sampling1- ppt

7/28/2019 Sampling1- ppt

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Learning Objectives

Upon completion of this chapter, you will be able to:

Understand the importance of sampling

Differentiate between random and non-random sampling

Understand the concept of sampling and non-sampling errors

Understand the concept of sampling distribution and the

application of central limit theorem

Understand sampling distribution of sample proportion


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Sampling

A researcher generally takes a small portion of the population

for study, which is referred to as sample. The process of

selecting a sample from the population is called sampling.


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Sampling Concepts

Population: Population refers to any group of people or objects that formthe subject of study in a particular survey and are similar in one or more

ways.

Element: An element comprises a single member of the population.

Sampling frame: Sampling frame comprises all the elements of a

population with proper identification that is available to us for selection at

any stage of sampling. Sample: It is a subset of the population. It comprises only some elements

of the population.

Sampling unit:A sampling unit is a single member of the sample.

Sampling: It is a process of selecting an adequate number of elements

from the population so that the study of the sample will not only help in

understanding the characteristics of the population but will also enable usto generalize the results.

Census (or complete enumeration):An examination of each and every

element of the population is called census or complete enumeration.


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Why Is Sampling Essential?

Sampling saves time.

Sampling saves money.

The study of a sample instead of complete enumeration

may, at times, produce more reliable results.

Sampling broadens the scope of the study in light of thescarcity of resources.

It has been noticed that sampling provides more accurate

results, as compared to census because in sampling, non-

sampling errors can be controlled more easily.

In most cases complete census is not possible and, hence,sampling is the only option left.

A census is appropriate when the population size is small.


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Figure 5.1: Steps in the sampling design process


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The Sampling Design Process

Step 1: Target population must be defined

Target population is the collection of the objects which

possess the information required by the researcher and about

which an inference is to be made.

Step 2: Sampling frame must be determined A researcher takes a sample from a population list, directory,

map, city directory, or any other source used to represent the

population. This list possesses the information about the

subjects and is called the sampling frame.

Sampling is carried out from the sampling frame and not from

the target population.


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The Sampling Design Process (Contd.)

Step 3:Appropriate sampling technique must be selected

In sampling with replacement, an element is selected from the

frame, required information is obtained, and then the element

is placed back in the frame. This way, there is a possibility of

the element being selected again in the sample.

As compared to this, in sampling without replacement, anelement is selected from the frame and not replaced in the

frame. This way, the possibility of further inclusion of the

element in the sample is eliminated.

Step 4: Sample size must be determined

Sample size refers to the number of elements to be includedin the study.

Step 5: Sampling process must be executed


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Random Versus Non-random Sampling

In random sampling, each unit of the population has the

same probability (chance) of being selected as part of the

sample.

In non-random sampling, members of the sample are not

selected by chance. Some other factors like familiarity of

the researcher with the subject, convenience, etc. are the

basis of selection


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Figure 5.2: Random and non-random sampling methods


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Random Sampling Methods

Simple Random Sampling

In simple random sampling, each member of the population

has an equal chance of being included in the sample.

Stratified Random Sampling

In stratified random sampling, elements in the population are

divided into homogeneous groups called strata.

Then, researchers use the simple random sampling method to

select a sample from each of the strata. Each group is called

stratum.

In stratified random sampling, stratum should be relatively

homogenous and the strata should contrast with each other.


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Random Sampling Methods (Contd.)

In cases where the percentage of

sample taken from each stratum

is proportionate to the actual

percentage of the stratum within

the whole population, stratified

sampling is termed asproportionate stratified

sampling.

In cases where the sample taken

from each stratum is

disproportionate to the actualpercentage of the stratum within

the whole population,

disproportionate stratified

random sampling occurs.

Figure 5.5: Stratified random

sampling based on educational

levels


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Random Sampling Methods (Contd.)

Cluster (or Area) Sampling In cluster sampling, we divide the population into non-overlapping

areas or clusters.

In stratified sampling, strata happen to be homogenous but in cluster

sampling, clusters are internally heterogeneous.

A cluster contains a wide range of elements and is a good

representative of the population.

Figure 5.6: Diagram for cluster sampling


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Systematic (or Quasi-random) Sampling

In systematic sampling, sample elements are selected from

the population at uniform intervals in terms of time, order, or

space.

A researcher wants to take a sample of size 30 from a

population of size 900 and he has decided to use

systematic sampling for this purpose.

For obtaining the sample, the first member can be selected

randomly and after that every 30th member of the population is

included in the sample. Suppose the first element 3 is selectedrandomly and after this, every 30th element, that is, 33rd, 63rd,

element up to a sample size of 30 are included in the sample.


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Multi-Stage Sampling

As the name indicates, multistage sampling involves the

selection of units in more than one stage.

Figure 5.7: Multi-stage (four stages) sampling


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Non-Random Sampling

Sampling techniques where selection of the sampling units is

not based on a random selection process are called nonrandom

sampling techniques.

Quota Sampling

In quota sampling, certain subclasses, such as age, gender,income group, and education level are used as strata. Stratified

random sampling is based on the concept of randomly selecting

units from the stratum.

However, in case of quota sampling, a researcher uses non-

random sampling methods to gather data from one stratum until

the required quota fixed by the researcher is fulfilled. Convenience Sampling

In convenience sampling, sample elements are selected based on

the convenience of a researcher.


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Non-Random Sampling (Contd.)

Judgement Sampling

In judgement sampling, selection of the sampling units is based

on the judgement of a researcher.

Snowball Sampling

In snowball sampling, survey respondents are selected on the

basis of referrals from other survey respondents.

A sampling procedure in which initial respondents are selected

by probability methods and additional respondents are

obtained from information provided by the initial respondents.

This technique is used to locate members of rare population by

referrals.


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Sampling and Non-Sampling Errors

Sampling Error: This error arises when a sample is not representative of

the population.

Sampling errors can occur due to some specific reasons:

Faulty selection of the sample.

Sometimes due to the difficulty in selection a particular sampling

unit, researchers try to substitute that sampling unit with another

sampling unit which is easy to be surveyed.

Sometimes researchers demarcate sampling units wrongly and

hence, provide scope for committing sampling errors.


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Sampling and Non-sampling Errors

(Contd.)

Non-Sampling Errors

All errors other than sampling can be included in the category of non-

sampling errors.

The following are some common non-sampling errors:

Plain lying by the respondent.

The error can arise while transferring the data from the questionnaire to

the spreadsheet on the computer.

There can be errors at the time of coding, tabulation and computation.

Population of the study is not properly defined

Respondent may refuse to be part of the study.

There may be a sampling frame error.


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Determination of Sample Size

The size of the population does not influence the size of thesample

Methods of determining the sample size in practice:

Researchers may arbitrary decide the size of samplewithout giving any explicit consideration to the accuracy ofthe sample results or the cost of sampling.

The total budget for the field survey in a project proposal isallocated.

Researchers may decide on the sample size based onwhat was done by the other researchers in similar studies.


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Confidence interval approach for determining the size of thesample

The following points are taken into account for determining thesample size in this approach.

The variability of the population: Higher the variability asmeasured by the population standard deviation, larger will be thesize of the sample.

The confidence attached to the estimate: Higher the confidencethe researcher wants for the estimate, larger will be sample size.

The allowable error or margin of error: Greater the precision theresearch seeks, larger would be the size of the sample.


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Sample size for estimating population mean -The formula for determining sample size is given

as:

Where

n = Sample size

= Population standard deviatione = Margin of error

Z = The value for the given confidence interval


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An economist is interested in estimating the average

monthly household expenditure on food items by the

households of a town. Based on past data, it is estimatedthat the standard deviation of the population on the monthly

expenditure on food item is Rs.30. With allowable error set at

Rs.7, estimate the sample size required at a 90 per cent

confidence interval. (z=1.645)

Example 1

It is desired to estimate the mean life time of a certain kind of

vacuum cleaner. Given that the population std. dev. is 320

days, how large a sample is needed to be able to assert witha confidence level of 96 per cent that the mean of the sample

will differ from the population mean by less than 45 days?

(z=2.055)

Example 2


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You have a population of approximately 1500 patients and wish

to find out their attitudes to a new voucher scheme. There is

insufficient time & money to collect data from all of them usinga questionnaire and so you decide to send the questionnaire to

a sample.

Your calculation of sample size reveals that to obtainacceptable levels of confidence & accuracy you need an actual

sample size of approximately 300 patients to whom you will

send the questionnaire.

You decide to select them using systematic sampling.

First you need to work out the sampling fraction:

300/1500=1/5

Sampling fraction of 1/5 means you need to select every 5th

patient from the sampling frame.

Case let 1: Systematic Sampling


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You use a random number to decide where to start on the

sampling frame. As your sampling fraction is1/5, the starting

point must be one of the first five patients. You therefore select

a one-digit random number between 1 to 5.

Once you have selected your first patient at random you select

every fifth patient until you have gone right through yoursampling frame.

If the random number you selected was3, then you would

select following patient numbers.3 8 13 18 23 28 33 38

and so on until 300 patients had been selected.

Cont


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Ceri needed to select a sample of firms to undertake an interview

based survey about the use of photocopiers.

As she had limited resources with which to pay for travel and other

associated data collection costs she decide to interview firms in 4

geographical areas selected from a cluster grouping of local

administrative areas.

A list of all local administrative areas formed her sampling frame.

Each of the local administrative areas (clusters) was given a unique

number, the first being 1 and so on.

The four sample clusters were selected from this sampling frame oflocal administrative areas using simple random sampling.

Ceris sample was all firms within the selected clusters.

She decided that the appropriate telephone directories would provide

a suitable list of all firms in each cluster.

Case let 2: Cluster Sampling


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A market research organisation needs you to interview a sample of

400 households in England & Wales.

The electoral register provides a possible sampling frame. Selecting

400 households using either systematic or random sampling would

probably result in these 400 households being dispersed throughout

England & Wales.

The time and cost of travelling to and interviewing your sample would

be enormous. By using multi-stage sampling these problems can be

overcome.

In the first stage the geographical area (England & Wales) is split intodiscrete sub areas (countries). These form the sampling frame. After

numbering, a small no. of countries are selected using simple

random sampling.

Since each case (household) is located in a country each has an

equal chance of being selected for the final sample.

Case let 3: Multi stage Sampling


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As the countries selected are still too large the selected countries are

subdivided into smaller geographically discrete areas (electoral

wards), which form the next sampling frame (Stage 2).

Another random sample is selected. A larger no. of wards are

selected to allow for likely important variations in households

between wards.

A sampling frame is generated for each ward using a combination of

the electoral register and UK Royal Mails postcode address file.

The cases (households) that will be interviewed are then selected

using either random or systematic technique.

Cont


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The distribution of the annual earnings of the employees of a cementfactory is normally distributed. This distribution has a mean of Rs

25,000 and standard deviation of Rs 3000. If a researcher draws a

random sample of size 50, what is the probability that their average

earnings will be more than Rs 26,000?

Example 1


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Figure 5.10: Probability that the average

earnings of employees is more than Rs

26,000

Figure 5.11: Corresponding zscores

for probability of average earnings

more than Rs 26,000

Example 1 (Contd.)


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END OF CHAPTER

sampling1- ppt

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