Sampling Methods I

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Sampling Methods

Probability , Non Probability and Mixed Probability Sampling Procedures

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What is Sampling

Sampling is simply the process of learning about the population on the basis of sample drawn from it.Sampling may be defined as selection of some part of an aggregate or totality on the basis of which a judgement or inference about the aggregate or totality is made.

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Key Terms

Mean,S.D,Correlation

Statistics

Parameter

Mean,S.D,Correlation

Population

Sample

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Key Terms

1. Sample

2. Population

3. Sampling frame

4. Sample statistics

5. Population parameter.

6. Estimator.

7. Estimate.

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Advantages of Sampling over Advantages of Sampling over Complete CensusComplete Census

1.1. Less Time.Less Time.

2.2. Reduced Cost of Survey.Reduced Cost of Survey.

3.3. Greater Accuracy of Results.Greater Accuracy of Results.

4.4. Greater Scope (statistical analysis).Greater Scope (statistical analysis).

5.5. Larger Population.Larger Population.

6.6. Hypothetical Population.Hypothetical Population.

7.7. Testing is Destructive.Testing is Destructive.

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Example I

A manufacturer of electric tubes is interested in knowing the average life of its product.Then it is desirable to take a sample of some tubes and perform experiments on tubes to know the average life of tubes .It is not wise to display all tubes .Infact this is an example where only sampling can be used.

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Advantages of Sampling over Advantages of Sampling over Complete CensusComplete Census

Prof.R.A Fisher (1950) in a report on “The Prof.R.A Fisher (1950) in a report on “The Subcommission on Statistical Sampling of Subcommission on Statistical Sampling of United Nations”sums the advantages of United Nations”sums the advantages of sampling techniques over complete census in sampling techniques over complete census in the following four words.the following four words.Adaptability.Adaptability.Speed.Speed.Economy.Economy.Scientific Approach.Scientific Approach.

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Sampling Errors and Non-Sampling Errors

Sampling Errors have their origin in Sampling and arise due to the fact that only a part of Population has been used to estimate the Population Parameters and draw inferences about the Population.As such Sampling Errors are absent in a complete Enumeration Survey.

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Sampling Errors and Non-Sampling Errors

Data obtained in a Complete Census,although free from sampling Errors would still be subjected to Non-Sampling Errors whereas data obtained in a sample survey would be subjected to both Sampling and Non-Sampling Errors.

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Sources of Non-Sampling Errors

1. Faulty Planning or Definitions.

2. Response Errors.

3. Non-Response Errors or Bias.

4. Errors in Coverage.

5. Compiling Errors.

6. Publication Errors.

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The Sampling Process

1. Define population .

2. Determine the Sampling Frame.

3. Sample Design.

4. Determine the Sample Size.

5. Execute the Sampling Process.

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Sample Designs

Designs

Probability Samples

Non-Probability Samples

Mixed ProbabilitySamples

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Lower class Upper class

People who have own houses/Cars/posh colonies

BiasedSample

Population

Lower Class Upper Class

Unbiased Sample

Population

Unbiased, representative sample drawn at random from the entire population.

Biased, unrepresentative sample drawn from people who have cars /own houses/posh colonies.

Sample survey –Standard of living in Delhi

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Probability versus Non-Probability Samples

Probability Samples (Statistical Samples)1. Representative Samples.2. Each element of the population has the

known probability of being included in the sample.

3. A chance mechanism is used in the selection process.

4. Eliminates bias in the selection process.

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Probability versus Non-Probability Samples

Non-Probability Samples (Non- Statistical Samples)

1. Use some non-random methods to choose items.

2. Open to selection Bias.

3. Do not make use of appropriate data collection methods.

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Probability Samples

1. Simple Random Sample.

2. Stratified Sample.

3. Systematic Sample.

4. Cluster Sample.

5. Area Sample.

6. Multistage Sample.

7. Sequential Sample.

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Simple Random Sample

I. Number each item unit from 1 to N.

II. Use a random number table or a random number generator to select n distinct numbers b/w 1 and N inclusively.

III. Notation: n = no. of items in Sample.

IV. N = no. of items in Population.

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Stratified Sample

I. A population is divided into subgroups called strata based on some criteria eg.Geographic Location,Gender,Age,Income,Profession.

II. A random sample is selected from each stratum (Items within strata are relatively homegeneous).

III. Reasons for stratifyingA. Ensure representation of subgroups.B. Compare Subgroups.

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Stratified Random Sample

Population of Radio FM listeners stratified by age

1. 20 – 30 Years old. ( Alike) Strata 1



Heterogeneity b/w 1and 2, 2 and 3,1 and 3.

Homegeneity within groups.

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Cluster Sampling

Population is divided into non-overlapping clusters or areas often based on geographical location.

I. Each cluster is a miniature ,or microcosm of the population.

II. A subset of clusters is selected randomly for the sample.

III. All items in clusters are enumerated.

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Example of Cluster Sampling

Cluster sampling is frequently used in consumer surveys in rural areas.We select a few villages randomly and include every household in the selected villages in our sample.A village can be regarded as the natural geographic cluster of households.

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Systematic Sample

Determine Sampling Interval (N/n)

Population : 500 MBA Students.

Sample : 50 MBA Students.

N/n = 500 = 10

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Draw a random number b/w 1 – 10

(Say number is 2 )

Include students numbered 2,12,22,--------.

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The selection of units within a sample involves human judgement rather than pure chance.The maximum information available “per rupee” which can be determined from a probability sample is not possible in this case and moreover, the degree of accuracy is not known.

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I. Convenience Sampling: Sample elements are selected for the convenience of the researcher.

II. Quota Sampling:Sample elements are selected until the quota controls are satisfied.

III. Judgement Sampling:Sample elements are selected by the judgement of the researcher.

IV. Volunteer Sampling.

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Example of Convenience Sampling

Suppose a marketing research study aims at estimating the proportion of shops which store Daburs Real Juices.Suppose a sample of 100 is needed .Then the researcher may go to the shops according to his convenience.

Note: This is definitely not a representative sample.

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Examples

I. “People- on- the- street interviews.

II. The first 100 customers to enter a departmental store.

III. The first three callers in a radio contest

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Example of Quota Sampling

We have a population of three categories,i.e.,Rich,Medium,Poor.These are given in the ratio 20%,30%,50% respectively.Using quota sampling determine the number of representatives for each category of a sample size of 200.Solution: Category

1. Rich = 20% of 200 = 40 2. Medium = 30% of 200 = 60 3. Poor = 50% of 200 = 100

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Deliberate or Purposive or Judgemental Sampling

I. Statisticians often use this method for in exploratory studies like pretesting of questionnaires and focus groups.

II. Medical research where choice of experimental subjects(animals,human beings, vegetable) reflects the investigators pre-existing beliefs about the population.

III. Expert interviews, panel discussions.

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Volunteer Sampling

A. Pre Poll survey (news channel).B. Post Poll surveys.C. Television and radio often use call-in

polls.D. In psychological experiments or

pharmaceuticals trials(drug testing), it would be difficult and unethical to enlist random participants from general public.

Sampling Methods I

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