67729082 Random Sampling

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Random Sampling

PresentedBy:Roll No. 14: Vaibhav Baid


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Roll No. 15: Gaurav Kuraria

Population & Sample

Population: Includes all people or items with the characteristic one wish to

understand or study.

Rarely Enough time or money to

gather information from everyone

or everything in a population.


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Sample: A Subset of some of the units in the population.

Sampling

Process of selecting units (e.g., people, organizations) from a population of

interest so that by studying the samplewe may fairly generalize our resultsback to the populationfrom which they were chosen.


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Importance of Sampling

Significance Saves Money

Population

Sample

Inference


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Saves Time & Energy

Makes Available more detailed Information

For measuring Physically Damaging Processes

Smaller Non-Response

Types of Sampling


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Types of Sampling Cont

Random Sampling: Every unit in the population has a chance of beingselected in the sample, and the probability can be accurately determined.


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Every element has a known Non-Zero probability of being sampled

Involves random selection at some point

Non Random Sampling: Some elements of the population have no chanceof selection or where th

e probability of selection cant be accuratelydetermined.

Methods of Random Sampling


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Sampling Terminology

Population: entire collection of people or things you are interested in. Sample: subset of some of the units in the population.


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Unit of Analysisis the type of object of interest. N =the number of cases in sampling Frame n= No. of Cases in Sample f = n/N= Sampling Fraction


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Simple Random Sampling

LBSIM

Each unit in the population is identified, and each unit has an equalchance of being in the sample.

Objective is to select n units out of N(Sampling Frame). Eg. A small service agency wishes to assess clients views of quality of

service over the past few years. To accomplish this, they identify every

client over the past 12 months, which comes out to be to 1000. Company

wants to survey 100 clients, so as to save time and cost of surveying 1000

clients. Thus, Sampling Fraction, f = n/N = 100/1000 = .1 or 10%


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LBSIM

Lottery method

A table of randomnumbers, a computer random number

generator, or a mechanical device to

select the sample.

Best suits situations where not muchinformation is available about the population


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LBSIM

and data collection can be efficiently conducted on randomly distributed

items

Advantages Simple Requires minimum advance knowledge of the population

Disadvantages Need of a complete list of all the members of the population Not statistically efficient method Doesnt represent Subgroup in population


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Stratified Random Sampling

LBSIM

Population embraces a number of distinct categories Eg. A small service agency wishes to assess clients views of quality of

service over the past few years. To accomplish this, they identify every

client over the past 12 months, which comes out to be to 1000. Company

wants to survey 100 clients. Say, clients can divided into 3 groups,Oceania, Europe and USA.

Divide Population into homogeneous sub groups (Strata) and then take asimple random sample.

Make non-overlapping groups, N1, N2, N3, .Ni such that N1 + N2 + N3+Ni = N


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Population

Sampling

Frame

Oceania AsiaUSA


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LBSIM

Proportional or Quota Random Sampling

Oceania

AsiaUSA

100 200700

25 25 100


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Stratified Random SamplingSelection of sample elements from each stratum, such that the ratio of sample

elements from each stratum to the sample size equals that of the populationelements within each stratum to the totalLBSIMnumber of population elements.

Useful when groups within the population are homogeneous and you areinterested in studying those groups.

Advantages Represents population and its subgroups (Draw Inferences about

Groups)

More statistical precision than Simple Random Sampling Different Sampling approaches can be applied to different strata


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Systematic Random Sampling

LBSIM

Number the units in the population from 1 to N Decide on Sample, n, size that we need Determine Interval Size, k=N/n Randomly select an integer between 1 to k


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LBSIM

For example, We need to select a sample of 25 (n) rooms in our collegefrom a total of 100 rooms (N) to see the overall maintenance quality

etc.

Interval Size = 100/25(N/n) = 4 Select a random no. between 1 and 4, say 3, so


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LBSIM

Useful when Units in the population are randomly ordered atleast withrespect to characteristic that we are measuring

1 2

9 10


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LBSIM

Advantages Useful for selecting large samples Less cumbersome than Simple Random Sample

Disadvantages Vulnerable to periodicities


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Cluster Random Sampling

LBSIM


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Cluster Random Sampling

LBSIM

Useful in Large Geographical Samples where list of all units is notavailable but population boundaries can be well defined.

Advantages Reduce Travel & Administrative Cost Does not require Sampling Frame listing all elements in Population

Can Show regional Variations

Disadvantages Variability of Sample Estimate Increases if clusters differ between

themselves


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LBSIM

Multi Stage Sampling

In Real Research, Single Sampling methoddoesnt address researchers needs

effectively and efficiently.

Multi Stage Sampling: Combining DifferentSampling Methods

Prime stimulus for multi-stagesampling Low Administrative convenience.


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LBSIM

More flexible than one-stage sampling.

SPSS and Random Sampling

Purpose of this Activity

To complete a random sample of 200 Individuals (20% of the total sample) fromthe original survey of 1001 people.

See if the sample is representative of the population on a key survey andpopulation characteristic.


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67729082 Random Sampling

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