Narayanan

s.r.m university

What is Sampling:

Sampling:

A process used in statistical analysis in which a predetermined number of observations will

be taken from a larger population. The methodology used to sample from a larger population

will depend on the type of analysis being performed, but will include simple random

sampling, systematic sampling and observational sampling.

It is technique of drawing samples, I.e., it is a technique of collecting data only on a part of

the population to reveal the characteristics of the entire population.

Purpose of Sampling

The purpose of sampling is to provide various types of statistical information of a qualitative

or quantitative nature about the whole by examining a few selected units. The sampling

method is the scientific procedure of selecting those sampling units which would provide the

required estimates with associated margins of uncertainity, arising from examining only a

part and not the whole.

Reasons for sampling instead of census / Need for sampling:

There are 6 reasons for sampling

(1) Economy

(2) Timeliness

(3) Large size of many population

(4) Inaccessibility of the entire population.

(5) Destructive nature of many Observation

(6) Reliability or accuracy.

(1) Economy:

Unit cost of collecting data in the case of census is significantly less then in the case of

sampling for example: In case of census is taka 200, while in the case of sampling is taka

1,000 but due to the larger number of items the total cost involve in the case of census of

census is significantly higher then in the case of sampling.

For example, We can find out the total cost of collecting information by multiplying the total

population with the unit cost in case of census. Here total population = N

We can find out the total cost of collecting information by multiplying the sample size with

the unit cost in case of census.

Here sample size=n.

10,00,000 x 200 = 20,00,00,000

5,000 x 1000 = 50,00,000

(2) Timeliness:

Unit time involve in the case of sampling then in the case census but due to the larger size of

population total time involve in the case of census in significantly higher then in the case of

census.

(3) Large size of many population:

In some cases the size of the population is extremely large. All of them are not treaseable due

in traveling, disease, death, mental abnormality, prisoners etc. In that situation the only way

to conduct the research is collecting data through a sample survey.

(4) Inaccessibility of the entire population:

In some cases the entire population may not be accessible. At that case sampling is necessary.

Suppose in some cases the entire population is inaccessible because of aircraft crash.

(5) Destructive nature of many population:

Due to destructive nature of many of the population, the resources is completed to collect

information only on a part of the population.

For example:

Blood test for a patient.

Life hours of a tube light.

(6) Reliability:

By using a scientific sampling technique one can minimize the sampling error and as

qualified investigators are included, the non-sampling error committed in the case of sample

survey is also minimum.

The amount of non-sampling error in the case of census is much higher than the total amount

of sampling and non-sampling error committed in the case of a sample survey ( as less

qualified investigator are involve in the case of census and the supervision, monitoring and

quality control mechanism in the case of census.

The degree of errors has a relationship with reliability. If error decrease than the reliability

increase sampling decrease both the sampling and non-sampling error. So, it enhance the

reliability of information.

How to Determine Sample Size, Determining Sample Size

In order to prove that a process has been improved, you must measure the process capability

before and after improvements are implemented. This allows you to quantify the process

improvement (e.g., defect reduction or productivity increase) and translate the effects into an

estimated financial result – something business leaders can understand and appreciate. If data

is not readily available for the process, how many members of the population should be

selected to ensure that the population is properly represented? If data has been collected, how

do you determine if you have enough data?

Determining sample size is a very important issue because samples that are too large may

waste time, resources and money, while samples that are too small may lead to inaccurate

results. In many cases, we can easily determine the minimum sample size needed to estimate

a process parameter, such as the population mean .

When sample data is collected and the sample mean is calculated, that sample mean is

typically different from the population mean . This difference between the sample and

population means can be thought of as an error. The margin of error is the maximum

difference between the observed sample mean and the true value of the population mean

:

where:

is known as the critical value, the positive value that is at the vertical boundary for the

area of in the right tail of the standard normal distribution.

is the population standard deviation.

is the sample size.

Rearranging this formula, we can solve for the sample size necessary to produce results

accurate to a specified confidence and margin of error.

This formula can be used when you know and want to determine the sample size necessary

to establish, with a confidence of , the mean value to within . You can still use

this formula if you don’t know your population standard deviation and you have a small

sample size. Although it’s unlikely that you know when the population mean is not known,

you may be able to determine from a similar process or from a pilot test/simulation.

Let’s put all this statistical mumbo-jumbo to work. Take for example that we would like to

start an Internet service provider (ISP) and need to estimate the average Internet usage of

households in one week for our business plan and model.

Sample Size Calculation Example

Problem We would like to start an ISP and need to estimate the average Internet usage of households

in one week for our business plan and model. How many households must we randomly

select to be 95 percent sure that the sample mean is within 1 minute of the population mean

. Assume that a previous survey of household usage has shown = 6.95 minutes.

Solution We are solving for the sample size .

A 95% degree confidence corresponds to = 0.05. Each of the shaded tails in the following

figure has an area of = 0.025. The region to the left of and to the right of = 0 is 0.5

– 0.025, or 0.475. In the table of the standard normal ( ) distribution, an area of 0.475

corresponds to a value of 1.96. The critical value is therefore = 1.96.

The margin of error = 1 and the standard deviation = 6.95. Using the formula for sample

size, we can calculate :

So we will need to sample at least 186 (rounded up) randomly selected households. With this

sample we will be 95 percent confident that the sample mean will be within 1 minute of the

true population of Internet usage.

This formula can be used when you know and want to determine the sample size necessary

to establish, with a confidence of , the mean value to within . You can still use

this formula if you don’t know your population standard deviation and you have a small

sample size. Although it is unlikely that you know when the population mean is not

known, you may be able to determine from a similar process or from a pilot

test/simulation.

STEPS IN SAMPLING PROCESS:

It is the procedure required right from defining a population to the actual selection of sample

elements. There are seven steps involved in this process.

Step 1: Define the population

It is the aggregate of all the elements defined prior to selection of the sample. It is necessary

to define population in terms of

(i) elements

(ii) sampling units

(iii) extent

(iv) time.

A few examples are given here.

If we were to conduct a survey on the consumption of tea in Gujarat, then these specifications

might be as follows

(i) Element: Housewives

(ii) Sampling units: Households, then housewives

(iii) Extent Gujarat State

(iv) Time January 1-10, 1999

If we were to monitor the sales of a product recently introduced by us, the population might

be

(i) Element Our product

(ii) Sampling units Retail outlets, super markets, then our product

(iii) Extent Delhi and New Delhi

(iv) Time January 7-14, 1999

It may be emphasized that all these four specifications must be contained in the designated

population Omission of any of them would render the definition of population incomplete

Step 2 : Identify the sampling frame

Identifying the sampling frame, which could be a telephone directory, a list of blocks and

localities of a city, a map or any other list consisting of all the sampling units. It may be

pointed out that if the frame is incomplete or otherwise defective, sampling will not be able to

overcome these shortcomings

The question is—How to ensure that the frame is perfect and free from any defect Leslie Kish

has observed that a perfect frame is one where “every element appears on the list separately,

once only once, and nothing else appears on the list” This type of perfect frame would

indicate one-to-one correspondence between frame units and sampling units But such perfect

frames are rather rare Accordingly, one has to use frames with one deficiency or another, but

one should ensure that the frame is not too deficient so as to be given up altogether

This raises a pertinent question -What are the criteria for a suitable frame? In order to

examine the suitability or otherwise of a sampling frame, a number of questions need be

asked. These are

1 Does it adequately cover the population to be surveyed?

2 How complete is the frame? Is every unit that should be included represented?

3 Is it accurate? Is the information about each individual unit correct? Does the frame as a

whole contain units, which no longer exist?

4 Is there any duplication? If so, then the probability of selection is disturbed as a unit can

enter the sample more than once

5 Is the frame up-to-date? It could have met all the criteria when compiled but could well be

deficient when it came to be used This could well be true of all frames involving the human

population as change is taking place continuously

6 How convenient is it to use? Is it readily accessible? Is it arranged in a way suitable for

sampling? Can it easily be re-arranged so as to enable us to introduce stratification and to

undertake multi-stage sampling?

These are demanding criteria and it is most unlikely that any frame would meet them all

Nevertheless, they are the factors to be borne in mind whenever we undertake random

sampling

In marketing research most of the frames are from census reports, electoral registers, lists of

member units of trade and industry associations, lists of members of professional bodies, lists

of dwelling units maintained by local bodies, returns from an earlier survey and large scale

maps.

Step 3: Specify the sampling unit

The sampling unit is the basic unit containing the elements of the target population. The

sampling unit may be different from the element. For example, if one wanted a sample of

housewives, it might be possible to have access to such a sample directly. However, it is

easier to select households as the sampling unit and then interview housewives in each of the

households.

As mentioned in the preceding step, the sampling frame should be complete and accurate

otherwise the selection of the sampling unit might be defective. It is necessary to get a further

specification of the sampling unit both in personal interviews and in telephone interviews.

Thus, in personal interviews, a pertinent question is—of the several persons in a household,

who should be interviewed? If interviews were held during office timings when the heads of

families and other employed persons are away, interviewing would under-represent employed

persons and over-represent elderly persons, housewives and the unemployed. In view of these

considerations, it is necessary to have a random process of selection of the adult residents of

each household. One method that could be used for this purpose is to list all the eligible

persons living at a particular address and then select one of them.

Step 4: Specify the sampling method

It indicates how the sample units are selected. One of the most important decisions in this

regard is to determine which of the two—probability and non-probability sample—is to be

chosen.

In case of a probability sample, the probability or chance of every unit in the population

being in the sample is known. Further, the selection of specific units in the sample depends

entirely on chance. No substitution of one unit for another is permissible. This means that no

human judgment is involved in the selection of a sample. In contrast, in a non-probability

sample, the probability of inclusion of any unit in the population in the sample is not known.

In addition, the selection of units within a sample involves human judgment rather than pure

chance.

In case of a probability sample, it is possible to measure the sampling error and thereby

determine the degree of precision in the estimates with the help of the theory of probability.

This theory also enables us to consider, from amongst the various possible sample designs,

the one that will give the maximum information per rupee. This is not possible when a non-

probability sample is used.

Probability sampling enables us to choose representative sample designs. It also enables us to

estimate the extent to which the results based on such a sample are likely to be different from

what we would have obtained had we covered the population in our study. Conversely, the

use of probability sampling enables us to determine the sample size for a given degree of

precision, indicating that our sample results do not differ by more than a specified amount

from those yielded by a study covering entire population.

Although non-probability sampling does not yield these benefits, on account of its

convenience and economy, it is often preferred to probability sampling. If the researcher is

convinced that the risks involved in the use of a non-probability sample are more than offset

by its being relatively cheap and convenient, his choice should be in favor of non-probability

sampling.

There are various types of sample designs that can be covered under the two broad groups,

random or probability samples and non-random or non-probability samples.

Step 5: Determine the sample size

In other words, one has to decide how many elements of the target population are to be

chosen.

Step 6: Specify the sampling plan

This means that one should indicate how decisions made so far are to be implemented. For

example, if a survey of households is to be conducted, a sampling plan should define a

household, contain instructions to the interviewer as to how he should take a systematic

sample of households, advise him on what he should do when no one is available on his visit

to the household, and so on. These are some pertinent issues in a sampling survey to which a

sampling plan should provide answers.

Step 7: Select the sample

This is the final step in the sampling process. A good deal of office and fieldwork is involved

in the actual selection of the sampling elements. Most of the problems in this stage are faced

by the interviewer while contacting the sample-respondents.

Why Sample?

Sampling is done in a wide variety of research settings. Listed below are a few of the benefits

of sampling:

1. Reduced cost: It is obviously less costly to obtain data for a selected subset of a

population, rather than the entire population. Furthermore, data collected through a

carefully selected sample are highly accurate measures of the larger population.

Public opinion researchers can usually draw accurate inferences for the entire

population of the United States from interviews of only 1,000 people.

2. Speed: Observations are easier to collect and summarize with a sample than with a

complete count. This consideration may be vital if the speed of the analysis is

important, such as through exit polls in elections.

3. Greater scope: Sometimes highly trained personnel or specialized equipment limited

in availability must be used to obtain the data. A complete census (enumeration) is not

practical or possible. Thus, surveys that rely on sampling have greater flexibility

regarding the type of information that can be obtained.

It is important to keep in mind that the primary point of sampling is to create a small group

from a population that is as similar to the larger population as possible. In essence, we want

to have a little group that is like the big group. With that in mind, one of the features we look

for in a sample is the degree of representativeness - how well does the sample represent the

larger population from which it was drawn? How closely do the features of the sample

resemble those of the larger population?

There are, of course, good and bad samples, and different sampling methods have different

strengths and weaknesses. Before turning to specific methods, a few specialized terms used in

sampling should be defined.

Sampling Terminology

Samples are always drawn from a population, but we have not defined the term "population."

By "population" we denote the aggregate from which the sample is drawn. The population to

be sampled (the sampled population) should coincide with the population about which

information is wanted (the target population). Sometimes, for reasons of practicality or

convenience, the sampled population is more restricted than the target population. In such

cases, precautions must be taken to secure that the conclusions only refer to the sampled

population.

Before selecting the sample, the population must be divided into parts that are called

sampling units or units. These units must cover the whole of the population and they must not

overlap, in the sense that every element in the population belongs to one and only one unit.

Sometimes the choice of the unit is obvious, as in the case of the population of Americans so

often used for opinion polling. In sampling individuals in a town, the unit might be an

individual person, the members of a family, or all persons living in the same city block. In

sampling an agricultural crop, the unit might be a field, a farm, or an area of land whose

shape and dimensions are at our disposal. The construction of this list of sampling units,

called a frame, is often one of the major practical problems.

Types of Sampling

We may then consider different types of probability samples. Although there are a number of

different methods that might be used to create a sample, they generally can be grouped into

one of two categories: probability samples or non-probability samples.

Probability Samples

The idea behind this type is random selection. More specifically, each sample from the

population of interest has a known probability of selection under a given sampling scheme.

There are four categories of probability samples described below.

Simple Random Sampling

The most widely known type of a random sample is the simple random sample (SRS). This is

characterized by the fact that the probability of selection is the same for every case in the

population. Simple random sampling is a method of selecting n units from a population of

size N such that every possible sample of size an has equal chance of being drawn.

An example may make this easier to understand. Imagine you want to carry out a survey of

100 voters in a small town with a population of 1,000 eligible voters. With a town this size,

there are "old-fashioned" ways to draw a sample. For example, we could write the names of

all voters on a piece of paper, put all pieces of paper into a box and draw 100 tickets at

random. You shake the box, draw a piece of paper and set it aside, shake again, draw another,

set it aside, etc. until we had 100 slips of paper. These 100 form our sample. And this sample

would be drawn through a simple random sampling procedure - at each draw, every name in

the box had the same probability of being chosen.

In real-world social research, designs that employ simple random sampling are difficult to

come by. We can imagine some situations where it might be possible - you want to interview

a sample of doctors in a hospital about work conditions. So you get a list of all the physicians

that work in the hospital, write their names on a piece of paper, put those pieces of paper in

the box, shake and draw. But in most real-world instances it is impossible to list everything

on a piece of paper and put it in a box, then randomly draw numbers until desired sample size

is reached.

There are many reasons why one would choose a different type of probability sample in

practice.

Stratified Random Sampling

In this form of sampling, the population is first divided into two or more mutually exclusive

segments based on some categories of variables of interest in the research. It is designed to

organize the population into homogenous subsets before sampling, then drawing a random

sample within each subset. With stratified random sampling the population of N units is

divided into subpopulations of units respectively. These subpopulations, called strata, are

non-overlapping and together they comprise the whole of the population. When these have

been determined, a sample is drawn from each, with a separate draw for each of the different

strata. The sample sizes within the strata are denoted by respectively. If a SRS is taken within

each stratum, then the whole sampling procedure is described as stratified random sampling.

The primary benefit of this method is to ensure that cases from smaller strata of the

population are included in sufficient numbers to allow comparison. An example makes it

easier to understand. Say that you're interested in how job satisfaction varies by race among a

group of employees at a firm. To explore this issue, we need to create a sample of the

employees of the firm. However, the employee population at this particular firm is

predominantly white, as the following chart illustrates:

If we were to take a simple random sample of employees, there's a good chance that we

would end up with very small numbers of Blacks, Asians, and Latinos. That could be

disastrous for our research, since we might end up with too few cases for comparison in one

or more of the smaller groups.

Rather than taking a simple random sample from the firm's population at large, in a stratified

sampling design, we ensure that appropriate numbers of elements are drawn from each racial

group in proportion to the percentage of the population as a whole. Say we want a sample of

1000 employees - we would stratify the sample by race (group of White employees, group of

African American employees, etc.), then randomly draw out 750 employees from the White

group, 90 from the African American, 100 from the Asian, and 60 from the Latino. This

yields a sample that is proportionately representative of the firm as a whole.

Stratification is a common technique. There are many reasons for this, such as:

1. If data of known precision are wanted for certain subpopulations, than each of these

should be treated as a population in its own right.

2. Administrative convenience may dictate the use of stratification, for example, if an

agency administering a survey may have regional offices, which can supervise the

survey for a part of the population.

3. Sampling problems may be inherent with certain sub populations, such as people

living in institutions (e.g. hotels, hospitals, prisons).

4. Stratification may improve the estimates of characteristics of the whole population. It

may be possible to divide a heterogeneous population into sub-populations, each of

which is internally homogenous. If these strata are homogenous, i.e., the

measurements vary little from one unit to another; a precise estimate of any stratum

mean can be obtained from a small sample in that stratum. The estimate can then be

combined into a precise estimate for the whole population.

5. There is also a statistical advantage in the method, as a stratified random sample

nearly always results in a smaller variance for the estimated mean or other population

parameters of interest.

Systematic Sampling

This method of sampling is at first glance very different from SRS. In practice, it is a variant

of simple random sampling that involves some listing of elements - every nth element of list

is then drawn for inclusion in the sample. Say you have a list of 10,000 people and you want

a sample of 1,000.

Creating such a sample includes three steps:

1. Divide number of cases in the population by the desired sample size. In this example,

dividing 10,000 by 1,000 gives a value of 10.

2. Select a random number between one and the value attained in Step 1. In this

example, we choose a number between 1 and 10 - say we pick 7.

3. Starting with case number chosen in Step 2, take every tenth record (7, 17, 27, etc.).

More generally, suppose that the N units in the population are ranked 1 to N in some order

(e.g., alphabetic). To select a sample of n units, we take a unit at random, from the 1st k units

and take every k-th unit thereafter.

The advantages of systematic sampling method over simple random sampling include:

1. It is easier to draw a sample and often easier to execute without mistakes. This is a

particular advantage when the drawing is done in the field.

2. Intuitively, you might think that systematic sampling might be more precise than SRS.

In effect it stratifies the population into n strata, consisting of the 1st k units, the 2nd k

units, and so on. Thus, we might expect the systematic sample to be as precise as a

stratified random sample with one unit per stratum. The difference is that with the

systematic one the units occur at the same relative position in the stratum whereas

with the stratified, the position in the stratum is determined separately by

randomization within each stratum.

Cluster Sampling

In some instances the sampling unit consists of a group or cluster of smaller units that we call

elements or subunits (these are the units of analysis for your study). There are two main

reasons for the widespread application of cluster sampling. Although the first intention may

be to use the elements as sampling units, it is found in many surveys that no reliable list of

elements in the population is available and that it would be prohibitively expensive to

construct such a list. In many countries there are no complete and updated lists of the people,

the houses or the farms in any large geographical region.

Even when a list of individual houses is available, economic considerations may point to the

choice of a larger cluster unit. For a given size of sample, a small unit usually gives more

precise results than a large unit. For example a SRS of 600 houses covers a town more evenly

than 20 city blocks containing an average of 30 houses apiece. But greater field costs are

incurred in locating 600 houses and in traveling between them than in covering 20 city

blocks. When cost is balanced against precision, the larger unit may prove superior.

Important things about cluster sampling:

1. Most large scale surveys are done using cluster sampling;

2. Clustering may be combined with stratification, typically by clustering within strata;

3. In general, for a given sample size n cluster samples are less accurate than the other

types of sampling in the sense that the parameters you estimate will have greater

variability than an SRS, stratified random or systematic sample.

Nonprobability Sampling

Social research is often conducted in situations where a researcher cannot select the kinds of

probability samples used in large-scale social surveys. For example, say you wanted to study

homelessness - there is no list of homeless individuals nor are you likely to create such a list.

However, you need to get some kind of a sample of respondents in order to conduct your

research. To gather such a sample, you would likely use some form of non-probability

sampling.

To reiterate, the primary difference between probability methods of sampling and non-

probability methods is that in the latter you do not know the likelihood that any element of a

population will be selected for study.

There are four primary types of non-probability sampling methods:

Availability Sampling

Availability sampling is a method of choosing subjects who are available or easy to find. This

method is also sometimes referred to as haphazard, accidental, or convenience sampling. The

primary advantage of the method is that it is very easy to carry out, relative to other methods.

A researcher can merely stand out on his/her favorite street corner or in his/her favorite

tavern and hand out surveys. One place this used to show up often is in university courses.

Years ago, researchers often would conduct surveys of students in their large lecture courses.

For example, all students taking introductory sociology courses would have been given a

survey and compelled to fill it out. There are some advantages to this design - it is easy to do,

particularly with a captive audience, and in some schools you can attain a large number of

interviews through this method.

The primary problem with availability sampling is that you can never be certain what

population the participants in the study represent. The population is unknown, the method for

selecting cases is haphazard, and the cases studied probably don't represent any population

you could come up with.

However, there are some situations in which this kind of design has advantages - for

example, survey designers often want to have some people respond to their survey before it is

given out in the "real" research setting as a way of making certain the questions make sense

to respondents. For this purpose, availability sampling is not a bad way to get a group to take

a survey, though in this case researchers care less about the specific responses given than

whether the instrument is confusing or makes people feel bad.

Despite the known flaws with this design, it's remarkably common. Ask a provocative

question, give telephone number and web site address ("Vote now at CNN.com), announce

results of poll. This method provides some form of statistical data on a current issue, but it is

entirely unknown what population the results of such polls represents. At best, a researcher

could make some conditional statement about people who are watching CNN at a particular

point in time who cared enough about the issue in question to log on or call in.

Quota Sampling

Quota sampling is designed to overcome the most obvious flaw of availability sampling.

Rather than taking just anyone, you set quotas to ensure that the sample you get represents

certain characteristics in proportion to their prevalence in the population. Note that for this

method, you have to know something about the characteristics of the population ahead of

time. Say you want to make sure you have a sample proportional to the population in terms of

gender - you have to know what percentage of the population is male and female, then collect

sample until yours matches. Marketing studies are particularly fond of this form of research

design.

The primary problem with this form of sampling is that even when we know that a quota

sample is representative of the particular characteristics for which quotas have been set, we

have no way of knowing if sample is representative in terms of any other characteristics. If

we set quotas for gender and age, we are likely to attain a sample with good

representativeness on age and gender, but one that may not be very representative in terms of

income and education or other factors.

Moreover, because researchers can set quotas for only a small fraction of the characteristics

relevant to a study quota sampling is really not much better than availability sampling. To

reiterate, you must know the characteristics of the entire population to set quotas; otherwise

there's not much point to setting up quotas. Finally, interviewers often introduce bias when

allowed to self-select respondents, which is usually the case in this form of research. In

choosing males 18-25, interviewers are more likely to choose those that are better-dressed,

seem more approachable or less threatening. That may be understandable from a practical

point of view, but it introduces bias into research findings.

Purposive Sampling

Purposive sampling is a sampling method in which elements are chosen based on purpose of

the study. Purposive sampling may involve studying the entire population of some limited

group (sociology faculty at Columbia) or a subset of a population (Columbia faculty who

have won Nobel Prizes). As with other non-probability sampling methods, purposive

sampling does not produce a sample that is representative of a larger population, but it can be

exactly what is needed in some cases - study of organization, community, or some other

clearly defined and relatively limited group.

Snowball Sampling

Snowball sampling is a method in which a researcher identifies one member of some

population of interest, speaks to him/her, then asks that person to identify others in the

population that the researcher might speak to. This person is then asked to refer the researcher

to yet another person, and so on.

Snowball sampling is very good for cases where members of a special population are difficult

to locate. For example, several studies of Mexican migrants in Los Angeles have used

snowball sampling to get respondents.

The method also has an interesting application to group membership - if you want to look at

pattern of recruitment to a community organization over time, you might begin by

interviewing fairly recent recruits, asking them who introduced them to the group. Then

interview the people named, asking them who recruited them to the group.

The method creates a sample with questionable representativeness. A researcher is not sure

who is in the sample. In effect snowball sampling often leads the researcher into a realm

he/she knows little about. It can be difficult to determine how a sample compares to a larger

population. Also, there's an issue of who respondents refer you to - friends refer to friends,

less likely to refer to ones they don't like, fear, etc.