Unit 4 Sampling

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Unit 4

1Teena Y. Sharma


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Introduction Theory of Sampling:

It is the study of relationships existing between a populationand various populations drawn from this population. The

sample so selected has to be truly representative of thepopulation.

Sampling is one of the most fundamental conceptunderlying any research work.

A sample enables a researcher to intelligently estimate the

population parameters. Most of the researchers utilize the concept of Sampling.

The other method used by researchers is Census Method,but Sampling is more predominant.

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Theory of Sampling Mainly studies relationship between a population and

the samples drawn form that population.

It helps in moving from particular to generalconcept, by moving from a sample to population

Generally applicable to random samples only.

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Sample v/s CensusCensus Method Sampling Method

Has almost 100% accuracy, asall elements are studied (+)

All units are studied (+)

Consumes a lot of resources(time &money) (-)

Expensive (-)

Unmanageable whenpopulation is large (-)

No cautions required forchoosing elements, as all areconsidered for study (+)

Has good accuracy (+)

Only some units, whichrepresent all units are studied (-)

Saves resources

Reasonable (+)

Sample is of a reasonable size, so

manageable (+) Caution is required for selecting

elements which will fall in thesample, so that they trulyrepresent the population (-)

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Sample v/s CensusParameter Conditions favoring use of

SAMPLE CENSUS

Budget Small Large

Time Available Short Long

Population Size Large Small

Variance in Characteristics of Elements Small Large

Cost of Sampling Errors Low High

Cost of Non-Sampling Errors High Low

Attention to Individual Cases Required No Yes

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Concepts in Sampling Population/ Universe- Finite / Infinite

Census

Sample Sample Survey

Parameters

Statistics

Sampling Unit

Sampling Frame

Sampling Error

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Concepts.. Non-sampling Errors

Sample Size

Random error Bias

Precision

Non-response Errors

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Objectives of Sampling Statistical estimation: The prime objective of

Sampling is to intelligently estimate populationparameters

Testing a hypothesis: Sampling is also used to test astatistical hypothesis. A sample is drawn and the datacollected from the sample is analyzed so as to accept orreject the hypothesis based on the difference between

the two values. (hypothesis value and sample statistic) Statistic Interference: Generalizations regarding

populations and accuracy of these generalizations canbe done using the theory of Sampling.

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Need of Sampling Sampling saves time and money. A Sampling study is

usually less expensive than census study and producesresults at relatively faster speed.

Sampling usually enables more accurate measurements fora study, as it is generally conducted by trained andexperienced.

Sampling remains the only way when population containsinfinitely many members.

It also remains the only way when a test involves thedestruction of the items under study. Sampling usually enables to estimate sampling errors and

thus assist in obtaining information concerning somecharacteristics of this population.

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Limitations of sampling Need of specialized knowledge

Need of discipline

Chances of bias Need of large samples as there are Errors due to small

samples

Complicated sampling plans

Sampling errors

Difficulties in sticking to a sample

Impossibility of sampling

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Sample Design Definition : Sample design is a definite plan for

obtaining a sample from a given population

It refers to the technique or procedure the researcherwould adopt in selecting items for the sample

Sample design also lays down the number of items tobe included in a sample.

It is determined prior to data collection.

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Steps in Sample design Type of Universe: Whether finite or infinite.

Sampling unit:Whether geographic, social, or

construction or any other. Source list:Also known as Sampling Frame , and

contains all names of the universe. Hence, it should becomprehensive, correct, reliable and appropriate.

Size of sample: should neither be large nor too small. Itshould be optimum. Before deciding about thesample, researcher should determine the desiredprecision needed and the parameters to be estimated.

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Steps.. Parameters of interest

Budgetary constraints

Sampling procedure

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Characteristics of a good sample

design Sample design must result in truly representative

sample.

It should result in small sampling errors. Sample design must be viable in context of funds

available for research study.

It should be such that systematic biases can be

controlled. Sample should be such that the results of sample study

can be applied for the universe with a reasonable levelof confidence.

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Types of Sampling Techniques

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Different types of Sampling

Techniques

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Element SelectionTechnique

Probability Sampling Non-probabilitySampling

Unrestricted Sampling Simple Random Sampling Haphazard Sampling orConvenience Sampling

Restricted Sampling Complex RandomSampling ( ClusterSampling, SystematicSampling, StratifiedSampling)

Purposive Sampling( Quota Sampling,Judgment Sampling)


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Probability Sampling Concept of Probability: Probability is termed as the

chance of a certain event happening or not happening.

Probability Sampling:

It gives each element in the population an equal probability ofgetting into the sample.

All choices are independent of each other.

Probability of any bias taking place is generally done away.

If we design a random sample of size n from a finitepopulation N then NCnpossible samples has sameprobability.

Each element has 1/NCn of being chosen.

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Uses of Probability Sampling

method Generally applied in the case of critical decisions

where accuracy is at premium, regardless of time andcost involved.

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Merits of Probability Sampling It is the only approach where in it is possible to

formulate determinable representative sampling plans.

The population parameters are more accurate andreliable.

Most widely applied method in descriptive researchstudies aiming at quantitative estimates.

It results in more apt representative samples

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Demerits of Probability Sampling

method For reliable results , and generalizations, the size of

sample required is considerably large.

Cannot be used in situations with budgetaryconstraints.

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Types of Probability Sampling

method.

ProbabilitySampling

Simple RandomSampling

SystematicSampling

Cluster Sampling Area SamplingMulti-phase

Sampling Stratified RS

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Random Sampling Simple Random Sampling

There is total absence of human judgment.

Each element has equal chances of getting selected

It does not mean picking up in haphazard manner

There are various methods present to do so:

Lottery Method

Using Random number tables Use of Computers

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Advantages of Random Sampling Produces least biased and most representative

samples.

Simple, as researcher does not need to make a decisioncriteria

Does not require prior knowledge of composition ofpopulation

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Systematic Sampling Also known as Quasi-random or Pseudo-random sampling. Is a special form of Simple Random Sampling. Is not a true random sampling in the sense in selecting a

sample of n units from a population of N units, only firstelement is selected randomly and thereafter every (N/n)this selected for inclusion into the sample.

The number (N/n) is designated as i and is termed assampling fraction.

First, element is k, a random number between 1 to i, laterall elements are chosen corresponding to k. Hence, we have the elements as k, k+(i),

k+2(i)..k+z(i)

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Cluster Sampling Generally used when , the population element are

spread over a wide area.

In this case, sampling unit is a cluster.

Certain clusters are selected.

For each cluster a simple or stratified samplingmethod is applied to arrive at a sample.

This method is widely applicable in test-marketing ofproducts, socio-economic surveys, demographicstudies, public opinion polls etc.

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Steps in Cluster Sampling Divide the population in sub-groups, call a group of

sub-groups as a Cluster.

Identify a cluster based on objective of study anddistribution of population.

Examine cluster for intra-cluster homogeneity.

Determine the stages single or multi-stage sampling.

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Area Sampling It is a peculiar type of cluster sampling in which

samples are clustered together on the basis ofgeographical area basis

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Multiphase or Sequential SamplingA multi-phase sample is such a sample which is

designed in such a way that some information iscollected from the entire sample and the other

information is collected only from a part of the sample.

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Stratified Random Sampling

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If a population from which a sample is to be drawndoes not constitute a homogenous group , Stratifiedtechnique is generally applied to obtain a

representative sample. Here a population is divided into several sub-

populations that are individually more homogenousthan total population, and then select samples fromeach stratum.


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Major issues in Stratified Sampling How to form a strata?

How many stratum should be formed?

The sample size within each stratum.

How to form a strata? It is determined according to the objective of the study or

variable being studied.

Number of stratum: If more than always beneficial

But budget is also to be considered

Hence, most cost-effective number should be thought of.

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Issues Sample Size within each Stratum:

Can be done in two ways:

Proportionate stratified random sampling: Here cases are

drawn from each sample in same proportion as they appear inthe original population.

Disproportionate stratified random sampling: Dependson the variability, size, characteristics of the stratum.

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Non-probability Sampling These are methods which are not based on the concept

of probability.

These methods are also called non-random samplingtechniques.

Here there is no rule or formulae or method by whichone can determine the chance or probability that a

specific element is selected in a sample.

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Non-probability Can be of following types

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Non-probabilitysampling

Purposive/JudgmentalSampling

Convenience/Accidental sampling

Quota Sampling Snowballing


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Purposive / Judgmental Sampling Elements are selected on a pre-determined criteria.

This criteria of decision is given by some experts.

It is a kind of sampling where, special elements are putinto the sample.

These elements are special because, they possess someknowledge, which is not possessed by any other element

of the population.

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Convenience/ Accidental Sampling Convenience of the researcher, convenient location for

field work is the prime criteria for selection.

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Quota Sampling Most widely used non-probability sampling method.

It is a non-probabilistic version of stratified method.

Population is divided into Stratum, and each strata hasa quota, reserved to give a sample in the total sample.

Here clear understanding of the population isrequired.

The parameters should also be known. Then the quotas can be decided.

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Snowballing Here initial members of the sample lead the researcher

to newer sample constituents.

The first element, gives you information about thenext element.

Example:Suppose a survey is being conducted on the

problems faced by dentists who treat small children,the first dentist you identify can tell you about theother dentist who specializes for treatment of dentaldiseases in children.

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Unit 4 Sampling

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