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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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Simple Random Sampling
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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Simple Random Sampling
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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Stratified Random Sampling
Population
Sampling
Frame
Oceania AsiaUSA
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Stratified Random Sampling
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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Systematic Random Sampling
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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Systematic Random Sampling
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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Systematic Random Sampling
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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