Sampling ion 1

8/6/2019 Sampling ion 1

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Chapter 3

Sampling and Sampling Distribution


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Introduction:

Collecting data , relying on the entire

population is neither feasible nor practical. Researcher has to select a sample instead

of going in for a complete census .

Inferential or inductive statistics is

primarily concerned with makingconclusions about a certain population

or populations.


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On the basis of information obtained from thesample (through sample statistic) , an

inference about the population (populationparameter) is made.

In this process , we need to keep in mindthat the sample contains only a portion of the

population and not the entire population . Soa proper sampling method should be usedfor selecting a sample.

In order to make a good estimate of thepopulation characteristics , selecting areasonably good sampling method is of paramount importance.


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Two methods

Census method ( Complete enumeration )

Sample method (Partial enumeration)


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Census

100% inspection of the population

Enumeration of each and every unit of population.

It seems to provide more accurate and exact information .For instance , census conducted by Govt of India every 10 years

(Regarding age, martial status, occupation, religion, education,

employment , income, property etc.)


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Population

This is a collection of all the units of a specified type defined over agiven space or time

It is defined by :

Content this refers to who or what exactly are the subjects of

interest. Eg. All persons above aged 18 and over

Units this refers to how the subjects are grouped. Eg. Withinhouseholds

Extent this refers to the spatial feature of the population. Eg.

The subjects can only be living in Delhi.

Time this refers to what period of time that your subjects must

possess the particulars named above. Eg. June October 1998


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Advantages Accurate

Reliable


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Disadvantages

More resources in terms of manpower , money,time and administrative staff etc.

If the test is destructive i.e. the item is destroyedwhile collecting the information about the item ,this option is totally ruled out.

Census method generally time consuming, by the

time results are available it is not of much usedue to changed conditions.


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When to use :

Information required about each unit of the

population.

In any manufacturing process in industry, 100%

enumeration should be considered under

following conditions:

1. Serious casualty or loss of life bcoz of defect.

2. A defect may cause loss or serious casulaty.

3. Lot size is small .


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Sampling method

Sampling is the most widely used tool for gathering important and useful information fromthe population.

A researcher generally takes a small portion ofthe population foe study, which is referred to assample.

The process of selecting a sample from thepopulation is called sampling.

Sampling over census are defined just in four

word speed, economy, adaptability and scientificapproach.

A properly designed and carefully executedsampling plan yields fairly good results than those

obtained by the census method.


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Why is sampling essential?

Sampling saves time.

Sampling saves money

When the research process is destructive in

nature , sampling minimizes the destruction.

Sampling broadens the scope of the study in lightof the scarcity of resources.

It has been noticed that sampling provides more

accurate results , as compared to censusbecause in sampling , non sampling error can becontrolled more easily .

In most cases complete census is not possiblesampling is the only option left.


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Merits of sample method over the census:

1. Speed :less time

2. Economy : reduced cost of the enquiry

3. Administrative convenience: less personal staffand limited field of enquiry

4. Reliability :

Sample method contains sampling and nonsampling errors both.

Carefully designed and scientifically executedsample survey gives results more reliable thanthose obtained from a complete census.


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Sampling errorsOnly a small portion of the population is studied ,

results are different from census and have certain

amount of error. If the sample is random and

highly representative of the population then alsoerror would always be there. Sampling error is

always due to fluctuations of sampling .


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Reasons are:

1. Faulty selection of sample( purposive or judgement

sampling2. Substitution : due to difficulty unit is replaced by anotherof target population

3. Faulty demarcation of sampling units: depends ondiscretion of investigators.

4. Errors due to bias in estimation method

5. Variability of population


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In a sample survey these errors can

be controlled by Employing highly qualified ,skilled and

trained personal

Imparting adequate training to theinvestigators for conducting the enquiry.

Better supervision

Using more sophisticated equipment andstatistical techniques for the processing

and analysis of the relatively limited data.


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Non-sampling errors

Non-sampling errors are not attributed dueto chance and are a consequence offactors which are within human control. It

presents both in census and sample .


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Non-sampling errors

Important factors for non-sampling errors are

1. measuring and recording observations, 2.inaccuracy or incomplete information

3.non response , incomplete response4. training of investigators ,

5. interpretation of questions

6. Lack of coverage

7. Defective method of interviewing and askingquestions.

8. Publication errors


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Sampling

Sampling is the process

of selecting a small number of elements

from a larger defined target groupof elements such that

the information gathered

from the small group will allow judgments

to be made about the larger groups


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Objectives To obtain the optimum results .

To obtain the best possible estimates of the

population parameters.


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Sampling Frame This is a list of the all the units with their

identifications in the target population fromwhich the sample is to be chosen

A subset of subjects for a survey should only betaken from a sampling frame

Generally we identify each unit of the populationby giving it a distinct number, generally from

1,2,3,,N where N is the population size.


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Unit of Analysis Sometimes referred to as Sampling Units

A Unit is an element or group of elements ,

living , non- living, on which observationscan be made.

This is the items/units being investigated

A person living in city /household

/employee/a branch/in a bank etc.

Eg : Individuals, households, hospitals


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Sampling Units This refers to the items/units selected for

inclusion in the sample

Eg : If Mr. Brown was selected to be

included in the sample then he is a

sampling unit


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6L]HRIDVDPSOH

Population size:Normally proportionate

Heterogeneity : More heterogeneity in data , more

the size of sample is required.

Accuracy and Reliability :Bigger size sample

would be more accurate and reliable.

Allocation of Resources : Sample size depends

on the resources allocated . More the resources

(manpower, money, time )are made available,

more the sample size can be increased.


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Basics of SamplingT

heoryPopulation

Element

Defined target

population

Sampling frame

Sampling unit


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Sampling Methods

Probability

sampling

Non probability

sampling


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T

ypes of Sampling MethodsProbability

Simple random

sampling

Systematic random

sampling

Stratified random

sampling Cluster sampling

Non-probability

Convenience

sampling Judgment sampling

Quota sampling


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Probability Sampling Probability Samples

Random Samples (though sample units are not chosen

haphazardly)

The probabilities for selecting different samples are

specified

For each unit of the population the probability of it

appearing in any sample is known (I/N: of being selected

in the group ;with replacement)


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Example 1 Let a, b and c be three units in the

population , and we want to select a

sample of2

units from the 3 units.


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Solution:

Sampling with replacement

Total number of possible samples: Pr

= 3!/1! = 6

Sampling without replacement

Total number of possible samples: Cr

= 3!/(2!)(1!) = 3


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There are 3 main steps involved in

choosing a probability sample :

1. Decide on the population of interest

2. Establish a sampling frame

3. Select units from the frame using aprobabilistic algorithm


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Simple Random Sampling

Simple random sampling is a method of

probability sampling in whichevery unit has an equal nonzero

chance of being selected


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Simple Random Sampling IV

There are two main ways of choosing asimple random sample

1. Table of Random Numbers

2. Lottery Method


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Example

Suppose our population consists of

500 units and we have to select a

sample of size5

. In the random number tables, the digits

0 to 9 have equal chance of appearing

in a particular position. The steps of

selecting the sample are as follows:


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Procedure:

First identity all sampling unit with 1 to 500

We choose any three columns(row or

diagonal) anywhere in the randomnumber table.

Now we move downwards-selecting 3

digited numbers less than 500 till 5

numbers.


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Random Table

12135 65186 86886

49031 45451 07369

70387 53186 97116 93451 53493 56442

74077 66687 45394


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Ans

121 490

454

073 453


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Systematic (Quasi) Random Sampling

Systematic random sampling is a

method of

probability sampling

in which the defined

target population is ordered

and the sample is selected

according to position using a skip interval


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Procedure:

In this method only the 1st unit is

selected at random( by Random

Table). The rest of the units are

selected according to a pattern

depending on a factor which is also

called the sampling ratio.

e.g once in a day, a unit after every 2lots of production


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Steps in Drawing a Systematic Random

Sample

1: Obtain a list of units that contains an acceptableframe of the target population

2: Determine the number of units in the list and the

desired sample size3: Compute the skip interval

4: Determine a random start point

5: Beginning at the start point, select the units by

choosing each unit that corresponds to the skipinterval

n

Nk !


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Case Let 1

There are 50 employees in an organization

, and each of them has the employee

number from 1 to 50 . We wish to select

10% for assessment of their view on job

satisfaction among the employee of the

organisation . Discuss


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Procedure

N = 50; n = 5 = 10% ofN

We may select one random number as

single digit random number varying from 0to 9 say 5.

K = N/ n = 10

Thus the five employee numbers :

5,15,25,35,45 .


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Stratified Random Sampling

Stratified random sampling is a

method of probability sampling in which the

population is divided into different subgroups

of non-overlapping homogenous and

Samples are selected from each.


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Steps in Drawing a Stratified Random

Sample

1: Divide the target population into

homogeneous subgroups or strata

(strata could be on the basis of geographical

area, different age groups, gender , rural andurban etc. )

2: Draw random samples from each stratum

3: Combine the samples from each stratum into

a single sample of the target population


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Stratified Random Sampling III


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Eg :

N

N2N1 Nk

n1 n2 nk


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Stratified Random Sampling IV

Examples :

Household income or expenditure surveys urban rural

Business surveys employee size

Production

sales

industrial classification

Agricultural surveys

Stratification depends on purpose of survey


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Cluster Sampling

Cluster sampling is a method of probability

sampling where the sampling units

are selected on SRS basis in non-overlapping groups

rather than individually.In cluster sampling , the sampling unit is cluster.

But Clusters should be as small as possible consistent

with resources

The number of sampling unit in each cluster should beapproximately same. In stratified sampling , strata

happens to be homogenous but in cluster sampling,

clusters are internally heterogeneous.


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Thus cluster sampling involves formation of

suitable clusters of units, and then

selecting a sample of clusters treating them

as unit


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Steps

first select a random sample of clusters

from these selected clusters random units

are then selected for study.


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Example:

A sample of districts is first selected and

then households are again randomly

chosen from the selected districts.

Cluster sampling is generally used when

the population has natural groupings,

usually in terms of geographical areas.


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Case let 2

A survey is conducted among 240 students

of PGDM. They are grouped into 4

divisions of60 each. Then a division could

be considered a cluster. If a sample size is

decided to be 60, then one of the four

cluster could be selected as a sample, and

each of the student of this cluster could beincluded in the sample if n =60.


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Non-Probability Sampling

In probability sampling , each unit in the

population or specified group has a chance of

being selected in the sample. The prerequisite in

such sampling is defining the sampling frame i.eidentifying and numbering each and every unit of

the population. However there are certain

situations when it is not feasible and selection is

done on per the convenience . Such samplingcompromising accuracy for convenience , is

referred as Non-probability sampling .


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Non-Probability Sampling II

Non-Probability Sampling This involves the selection of a units by arbitrary

methods

The probability of selection for each unit is unknown

It is dangerous to make inferences about the targetpopulation

It is often used to test aspects of a survey such asquestionnaire design rather than make inferencesabout the target population


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Convenience sampling

This sampling is also by taking into consideration of

convenience of the investigator .

This method is not very efficient.

It is also used quite a lot in pilot surveys before

,say, launching of a product in the market.

Used for pre-testing of questionnaire.

Convenience sampling relies upon convenience and access


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Such sampling is dictated by the needs of

convenience rather than any other

consideration. For opinion poll when one may find it easier

to get the opinion of those in shops, or

restaurants , on pavement rather than

going house to house.


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Judgement sampling

In this type of sampling, the investigator decideswhich units to include or exclude in the sample.

Judgement sampling is very simple andconvenient.

It is not as economical as convenience sampling.

Also used for pre-testing of questionnaire. It is useful if the sample size is small.

Judgment sampling relies upon belief

that participants fit characteristics


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There is no well-defined scientific method which can

tell us that how one persons judgment is better

than another persons judgment.

Generally , judgment sampling is useful when asample size is small. In case of large samples,

the bias from researchers end may be high.

Disadvantages :

There is scope for personal bias .It may be

influenced by personal bias of the investigator.


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Quota sampling

Quota sampling emphasizes representation ofspecific characteristics.,

For example to study eating habits of schoolchildren and college students ,students under18 years.

The quota is fixed due to constraints onavailability of time, cost.

Within the quota stipulated , one has to selecta sample which is representative of thepopulation.


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Example

Within the overall quota of interviewing 100

persons for some opinion poll, one may contact

some persons from various categories like college

students, housewives, shopkeepers, office goers ,daily wage earners etc.

In an organization , one might include persons

from all categories of staff cadre-wise as well as

function-wise, department-wise etc.


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Advantages

:

The benefits of stratification are available.

Disadvantages :

There is scope for personal bias.

Suitability

It is suitable in marketing research studies

where it is not possible to stick to it without

delay and expenditure.


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Sampling and Non Sampling

Errors

Sampling errors arise from the fact that a

sample has been used to study the population.

These errors are generally not present in a

complete census as they are associated withthe process of selecting a sample.

A sampling error is the difference between the

estimate obtained from sampling and the truevalue for the entire population.


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Sampling errors may be due to

faulty selection of the sample,

improper data collection method,

Human beings limitation of recording data

due to lack of competence, training or human

fatigue.

incorrect methodology of analyzing the data

Wrong calculation


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Sampling Errors

Sample size


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Non-sampling errors are errors arising

during the course of all survey

activities other than sampling.

They exist both in sample surveys as well

as censuses.


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Figure 1

Sample Size

Non-Sampling

Error


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Factors to Consider in Sample Design

Research objectives Degree of accuracy

Resources Time frame

Knowledge of

target population Research scope

Statistical analysis needs

Steps in Developing a Sampling


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1. Define the Target Population

3. Identify the Sampling Frame(s) Needed

4. Identify the Appropriate Sampling Method

5. Determine Sample Sizes and Contact Rates

6. Create Plan forSelecting Sampling Units

7. Execute the Operational Plan

Steps in Developing a Sampling

Plan

2. Select the Data Collection Method

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